diff --git a/research/connected-l18-root-caller/COALESCING-WINDOW.json b/research/connected-l18-root-caller/COALESCING-WINDOW.json
new file mode 100644
index 0000000000..975d44be4c
--- /dev/null
+++ b/research/connected-l18-root-caller/COALESCING-WINDOW.json
@@ -0,0 +1,109 @@
+{
+  "status": "PASS_UNIFORM_NEGATIVITY",
+  "root_sha256": "be4a2beed3a40de6d2c5dcc6e4f25f3c2a4375551b70e63fb0e9a03041db6a34",
+  "native_invoice_sha256": "87a41b13bdd9248d538805f76a970f51335567845dfc0070698b6979a08b70d6",
+  "engine_sha256": "60a743d13f668ef86db4b8215b4d5d04430a671ba6f1fe06d9c1c4c3dfe86da5",
+  "interval": [
+    "181350941/50000000000",
+    "1/100"
+  ],
+  "T": {
+    "1": 252,
+    "2": 144,
+    "3": 72,
+    "4": 1962,
+    "5": 306,
+    "6": 54,
+    "7": 180,
+    "8": 720,
+    "9": 6774,
+    "17": 312,
+    "25": 520,
+    "33": 416,
+    "41": 312,
+    "49": 520,
+    "57": 416,
+    "65": 520,
+    "73": 416,
+    "81": 104,
+    "145": 104
+  },
+  "P": {
+    "1": 42396,
+    "2": 8172,
+    "3": 8802,
+    "4": 1980,
+    "5": 2736,
+    "6": 126,
+    "7": 162,
+    "8": 330,
+    "16": 208,
+    "24": 520,
+    "32": 416,
+    "40": 312,
+    "48": 520,
+    "56": 416,
+    "64": 312,
+    "72": 208,
+    "80": 104,
+    "144": 104
+  },
+  "rank_surplus": 760,
+  "optimal_degrees": [
+    18,
+    9,
+    7,
+    7,
+    8,
+    6,
+    6,
+    7,
+    4,
+    4,
+    5,
+    3,
+    3,
+    4,
+    1,
+    1,
+    1,
+    0,
+    0,
+    3,
+    0,
+    0,
+    4,
+    2,
+    2,
+    6,
+    3,
+    3,
+    7,
+    5,
+    5,
+    9,
+    6,
+    6,
+    10,
+    8,
+    8,
+    0
+  ],
+  "left_endpoint_margin": [
+    "-1947598170433159634755026544042426492172302230996912227162842431465986628465463463/50000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "-243449771304144954344378318005303311521537778874614028395355303933248328556043649/6250000000000000000000000000000000000000000000000000000000000000000000000000000"
+  ],
+  "left_endpoint_margin_float": [
+    -38.95196340866319,
+    -38.95196340866319
+  ],
+  "uniform_derivative_upper_interval": [
+    "-4959594734641481397754468477409242373438945362069616735797101018360054020832519343721/25000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "-9919189469282962795508936954818484746877890724139233471594202036720108041664860049897/50000000000000000000000000000000000000000000000000000000000000000000000000000000"
+  ],
+  "uniform_derivative_upper_float": [
+    -198383.78938565924,
+    -198383.78938565924
+  ],
+  "scope": "Fixed104-port F+H1 supplier,18 full paid/helper invoices,3thinH1 perport,and181 idle incidences optimally coalesced in the fixed38 coordinate-role relaxation. Ordinary implementation work is optimistically free. Not a general root/native obstruction."
+}
diff --git a/research/connected-l18-root-caller/COALESCING-WINDOW.md b/research/connected-l18-root-caller/COALESCING-WINDOW.md
new file mode 100644
index 0000000000..e2cded088e
--- /dev/null
+++ b/research/connected-l18-root-caller/COALESCING-WINDOW.md
@@ -0,0 +1,51 @@
+# The fixed repair fails throughout the improvement window
+
+The coordinate-role compression proof in `IDLE-COALESCING.md` selects the same
+degree vector for every `0 < kappa < 1`: union/intersection compression uses
+only concavity, and the two final bridge choices are decided by
+`f(1)+f(3) < 2 f(2)`. Thus a single pair of complete histograms bounds the best
+possible moment in that precisely stated relaxation throughout this range.
+
+Let `M(k) = sum_r (T_r-P_r) r^(1-k)`. `COALESCING-WINDOW.json` records both
+complete histograms. They include 104 copies of the root target profile,
+18 entire F-native paid and helper profiles, 18*104 extra paid rank-one
+adapters, 3*104 thin jobs, and 104 copies of the optimally coalesced idle
+profile. Their rank surplus at zero is 760. All ordinary implementation,
+coalescing and outer overhead is optimistically free.
+
+For `a = .00362701882` and `b = .01`, exact outward-rounded intervals give:
+
+- `M(a) < -38.95196340866319`;
+- `M'(k) < -198383.7893856592` for every `a <= k <= b`.
+
+To obtain the second bound, put `c_r=T_r-P_r`. Each derivative term is
+`-c_r log(r) r^(1-k)`. For positive c_r its upper bound occurs at b; for
+negative c_r it occurs at a. Summing those independently valid upper bounds
+gives the displayed uniform negative bound. Therefore `M(k)<0` on the whole
+closed interval. This includes the newly proposed .00363005817 candidate and
+the aspirational .01 endpoint; it says nothing about other constructions.
+
+The independent checker reconstructs stage eligibility and the two compressed
+bridge cases from the pinned root; it authenticates the actual caller and
+retained F invoice and recomputes every target and paid multiplicity. Its
+integer fixed-grid logarithm/exponential engine is the independently authored
+engine published at `93effe2a135bf57b9e484cb630d8dd057159aec9`,
+`research/shared-wire-split-composition/interval_gate.py`, unchanged here as
+`review/interval_engine.py`. Exact byte pins are in `INPUT-PINS.json`.
+This is attributed reuse of that arithmetic engine with a new profile and
+uniform derivative proof, not another independent arithmetic implementation.
+
+The seventh registered command recomputes and compares the complete receipt.
+Omitting the paid adapter causes its endpoint test to fail; a reversed
+interval is also rejected. Optimized Python is explicitly rejected. The
+checker reads its inputs and receipt without rewriting them.
+
+This result is restricted to the fixed 38 coordinate roles, fixed stage
+masks, two coordinate hosts per stage, and arbitrary free merging of all
+same-role idle occurrences. Noncoordinate idle directions, changed root
+geometry, a cheaper native, helper mixing, or a larger coupled construction
+are outside it. The F+H1 word itself remains unbuilt. **No new κ.**
+
+Prepared for @CubeJerry with substantial OpenAI Codex assistance. The root,
+native, compression and interval predecessors retain the credit stated in
+`README.md`, `NOTICE` and `NATIVE.md`.
diff --git a/research/connected-l18-root-caller/COST.json b/research/connected-l18-root-caller/COST.json
new file mode 100644
index 0000000000..71ffcc064f
--- /dev/null
+++ b/research/connected-l18-root-caller/COST.json
@@ -0,0 +1,163 @@
+{
+  "3": {
+    "roles": 8,
+    "stages": 3,
+    "events": 191,
+    "event_counts": {
+      "ADD": 87,
+      "SCALE": 28,
+      "SWAP": 44,
+      "LAMBDA": 20,
+      "QUERY": 3,
+      "HOST": 3,
+      "IDLE_ONE": 6
+    },
+    "ordinary_events": 179,
+    "target_histogram": {
+      "9": 5,
+      "17": 2,
+      "25": 1
+    },
+    "target_rank_mass": 104,
+    "paid_outside_native": {
+      "8": 6,
+      "1": 3
+    },
+    "paid_outside_native_mass": 51,
+    "ordinary_scalar_denominator_lcm": "6",
+    "max_abs_ordinary_scalar": "3",
+    "native_gates": {
+      "selected_complex": {
+        "comparison_kappa": "0.003125804",
+        "max_native_signed_cost_per_port_per_call_before_ordinary_outer": "17.4843080869728003788800832613933994107627318594142812410079",
+        "allowance_above_two_H8": "1.5879696527372231758936282716102426015761391318128899249442",
+        "direct_baseline_signed_moment": "-1.236091041788330472319115185169272195271582604561330225167"
+      },
+      "pending_complex_6936": {
+        "comparison_kappa": "0.00362701882",
+        "max_native_signed_cost_per_port_per_call_before_ordinary_outer": "17.4552303348641031828548299485292027354066579477326847872936",
+        "allowance_above_two_H8": "1.5754511794416558860023781546789599010436945883769335958376",
+        "direct_baseline_signed_moment": "-1.273646461675032341992865535963120296868916234869199212487"
+      },
+      "ordinary_BIT_6726": {
+        "comparison_kappa": "0.00376669",
+        "max_native_signed_cost_per_port_per_call_before_ordinary_outer": "17.4471353689880173282352372261088732550512243452946422105081",
+        "allowance_above_two_H8": "1.5719676360206178990526638106345372230747882511325091855385",
+        "direct_baseline_signed_moment": "-1.284097091938146302842008568096388330775635246602472443385"
+      }
+    }
+  },
+  "9": {
+    "roles": 20,
+    "stages": 9,
+    "events": 776,
+    "event_counts": {
+      "ADD": 339,
+      "SCALE": 84,
+      "SWAP": 245,
+      "LAMBDA": 44,
+      "QUERY": 3,
+      "HOST": 9,
+      "IDLE_ONE": 52
+    },
+    "ordinary_events": 712,
+    "target_histogram": {
+      "9": 1,
+      "17": 4,
+      "25": 6,
+      "33": 6,
+      "41": 2,
+      "73": 1
+    },
+    "target_rank_mass": 580,
+    "paid_outside_native": {
+      "8": 52,
+      "1": 3
+    },
+    "paid_outside_native_mass": 419,
+    "ordinary_scalar_denominator_lcm": "6",
+    "max_abs_ordinary_scalar": "3",
+    "native_gates": {
+      "selected_complex": {
+        "comparison_kappa": "0.003125804",
+        "max_native_signed_cost_per_port_per_call_before_ordinary_outer": "17.495701886657033145636409723610846431616109791663676616169",
+        "allowance_above_two_H8": "1.5993634524214559426499547338276896224295170640622853001053",
+        "direct_baseline_signed_moment": "-3.605728928206896516150407395550793398134346423439432299053"
+      },
+      "pending_complex_6936": {
+        "comparison_kappa": "0.00362701882",
+        "max_native_signed_cost_per_port_per_call_before_ordinary_outer": "17.4331797209823169335965523056515178829992190357283974839384",
+        "allowance_above_two_H8": "1.5534005655598696367441005118012750486362556763726462924824",
+        "direct_baseline_signed_moment": "-4.019394909961173269303095393788524562273698912646183367658"
+      },
+      "ordinary_BIT_6726": {
+        "comparison_kappa": "0.00376669",
+        "max_native_signed_cost_per_port_per_call_before_ordinary_outer": "17.4157826512019132391499231525983617384070475822265108385921",
+        "allowance_above_two_H8": "1.5406149182345138099673497371240257064306114880643778136225",
+        "direct_baseline_signed_moment": "-4.134465735889375710293852365883768642124496607420599677397"
+      }
+    }
+  },
+  "18": {
+    "roles": 38,
+    "stages": 18,
+    "events": 2370,
+    "event_counts": {
+      "ADD": 1041,
+      "SCALE": 189,
+      "SWAP": 858,
+      "LAMBDA": 80,
+      "QUERY": 3,
+      "HOST": 18,
+      "IDLE_ONE": 181
+    },
+    "ordinary_events": 2168,
+    "target_histogram": {
+      "9": 3,
+      "17": 3,
+      "25": 5,
+      "33": 4,
+      "41": 3,
+      "49": 5,
+      "57": 4,
+      "65": 5,
+      "73": 4,
+      "81": 1,
+      "145": 1
+    },
+    "target_rank_mass": 1774,
+    "paid_outside_native": {
+      "8": 181,
+      "1": 3
+    },
+    "paid_outside_native_mass": 1451,
+    "ordinary_scalar_denominator_lcm": "2",
+    "max_abs_ordinary_scalar": "5/2",
+    "native_gates": {
+      "selected_complex": {
+        "comparison_kappa": "0.003125804",
+        "max_native_signed_cost_per_port_per_call_before_ordinary_outer": "17.24273344786332293410495368703241064490922674815243677043",
+        "allowance_above_two_H8": "1.3463950136277457311184986972492538357226340205510454543663",
+        "direct_baseline_signed_moment": "-11.76488975470057683986702344951343095699258763008118182141",
+        "retained_F_plus_H1_cost_per_port": "17.6703991996227234141399345320028861136206598559402746515482",
+        "retained_F_plus_H1_excess": "0.4276657517594004800349808449704754687114331077878378811182"
+      },
+      "pending_complex_6936": {
+        "comparison_kappa": "0.00362701882",
+        "max_native_signed_cost_per_port_per_call_before_ordinary_outer": "17.1313409028543326190363539979855487854614834640682540794906",
+        "allowance_above_two_H8": "1.2515617474318853221839022041353059510985201047125028880346",
+        "direct_baseline_signed_moment": "-13.47188854622606420068976032556449288022663811517494801538",
+        "retained_F_plus_H1_cost_per_port": "17.6914424603474237437422676600591888259630220558867211828222",
+        "retained_F_plus_H1_excess": "0.5601015574930911247059136620736400405015385918184671033316"
+      },
+      "ordinary_BIT_6726": {
+        "comparison_kappa": "0.00376669",
+        "max_native_signed_cost_per_port_per_call_before_ordinary_outer": "17.1003547369028679713425656375523992710112972290322356119039",
+        "allowance_above_two_H8": "1.2251870039354685421599922220780632390348611348701025869343",
+        "direct_baseline_signed_moment": "-13.94663392916156624112014000259486169737249957233815343518",
+        "retained_F_plus_H1_cost_per_port": "17.6973009591869876138450219486899064090893373235044463699870",
+        "retained_F_plus_H1_excess": "0.5969462222841196425024563111375071380780400944722107580831"
+      }
+    }
+  }
+}
diff --git a/research/connected-l18-root-caller/IDLE-COALESCING.json b/research/connected-l18-root-caller/IDLE-COALESCING.json
new file mode 100644
index 0000000000..3ed964ba05
--- /dev/null
+++ b/research/connected-l18-root-caller/IDLE-COALESCING.json
@@ -0,0 +1,153 @@
+{
+  "candidate_native_per_stage": "17.69144246035",
+  "degree_only_upper_interval": [
+    "10.7650306667069383548587527126645864429494031",
+    "10.7650306667069383548587527126645864429522214"
+  ],
+  "host_roles_by_stage": [
+    [
+      2,
+      3
+    ],
+    [
+      5,
+      6
+    ],
+    [
+      8,
+      9
+    ],
+    [
+      8,
+      9
+    ],
+    [
+      11,
+      12
+    ],
+    [
+      14,
+      15
+    ],
+    [
+      14,
+      15
+    ],
+    [
+      17,
+      18
+    ],
+    [
+      16,
+      37
+    ],
+    [
+      20,
+      21
+    ],
+    [
+      20,
+      21
+    ],
+    [
+      23,
+      24
+    ],
+    [
+      26,
+      27
+    ],
+    [
+      26,
+      27
+    ],
+    [
+      29,
+      30
+    ],
+    [
+      32,
+      33
+    ],
+    [
+      32,
+      33
+    ],
+    [
+      35,
+      36
+    ]
+  ],
+  "idle_actions": 181,
+  "independent_roles": 38,
+  "kappa_probe": "181350941/50000000000",
+  "optimal_degree_histogram": {
+    "0": 5,
+    "1": 3,
+    "10": 1,
+    "18": 1,
+    "2": 2,
+    "3": 5,
+    "4": 4,
+    "5": 3,
+    "6": 5,
+    "7": 4,
+    "8": 3,
+    "9": 2
+  },
+  "optimal_degrees": [
+    18,
+    9,
+    7,
+    7,
+    8,
+    6,
+    6,
+    7,
+    4,
+    4,
+    5,
+    3,
+    3,
+    4,
+    1,
+    1,
+    1,
+    0,
+    0,
+    3,
+    0,
+    0,
+    4,
+    2,
+    2,
+    6,
+    3,
+    3,
+    7,
+    5,
+    5,
+    9,
+    6,
+    6,
+    10,
+    8,
+    8,
+    0
+  ],
+  "optimal_savings_interval": [
+    "9.70728992517695569956124850500966948053128943",
+    "9.70728992517695569956124850500966948053400299"
+  ],
+  "proof": "eligibility union/intersection compression plus two exact bridge cases; rational ln/exp enclosures",
+  "required_saving_interval": [
+    "10.0818280348756402447064459173255207290250791",
+    "10.0818280348756402447064459173255207290288747"
+  ],
+  "required_saving_lower": "10.081828",
+  "scope": "fixed38 coordinate roles;181 idles;two coordinate hosts perstage;free all-occurrence same-role merging;no noncoordinate or general native obstruction;no supplier or kappa claim",
+  "shortfall_lower": "0.374538109698684545145197412315851248491076115",
+  "stages": 18,
+  "status": "OPTIMISTIC_COALESCING_ONLY_ROUTE_CLOSED",
+  "uncoalesced_gate_per_stage": "17.13134090285"
+}
diff --git a/research/connected-l18-root-caller/IDLE-COALESCING.md b/research/connected-l18-root-caller/IDLE-COALESCING.md
new file mode 100644
index 0000000000..91df672c3d
--- /dev/null
+++ b/research/connected-l18-root-caller/IDLE-COALESCING.md
@@ -0,0 +1,59 @@
+# Exact optimum of the optimistic L18 same-role idle-coalescing relaxation
+
+Scope: the 38 independent root fields and 18 stage masks in `root_L18.json`, bound to `caller_L18.json` by exact masks and SHA-256 in `idle_coalescing.py`. No new native word or kappa is claimed. This closes only the proposed native profile plus coalescing-only repair at the stated comparison point. A cheaper native, changed root, changed role encoding, changed idle count, or arbitrary noncoordinate shared-direction decomposition is outside the result. Actual rank-one idle bases may rotate; this theorem does not constrain all such rotations.
+
+The masks contain 217 role/stage incidences. At each stage arbitrarily choose any two eligible mask-coordinate roles as hosts, leaving exactly 181 idle incidences. No actual host-position restrictions are imposed. For each role r, coalesce ALL its idle incidences, even across actual chronological barriers, into one paid rank `8 d_r` child for free, where d_r is its idle degree. Do not combine independent roles. At k=0.00362701882 the relaxed cost is sum_r f(d_r), with f(d)=(8d)^(1-k), f(0)=0. All root targets, three thin jobs, 18 HOSTs, and proposed native cost remain fixed. Coalescing setup, uncomputation, chronology and ordinary costs are free.
+
+## Compression proves the exact optimum
+
+Let E_r be the set of stages where role r is eligible, and I_r subset E_r its idle stages. Every stage has exactly its mask size minus two idle roles.
+
+If E_j is a strict subset of E_i, replace I_i by I_i union I_j and I_j by I_i intersection I_j. The new sets are eligible. At every stage the total number of idle roles stays unchanged. Their sizes have the same sum as before, with the union at least as large as either old size and the intersection at most as large. Concavity of f makes their total cost nonincreasing.
+
+Whenever I_j was not already contained in I_i, this operation strictly increases the finite integer potential sum_r |E_r| |I_r|: precisely |I_j minus I_i|(|E_i|-|E_j|)>0. Repeated compression therefore terminates. Some optimum satisfies I_j subset I_i for every strict eligibility inclusion.
+
+The two host roles at a stage must consequently be closed downwards under strict eligibility inclusion: if i is hosted and E_j is a strict subset of E_i, every eligible j must also be hosted. The checker enumerates all two-element subsets of each mask under this exact condition. Seventeen stages have a unique allowed pair. The bridge stage has exactly two:
+
+- hosts {16,37}, giving idle degrees (1,3) on roles (16,19);
+- hosts {19,37}, giving degrees (2,2) there.
+
+All other degrees agree. Concavity gives f(1)+f(3)<=2f(2), so the first case is optimal. This proves the finite relaxation's optimum without trusting a solver.
+
+The optimal host pairs in stage order are:
+
+[2,3], [5,6], [8,9], [8,9], [11,12], [14,15], [14,15], [17,18], [16,37], [20,21], [20,21], [23,24], [26,27], [26,27], [29,30], [32,33], [32,33], [35,36].
+
+The optimal degree vector in role order 0..37 is:
+
+[18,9,7,7,8,6,6,7,4,4,5,3,3,4,1,1,1,0,0,3,0,0,4,2,2,6,3,3,7,5,5,9,6,6,10,8,8,0].
+
+The degree histogram is {0:5, 1:3, 2:2, 3:5, 4:4, 5:3, 6:5, 7:4, 8:3, 9:2, 10:1, 18:1}. Thus the coalesced paid ranks are 8 times these degrees, with zero-degree roles omitted.
+
+## Full bill at the assigned gate
+
+The maximum idle saving over 181 separate H8 jobs is enclosed by exact rational arithmetic in [9.70728992517695569956124850500966948053128943, 9.70728992517695569956124850500966948053400299].
+
+The required saving is computed directly from the pinned F profile plus H1, all eighteen native calls, the caller targets and all nonnative jobs. Exact rational intervals give a requirement greater than10.08182803487564 and a strict shortfall greater than0.37453810969868 per port, before ordinary and outer margins. The best coalesced native gate is below17.6706347875832 per stage. This is not a general root, fusion or native ceiling.
+
+Ignoring stage eligibility would give an apparent saving of 10.765030666707, enough to pass. Therefore degree caps alone do not establish the negative result; incidence constraints are essential.
+
+## Pins and reproduction
+
+Root SHA-256: be4a2beed3a40de6d2c5dcc6e4f25f3c2a4375551b70e63fb0e9a03041db6a34.
+Caller SHA-256: f4090329f219edd493b4ca592128521e867a355fb528556b15201e759783568b.
+
+Run `python3 -I -O -B idle_coalescing.py` from the package directory, or pass `--package-root PATH`. An optional `--receipt PATH` compares a retained JSON receipt without writing it. Standard library only; it imports no solver or producer, verifies hashes and caller/root masks, checks the 17+2 compressed assignment census, and computes rational enclosures. Logarithms use the positive atanh series with geometric tail bound after reduction to z<=1/3. Exponentials use odd/even alternating Taylor sums for exp(-x), x<1. No floating-point solver output is trusted.
+
+Three controls actively reject an ineligible host, one deleted real idle incidence (via the per-stage incidence validator), and an eligible but non-downward-closed hostset (via the compressed-assignment validator). A separate scope control confirms that the looser degree-only relaxation incorrectly leaves this route open. The exploratory MILP files are not proof dependencies.
+
+The portable checker also binds `inputs/base_invoice.json` by SHA-256
+87a41b13bdd9248d538805f76a970f51335567845dfc0070698b6979a08b70d6.
+It derives the required saving directly as 18*((local_paid-helpers)/104+1)
+minus the caller target moment plus 181 H8+3 H1, using rational intervals.
+The result is greater than 10.08182803487564 and yields a shortfall greater
+than 0.37453810969868. Ordinary and outer charges remain omitted in this
+favorable necessary screen; they cannot rescue the failed inequality.
+The F invoice is the retained source profile reviewed in NATIVE.md, not an
+emitted or authenticated F-to-HOST conversion word. The base native is
+attributed to PR #6824, retained by PR #6833 head
+51f54e3c31f2f3a3e056a483b3ed66ae916ad06a and copied through #6936.
diff --git a/research/connected-l18-root-caller/INDEPENDENT.json b/research/connected-l18-root-caller/INDEPENDENT.json
new file mode 100644
index 0000000000..b8b28d760a
--- /dev/null
+++ b/research/connected-l18-root-caller/INDEPENDENT.json
@@ -0,0 +1,100 @@
+{
+  "status": "PASS_INDEPENDENT_CONNECTED_L18_CALLER",
+  "caller_sha256": "f4090329f219edd493b4ca592128521e867a355fb528556b15201e759783568b",
+  "root_sha256": "be4a2beed3a40de6d2c5dcc6e4f25f3c2a4375551b70e63fb0e9a03041db6a34",
+  "formal_ring": "Q(i)[Q,D0,...,D17]/(Q^4-1); unrestricted tuple D powers; direct reverse covectors, no evaluation of Q or D",
+  "coefficients": 1444,
+  "peak_reverse_polynomial_terms": 42,
+  "event_counts": {
+    "ADD": 1041,
+    "SCALE": 189,
+    "SWAP": 858,
+    "LAMBDA": 80,
+    "QUERY": 3,
+    "HOST": 18,
+    "IDLE_ONE": 181
+  },
+  "ordinary_events": 2168,
+  "target_histogram": {
+    "9": 3,
+    "17": 3,
+    "25": 5,
+    "33": 4,
+    "41": 3,
+    "49": 5,
+    "57": 4,
+    "65": 5,
+    "73": 4,
+    "81": 1,
+    "145": 1
+  },
+  "target_rank_mass": 1774,
+  "paid_non_native": {
+    "1": 3,
+    "8": 181
+  },
+  "native_contract_calls": 18,
+  "native_contract": "HOST(x,y,s): D_s*(x+Q*y,-Q^-1*x), t=-1; supplied macro only, no native implementation or tariff verified",
+  "scalar_max_denominator": 2,
+  "scalar_max_magnitude": "5/2",
+  "controls": {
+    "missing_HOST": {
+      "event": 32,
+      "witness": [
+        0,
+        0
+      ]
+    },
+    "missing_QUERY": {
+      "event": 10,
+      "witness": [
+        0,
+        0
+      ]
+    },
+    "missing_IDLE_ONE": {
+      "event": 36,
+      "witness": [
+        0,
+        0
+      ]
+    },
+    "missing_LAMBDA": {
+      "event": 9,
+      "witness": [
+        0,
+        0
+      ]
+    },
+    "wrong_HOST_lower_left_sign": {
+      "event": 32,
+      "witness": [
+        0,
+        2
+      ]
+    },
+    "wrong_QUERY": {
+      "event": 10,
+      "witness": [
+        0,
+        0
+      ]
+    },
+    "wrong_LAMBDA": {
+      "event": 9,
+      "witness": [
+        0,
+        0
+      ]
+    },
+    "wrong_IDLE_ONE": {
+      "event": 36,
+      "witness": [
+        0,
+        0
+      ]
+    }
+  },
+  "scope": "Exact finite caller and root-mask binding, event and symbolic profile audit only. No HOST native construction, physical/routing or ordinary-tariff admission, finite supplier, kappa or general root theorem.",
+  "seconds": 0.5741335839993553
+}
diff --git a/research/connected-l18-root-caller/INPUT-PINS.json b/research/connected-l18-root-caller/INPUT-PINS.json
new file mode 100644
index 0000000000..da121acf97
--- /dev/null
+++ b/research/connected-l18-root-caller/INPUT-PINS.json
@@ -0,0 +1,59 @@
+{
+  "schema_version": 1,
+  "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a",
+  "inputs": [
+    {
+      "local_path": "inputs/root_L3_tHHtHt.json",
+      "source_commit": "a98df73ddae1d1ea85a62b6bdf2714b28cb7b359",
+      "source_path": "research/p104-two-chain-findings/data/root_L3_tHHtHt.json",
+      "git_blob": "15071c325b0badf01b090979a8a72b91c61d62e9",
+      "sha256": "eb79a0d89c1c09138a3e8a260f04b6a0c88d51d1314650364cb88441333b8f28"
+    },
+    {
+      "local_path": "inputs/root_L3_tHtHHt.json",
+      "source_commit": "a98df73ddae1d1ea85a62b6bdf2714b28cb7b359",
+      "source_path": "research/p104-two-chain-findings/data/root_L3_tHtHHt.json",
+      "git_blob": "67ea0628435e289a4a1db0fd5ab53e103c83c4b5",
+      "sha256": "60bf936299c3a553398e943ba6d67b05ee4d29007cd1af9da6227685aa226309"
+    },
+    {
+      "local_path": "inputs/root_A.json",
+      "source_commit": "d360b1182b6d21b1ee2354856abcb50646ad618b",
+      "source_path": "research/p104-main-wire-native/data/root_A.json",
+      "sha256": "b9400ca6087c8fd9d527c3203afa43caaddaa46cb73996cc05a0ac5cbb240e3c",
+      "usage": "Positive control for unchanged g=9 raw single chain, even-index units on first20 coordinates."
+    },
+    {
+      "local_path": "inputs/base_invoice.json",
+      "source_commit": "d360b1182b6d21b1ee2354856abcb50646ad618b",
+      "source_path": "research/p104-main-wire-native/data/base_invoice.json",
+      "sha256": "87a41b13bdd9248d538805f76a970f51335567845dfc0070698b6979a08b70d6",
+      "usage": "Retained F profile screen only, not a modified native proof."
+    },
+    {
+      "local_path": "inputs/final_native.json.gz",
+      "source_commit": "93effe2a135bf57b9e484cb630d8dd057159aec9",
+      "source_path": "research/shared-wire-split-composition/data/final.json.gz",
+      "sha256": "2b94953dc14a122e3ef089633f05b58ec689ec5156feb7c784ed3e137dc01883",
+      "usage": "Exact coefficient endpoint for the narrowly scoped main-plane remix screen; not a new all-width native replay."
+    },
+    {
+      "local_path": "review/interval_engine.py",
+      "source_commit": "93effe2a135bf57b9e484cb630d8dd057159aec9",
+      "source_path": "research/shared-wire-split-composition/interval_gate.py",
+      "sha256": "60a743d13f668ef86db4b8215b4d5d04430a671ba6f1fe06d9c1c4c3dfe86da5",
+      "usage": "Unchanged independently authored integer interval engine; uniform profile proof is new."
+    }
+  ],
+  "contract_source": {
+    "source_commit": "ec0796c950b4bb015c36b9f2d11907c8cc8b98fe",
+    "source_path": "research/p104-root-cut-laws/THEOREM.md",
+    "section": "0. Setting"
+  },
+  "normalization_reference": {
+    "pr": 6842,
+    "head": "7bc8aad1357d5b3d2c15af653c1eaf8e70a6a838",
+    "path": "research/p104-header-braid-classification/PROOF.md",
+    "scope": "Path units I+q ab; q\u00b2=1; M(-1)=-M(1), ordinary normalization."
+  }
+}
diff --git a/research/connected-l18-root-caller/LICENSE b/research/connected-l18-root-caller/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/connected-l18-root-caller/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
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+      You may add Your own copyright statement to Your modifications and
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+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
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+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
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+      Contributor provides its Contributions) on an "AS IS" BASIS,
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+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
+      liable to You for damages, including any direct, indirect, special,
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diff --git a/research/connected-l18-root-caller/NATIVE.md b/research/connected-l18-root-caller/NATIVE.md
new file mode 100644
index 0000000000..5c6fe1becf
--- /dev/null
+++ b/research/connected-l18-root-caller/NATIVE.md
@@ -0,0 +1,89 @@
+# Native contract and complete substitution
+
+HOST_Q(x,y,j) must send arbitrary independent inputs simultaneously to
+x_out=D_j(x+Qy), y_out=-D_j Q^-1 x, with Q^4=1. This is alpha=1,beta=-1,
+t=alpha beta=-1. Sign gauges give the physical endpoint X=x-y,Y=x.
+Main transports are X line to full and Y zero to hyperplane. A native must
+supply compatible frames and phase maps, restore owned scratch, count every
+paid operation and disclose all productive helper targets. No second main
+plane or helper is silently discarded. The caller provides none of these
+physical obligations. HOST remains an unimplemented supplied macro.
+
+Diagonal gauge sends alpha to r alpha and beta to beta/r, preserving t.
+Thus a t=-1/2 native does not become resonant by free scalar rescaling.
+Mixing different physical frames also needs a delivered legal word.
+
+| Event | Action on current arbitrary rows | Root price |
+|---|---|---|
+| ADD d,s,c | r_d += c r_s | ordinary |
+| SCALE d,c | r_d *= c | ordinary |
+| SWAP d,s | exchange rows | ordinary |
+| QUERY d,s,1 | r_d += Q r_s | H1 |
+| IDLE_ONE d,[j] | r_d *= D_j | H8 |
+| LAMBDA d,s | multiply by ((1+s i)+(1-s i)Q^2)/2 | ordinary, tariff open |
+| HOST x,y,j,1,-1 | simultaneous map above | native invoice open |
+
+For p ports, native paid profile Pnative and productive helper profile Thelp,
+the full substitution is
+
+    Ttotal = p Troot + 18 Thelp,
+    Ptotal = p (181H8+3H1) + 18 Pnative.
+
+H_r contributes r^(1-kappa). Per-port native signed price must be below
+(Troot(kappa)-181*8^(1-kappa)-3)/18, before ordinary and outer margins.
+COST.json compares selected complex .003125804, pending #6936 .00362701882
+and ordinary BIT .00376669. BIT is a benchmark, not automatically a supplier.
+At kappa 0 the surplus is 323p-18 mass(Pnative-Thelp).
+
+Direct native bill 2H8+2H1 gives 217H8+39H1: paid mass 1775 versus target 1774.
+Target ranks>=9 and paid ranks<=8 imply moment<=-8^(-kappa)<0 for 0<=kappa<1.
+This controls that unbundled baseline, not all native constructions.
+
+A second screen is retained F plus an owned rank-one input shear: F sends
+X=x,Y=x+y; preceding x<-x-y gives X=x-y,Y=x. It requires owned ascent and
+erasure. Source #6833 head 51f54e3c31f2f3a3e056a483b3ed66ae916ad06a,
+research/p104-chain-nested-root, retains #6824 native
+2a7ca44fbda3abaa4df355b183ed7d7478eef7c1. The #6936 base_invoice profile
+prices F+H1 at 17.691442460347425 per port at .00362701882, exceeding the
+17.131340902854333 gate. No modified native word is emitted or admitted.
+
+Ordinary caller work is 2,168 events including 80 LAMBDA, with dyadic scalars.
+Its coefficient bounds concern this caller and exact HOST only. Native
+precision, approximate children, tape, raw tariff and outer margin remain
+open. No new κ. No framework assumption or operation admission is removed.
+
+## Scoped limitation of the retained two-plane native
+
+Companion commit93effe2a135bf57b9e484cb630d8dd057159aec9,
+`research/shared-wire-split-composition/data/final.json.gz`, has96 type A
+ports with endpoint, in order(X1,X2,Y1,Y2),
+
+    M = [[I, diag(0,-1)], [diag(1,0), I]].
+
+Separate exact replay on all1,480 independent public inputs checks this map,
+identity helper returns and boundary frames. X1,X2 share one boundary frame;
+Y1,Y2 share the other. Allow arbitrary invertible input/output remixes within
+each group, a relaxation of actual same-frame operations. The Y-from-Y block
+becomes P_Y I Q_Y, hence stays invertible. No nonzero Y output row can become
+independent of every Y input. A resonant HOST requires exactly that zero Y
+row for its second output, including independence from the unused plane.
+Thus these block-diagonal remixes cannot extract the demanded autonomous HOST.
+
+This excludes paid cross-frame operations, helpers, feedback, identified
+inputs, cross-port remixes and larger rewrites; it is not a general native
+ceiling. The coefficient replay inherits owned-erasure semantics and makes
+no new all-width claim. Exact bytes, checker and receipt are retained.
+The F-plus-input-shear screen above additionally requires104 dirty erasures,
+owned ascent(A6), legal owned lifetimes and ordinary INIT/COPY/ADD/CLEAR work;
+its optimistic numerical price omits those ordinary margins.
+
+## Coordinate-role idle merging cannot rescue F+H1
+
+`IDLE-COALESCING.md` fixes the38 coordinate roles and18 masks, allows any two
+eligible coordinate hosts per stage, and merges every same-role idle occurrence
+for free, even across barriers. Its solver-free exact optimum saves less than
+9.707289925176956 per port. The pinned F+H1 profile requires more than
+10.08182803487564, leaving a strict gap greater than0.37453810969868 before
+ordinary and outer work. This screen excludes arbitrary noncoordinate shared
+idle directions, changed encodings, roots, natives or idle counts. In
+particular, it does not cover every rotating rank-one basis of E_j-H_j.
diff --git a/research/connected-l18-root-caller/NOTICE b/research/connected-l18-root-caller/NOTICE
new file mode 100644
index 0000000000..f5d981b979
--- /dev/null
+++ b/research/connected-l18-root-caller/NOTICE
@@ -0,0 +1,15 @@
+Connected L18 root geometry and emitted caller: substantial OpenAI Codex-assisted research.
+Apache-2.0; no human or maintainer review.
+
+Prior complete-sign/single-chain mechanism and sector normalization: DreamingOfClouds,
+including PR6842, PR6936 and PR6937, prepared with Claude Opus 5.5 via Claude Code.
+Retained type A root: @CubeJerry (Jerry Chen), PR6912. Caller and native lineage
+includes Ali Romman, unpaidmoon and icekylinx, as credited by PR6936.
+Independent root, tariff and reverse replay implementations were prepared separately
+with OpenAI Codex assistance and import no primary construction/replay code.
+Input JSON exports are copied without modification and pinned in INPUT-PINS.json.
+
+The vendored companion native word retains its complete attribution in inputs/NATIVE-NOTICE.
+Its new shared-wire composition, seventeenth wire and enabling splits were developed with
+substantial OpenAI assistance in2026, Apache-2.0; predecessor native/compiler lineage
+remains DreamingOfClouds, Ali Romman and Jerry Chen / @CubeJerry as recorded there.
diff --git a/research/connected-l18-root-caller/PROOF.md b/research/connected-l18-root-caller/PROOF.md
new file mode 100644
index 0000000000..641c84a35b
--- /dev/null
+++ b/research/connected-l18-root-caller/PROOF.md
@@ -0,0 +1,98 @@
+# Exact root and caller argument
+
+Matrices act on columns; event order multiplies on the left. The field has
+characteristic zero. D_j commute and are algebraically independent. A coordinate
+mask is the diagonal idempotent on its listed roles.
+
+## Complete sign header
+
+For g in {3,9,18}, use n=2g+2 coordinates A,F_0,...,F_(g-1),
+H_0,...,H_(g-1),E and N=n+1 pairs (X_i,Y_i). `generate.py` gives the integral
+formula. Left units have X_i=A+F_i+2 sum_(j<i) F_j, Y_i=A*-F_i*;
+right units have X_m=-A+H_m+2 sum_(l>m) H_l, Y_m=A*+H_m*.
+Three explicit middle units connect the arms and E. A determinant-one basis
+change in each block of three F and H coordinates uses columns
+(1,1,1),(1,1,0),(0,1,1).
+
+Exact checks establish Y_i X_j=sign(i-j) for all N^2 entries and
+rank X=rank Y=n. Every unit is nilpotent; every two unit directions are coupled.
+There is no nontrivial decomposition into blocks preserved by all units:
+each rank-one unit would have to lie in one block, but every off-diagonal
+pairing is nonzero and X spans. This is the connectedness claimed here.
+
+For the bare endpoint, let B be the N by N strictly lower triangular all-ones
+matrix and A0=I+2B. The Gram is G=YX=A0-11^T. Since N is odd,
+A0^-1 1 is the alternating vector v=(1,-1,...,1), spanning ker G=ker X.
+In the ordered application of I-2X_iY_i, the scalar reads z satisfy
+A0 z=Y w. The endpoint is I-2X A0^-1 Y. But
+X A0^-1 Y X=X A0^-1 G=X; since X is surjective, X A0^-1 Y=I.
+Thus the endpoint is -I. At S=+1 all units I+(S-1)X_iY_i are identity,
+so the bare root is S I modulo S^2-1. This mechanism is prior work.
+
+The g=9 source control reverses the block basis change and compares every
+pair to the even-index units on the first twenty coordinates of retained
+#6936 root_A.json. The g=18 chain uses parity-correct middle units; it does
+not borrow the source's second independent chain.
+
+## Stage masks and all-stage operator
+
+A host uses consecutive units u,v=u+1. Its rank-two projector is
+H=X_uY_v-X_vY_u. The coordinate mask E_j contains both X directions and
+Y supports, so E_j H=H E_j=H; E_j-H is an idempotent of rank rank(E_j)-2.
+
+Left masks contain A and the complete blocks of three F coordinates through
+the pair's last unit. Right masks contain A and complete suffix blocks of H.
+The middle mask contains A,E and the first new coordinate of every block on
+both arms. Exact checks establish that each mask commutes with the prefix
+immediately before and after its hosted pair.
+
+For the middle mask, the raw left prefix sends
+
+a' = (-1)^g a + 2(-1)^(g-1) sum_i (-1)^i f_i,
+F' = -F + 2 a' (1,...,1).
+
+In each three-block, the last two new basis vectors have alternating sum zero;
+the first is the all-ones vector. The complement is acted on by -I and has no
+cross terms with the middle mask. Left masks follow from prefix support.
+Right masks follow by writing a prefix as minus the inverse of its remaining
+suffix. These explain the finite exact commutator checks.
+
+Each stage multiplies by D_j on its whole E_j: the hosted rank-two piece plus
+all rank-one idle directions of E_j-H. Prefix commutation moves this multiplier
+to exactly E_j in initial coordinates. All E_j are diagonal and commute.
+At S=+1 the full word is diag(prod D_j); at S=-1 it is minus that diagonal.
+Thus the full formal operator is S diag(prod D_j) modulo S^2-1, with no
+specialization or sampling of D variables.
+
+L18 mask ranks are
+4,7,10,10,13,16,16,19,14,19,19,16,13,13,10,7,7,4,
+summing to217. Every coordinate has a nonempty mask. Hosts supply36
+dimensions and residuals181 separate rank-one idles. Units0,17,20 are thin.
+L3 has joint dimensions {1:2,2:1,3:1,4:2,6:1,7:1}, agreeing with the two
+retained #6937 roots under its recovered projector decoder and #6842 ordinary
+normalization. This is a mask-pattern statement, not parameter equivalence.
+
+## Emitted caller and Q4 lift
+
+Choose a host basis beginning X_u,X_v, then im(E_j-H), then standard vectors
+outside E_j. In this basis Y_u=-e_1* and Y_v=e_0*. The pair product is
+
+    [[1,1-S],[S-1,2S-1]] = L [[1,S],[-S,0]] P,
+    P=[[1,1],[0,-1]], L=[[1,0],[-1,-1]].
+
+The middle matrix is supplied HOST_S before common D_j. P,L and basis changes
+are emitted ADD/SCALE/SWAP. Each residual basis coordinate has one IDLE_ONE;
+none are fused. A thin unit uses a basis starting X and v with Yv=1, then
+ADD(-1) and QUERY_S, giving I+(S-1)XY. All basis changes act on arbitrary
+live roles, with no zero or owned scratch.
+
+For Q^4=1 put lambda=((1+i)+(1-i)Q^2)/2 and R=lambda Q. Then
+lambda^2=Q^2 and R^2=1. QUERY_R is LAMBDA(source,+), QUERY_Q,
+LAMBDA(source,-). HOST_R is LAMBDA(first,-), HOST_Q, LAMBDA(first,+).
+Final LAMBDA(-) on each role changes R diag(prod D) to Q diag(prod D).
+Every operation occurs in the frozen word. Four exact character evaluations
+are complete for Q^4-1 over Q(i); D exponents remain formal. Independent
+reverse replay uses the quotient ring directly.
+
+This proves caller algebra given HOST. It does not prove a physical HOST at
+its required price, or accepted ordinary, LAMBDA, precision and outer tariffs.
diff --git a/research/connected-l18-root-caller/README.md b/research/connected-l18-root-caller/README.md
new file mode 100644
index 0000000000..6ef3bae7d8
--- /dev/null
+++ b/research/connected-l18-root-caller/README.md
@@ -0,0 +1,115 @@
+# Connected L18 root and emitted dyadic caller
+
+This package constructs a connected, integral, rho=1 root with 38 roles, 39
+rank-one units and 18 commuting stage masks. It emits a 2,370-event caller and
+checks its exact operator on arbitrary inputs in
+Q(i)[Q,D_0,...,D_17]/(Q^4-1). The result is
+`Q diag(product of D_j over the role's mask)`.
+
+The emitted caller invokes **18 explicitly specified HOST(t=-1) macros**; their
+native implementation remains unbuilt. It does not certify a multiplier or
+claim a new kappa. **No new κ.** All 181 idle
+calls, three thin queries and 2,168 ordinary events are present. No same-label
+idle fusion, clean scratch, discarded main plane or free native rescaling is
+credited. `PROOF.md` gives the identities; `NATIVE.md` fixes the native obligation
+and complete substitution equation.
+
+The family includes an 8-role L3 instance and a 20-role L9 control. The L3
+instance has the joint-mask dimensions retained by #6937. This extends that
+mask pattern, not its literal rational parameter vectors. The L9 raw single
+chain is byte-bound to #6936's retained type A root. The new L18 construction
+joins both arms in one complete sign Gram; it is not six independent L3 copies
+or the two-chain rho=2 source root.
+
+| Instance | Roles | Units | HOST | IDLE_ONE | QUERY | Ordinary events |
+|---|---:|---:|---:|---:|---:|---:|
+| L3 | 8 | 9 | 3 | 6 | 3 | 179 |
+| L9 | 20 | 21 | 9 | 52 | 3 | 712 |
+| L18 | 38 | 39 | 18 | 181 | 3 | 2,168 |
+
+For L18 the ordinary count is 1,041 ADD, 189 SCALE, 858 SWAP and 80 LAMBDA.
+Every emitted rational scalar is dyadic, maximum absolute value 5/2. Primary
+forward replay at Q=1,-1,i,-i retains every independent D variable; its
+characterwise prefix coefficients have common denominator at most 2 and
+maximum row l1 norm 83. These are caller measurements, not a native precision
+certificate. Independent chronological majorants are retained separately.
+
+The target histogram is
+`H145 + H81 + 4H73 + 5H65 + 4H57 + 5H49 + 3H41 + 4H33 + 5H25 + 3H17 + 3H9`.
+The paid work outside the native is `181H8 + 3H1`. At pending complex comparison
+kappa 0.00362701882, each native call's signed paid-minus-helper cost per port
+must be below **17.13134090285433**, before ordinary and outer margins.
+The direct `2H8+2H1` baseline fails. These are conditional comparison gates,
+not exponent certificates or admission of pending source assumptions.
+
+Two scoped completion screens are included. Same-frame boundary remixing of
+the retained two-plane native cannot supply this resonant endpoint. For the
+fixed coordinate-role idle-merging model, even its exact optimum cannot repay
+the F+H1 native deficit: maximum saving9.70728992518 versus required
+10.08182803488 per port. Arbitrary noncoordinate idle directions, changed
+roots and larger native rewrites remain open; see `NATIVE.md` and
+`IDLE-COALESCING.md`.
+
+From this package directory, run with Python 3.12 and the standard library:
+
+```
+python3 -I -B generate.py
+python3 -I -B replay.py
+python3 -I -B cost.py
+python3 -I -B review.py
+python3 -I -B independent.py --package . --out INDEPENDENT.json
+python3 -I -B idle_coalescing.py --receipt IDLE-COALESCING.json
+```
+
+`generate.py` checks local input SHA256, regenerates each root and caller
+without writing, compares the g=9 chain to the retained source, and checks both
+retained L3 sector normalizations and joint masks. `--write` explicitly
+regenerates output. `replay.py` checks all four Q characters and rejects deletion
+of HOST, QUERY, IDLE_ONE, LAMBDA and ADD. Independent root, formal-ring caller
+and tariff checks are registered in `VERIFY.json`. Registered commands are
+read-only. Expected receipts are package-local.
+
+Exports are authenticated by `INPUT-PINS.json`, including original commit/path
+and SHA256. Catalogue and selected-record provenance is bound at main
+`7c49fe32c55de02c2c873655c804b16e4c3fef0a` in `SOURCES.json`. Replay requires no
+unmerged source Git history.
+
+## Open next questions
+
+1. Can a physical native implement resonant HOST below its signed gate,
+   including owned lifetimes, helper outputs, ordinary work and frame delivery?
+   Start from `NATIVE.md`; a profitable native word is missing.
+2. Can the 181 separate rank-eight idles be fused by an emitted legal caller?
+   Start with a common carrier/basis schedule and replay it before pricing.
+3. What raw scalar, LAMBDA, tape and width tariff supports caller, native and
+   outer reduction? The dyadic caller removes one alphabet obstacle, but those
+   framework and physical obligations remain.
+
+Structured questions are in `TASK.json`. The five framework assumptions
+(native_all_columns, owned_erasure, compiler, precision_tape, analytic_recovery)
+are neither proved nor discharged. Pending per-port/HOST/LAMBDA/IDLE forms need
+their own admission. No frontier changes.
+
+Credit: DreamingOfClouds's #6937 data and #6842 sector normalization; #6936's
+retained root and grammar, including @CubeJerry (Jerry Chen)'s #6912 type A root, Ali Romman's
+helper mechanism, unpaidmoon's phase tests and icekylinx's grid. The complete
+sign header and bare sector endpoint are prior mechanisms; the new contribution
+is the connected eighteen-stage mask geometry and its emitted dyadic caller.
+Substantial OpenAI Codex assistance; separate implementations supplied independent
+checks. No human or maintainer review. Apache-2.0; see `NOTICE` and `REVIEW.json`.
+
+From the repository root, the registered replay command is:
+
+```
+python3.12 -B scripts/research_package.py --package research/connected-l18-root-caller
+```
+
+Direct checks end with `PASS_ROOT_CALLER 18 2370`,
+`PASS_FOUR_CHARACTER_CALLER`, `PASS_EMITTED_CENSUS` and
+`PASS_INDEPENDENT_CONNECTED_ROOT`.
+
+The source-bound window check in [COALESCING-WINDOW.md](COALESCING-WINDOW.md)
+extends the fixed coordinate-role repair exclusion to every κ in
+[0.00362701882, 0.01], using a uniformly negative derivative of its complete
+signed moment. It does not exclude noncoordinate idle directions, different
+natives or changed roots.
diff --git a/research/connected-l18-root-caller/REPLAY.json b/research/connected-l18-root-caller/REPLAY.json
new file mode 100644
index 0000000000..8e7c07e9fc
--- /dev/null
+++ b/research/connected-l18-root-caller/REPLAY.json
@@ -0,0 +1,119 @@
+{
+  "3": {
+    "characters": [
+      {
+        "ok": true,
+        "peak_monomials": 17,
+        "common_denominator": "6",
+        "denominator_bits": 3,
+        "max_coefficient_row_l1": "9"
+      },
+      {
+        "ok": true,
+        "peak_monomials": 19,
+        "common_denominator": "6",
+        "denominator_bits": 3,
+        "max_coefficient_row_l1": "22"
+      },
+      {
+        "ok": true,
+        "peak_monomials": 19,
+        "common_denominator": "6",
+        "denominator_bits": 3,
+        "max_coefficient_row_l1": "22"
+      },
+      {
+        "ok": true,
+        "peak_monomials": 17,
+        "common_denominator": "6",
+        "denominator_bits": 3,
+        "max_coefficient_row_l1": "9"
+      }
+    ],
+    "controls": {
+      "drop_HOST": true,
+      "drop_QUERY": true,
+      "drop_IDLE_ONE": true,
+      "drop_LAMBDA": true,
+      "drop_ADD": true
+    }
+  },
+  "9": {
+    "characters": [
+      {
+        "ok": true,
+        "peak_monomials": 43,
+        "common_denominator": "6",
+        "denominator_bits": 3,
+        "max_coefficient_row_l1": "17"
+      },
+      {
+        "ok": true,
+        "peak_monomials": 54,
+        "common_denominator": "6",
+        "denominator_bits": 3,
+        "max_coefficient_row_l1": "48"
+      },
+      {
+        "ok": true,
+        "peak_monomials": 54,
+        "common_denominator": "6",
+        "denominator_bits": 3,
+        "max_coefficient_row_l1": "48"
+      },
+      {
+        "ok": true,
+        "peak_monomials": 43,
+        "common_denominator": "6",
+        "denominator_bits": 3,
+        "max_coefficient_row_l1": "17"
+      }
+    ],
+    "controls": {
+      "drop_HOST": true,
+      "drop_QUERY": true,
+      "drop_IDLE_ONE": true,
+      "drop_LAMBDA": true,
+      "drop_ADD": true
+    }
+  },
+  "18": {
+    "characters": [
+      {
+        "ok": true,
+        "peak_monomials": 76,
+        "common_denominator": "2",
+        "denominator_bits": 2,
+        "max_coefficient_row_l1": "27"
+      },
+      {
+        "ok": true,
+        "peak_monomials": 141,
+        "common_denominator": "2",
+        "denominator_bits": 2,
+        "max_coefficient_row_l1": "83"
+      },
+      {
+        "ok": true,
+        "peak_monomials": 141,
+        "common_denominator": "2",
+        "denominator_bits": 2,
+        "max_coefficient_row_l1": "83"
+      },
+      {
+        "ok": true,
+        "peak_monomials": 76,
+        "common_denominator": "2",
+        "denominator_bits": 2,
+        "max_coefficient_row_l1": "27"
+      }
+    ],
+    "controls": {
+      "drop_HOST": true,
+      "drop_QUERY": true,
+      "drop_IDLE_ONE": true,
+      "drop_LAMBDA": true,
+      "drop_ADD": true
+    }
+  }
+}
diff --git a/research/connected-l18-root-caller/REVIEW.json b/research/connected-l18-root-caller/REVIEW.json
new file mode 100644
index 0000000000..493bc58419
--- /dev/null
+++ b/research/connected-l18-root-caller/REVIEW.json
@@ -0,0 +1,32 @@
+{
+  "scope": "Connected L18 root and conditional emitted caller, not native or exponent admission.",
+  "independence": "Root and tariff implementations were authored separately and import no primary generator, matrix helpers or forward replay.",
+  "root_checks": "Exact sign Gram, sector endpoint,36 prefix commutators, hosted/residual projectors, formal all18-D endpoint at both sectors, altered header/unit/mask controls.",
+  "tariff_checks": "Independent event census, actual unbundled profile, chronological noncancelling coefficient mass below2^158 and dyadic denominator height at most51; excludes native internals.",
+  "adapter": "review.py loads frozen independent modules and compares returned objects with frozen receipts; it writes no files. Modules are copied unchanged; standalone original CLI supports explicit output paths.",
+  "evidence": [
+    "review/ROOT-L18.json",
+    "review/ROOT-L3.json",
+    "review/ROOT-L9.json",
+    "review/TARIFF-L18.json",
+    "review/PINS.json",
+    "review/NATIVE-SCREEN.json",
+    "INDEPENDENT.json",
+    "IDLE-COALESCING.json",
+    "review/COALESCING-CORROBORATION.json"
+  ],
+  "source_boundary": "Complete sign header and bare sector endpoint are prior work. New connected18stage geometry and emitted dyadic caller are the contribution. OriginalL3 retained roots are checked as pattern and normalization controls, not claimed parameter-equivalent.",
+  "limitations": [
+    "HOST(t=-1) native word missing",
+    "No full ordinary bit tariff or native precision certificate",
+    "Five framework assumptions and pending operation admissions remain",
+    "No new kappa",
+    "No human or maintainer review"
+  ],
+  "native_screen": "Separate exact replay of all1480 independent public inputs authenticates96 typeA endpoints and same-frame groups. Frozen-source coefficient audit only; no new physical/all-width claim.",
+  "reverse_formal": "Separate reverse adjoint coefficient engine, Gaussian rationals with explicit Q exponent reduced modulo4 and unrestricted18-dimensional D exponent tuples; no character evaluations and no primary imports. All1444 coefficients and8 perturbation controls pass.",
+  "independent_script_sha256": "a83786791d0f93d98aa8c108e94f2162dd9b470249b2758a560a6a57e8018867",
+  "independent_original_sha256": "6543a41ec74e76e49a2819cc0c4e1f69fdc471ad008362cbcb16c22bd3e58955",
+  "reverse_adapter": "Only docstring wording and an explicit refusal of optimized Python were added; ring/replay/census/control logic unchanged.",
+  "coordinate_idle_screen": "Solver-free eligibility union/intersection compression,17 forced host pairs and2 bridge choices. Separate interval implementation corroborates the optimal saving and source-bound required bill. Excludes arbitrary noncoordinate/shared-direction idle decompositions and changed root/native/encoding."
+}
diff --git a/research/connected-l18-root-caller/SOURCES.json b/research/connected-l18-root-caller/SOURCES.json
new file mode 100644
index 0000000000..75ea7c3d55
--- /dev/null
+++ b/research/connected-l18-root-caller/SOURCES.json
@@ -0,0 +1,18 @@
+{
+  "schema_version": 1,
+  "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a",
+  "files": [
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec",
+      "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81"
+    },
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a",
+      "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa"
+    }
+  ]
+}
diff --git a/research/connected-l18-root-caller/TASK.json b/research/connected-l18-root-caller/TASK.json
new file mode 100644
index 0000000000..891cf054fe
--- /dev/null
+++ b/research/connected-l18-root-caller/TASK.json
@@ -0,0 +1,130 @@
+{
+  "schema_version": 1,
+  "task_id": "p104-side-correction",
+  "priority_revision": 8,
+  "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a",
+  "original_card": {
+    "id": "p104-side-correction",
+    "question": "Can joint helper bases and a legal causal split improve the complete P104 productive/paid invoice?",
+    "starting_points": [
+      "docs/research/current-priorities.md",
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md",
+      "research/p104-helper-subspace-splits/README.md",
+      "research/dyadic-helper-channel-capacity/README.md"
+    ],
+    "methods": [
+      "Construct and independently check one source-bound instance of the stated first experiment.",
+      "Seek an exact counterexample or target-specific complete-budget obstruction to that same proposed change."
+    ],
+    "acceptance_gate": "An exact arbitrary-input identity, source/target frame availability and restoration at the chosen cut, plus the complete channel+correction+idle/hosting bill or an explicit favorable bound. The native channel alone is not a supplier. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_selected_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read revision 8, the selected review and live exact-source handoffs. Then follow this card's bounded first_experiment.",
+      "scope": "Source-bound orientation only, not a supplier replay or theorem proof."
+    },
+    "first_experiment": "Start with the selected #5599 emitted word and review pending #5718 distinct input/output bases plus #5717/#5719 coverage before claiming work. Pick one uncovered source word, helper group and cut region. Prove the arbitrary-input relation and legal entry/exit corrections, then compare full target and paid profiles. Reject if completion, owned lifetimes or consumer costs repay the gain. A static pairing rank alone is not a physical split.",
+    "bottleneck_link": "Judge the actual current supplier contract and complete signed target/paid bill; frozen-profile ceilings require an applicability proof.",
+    "allowed_variations": [
+      "One exact source head, helper/cut region or quantified proposition and changed hypothesis; check live handoffs first. Different seeds are not different scopes."
+    ],
+    "scope_change_triggers": [
+      "Changing source head, helper/cut domain, operation alphabet or caller boundary without recording the new scope.",
+      "Treating an archived proposal or local numerical pass as complete supplier admission."
+    ],
+    "overlap_terms": [
+      "P104",
+      "helper basis",
+      "helper split",
+      "5718",
+      "dyadic capacity"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #4133: literal-slot defect",
+        "evidence": "research/p104-literal-slot-defect/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "88666f1dee93fbd85b31fd5d6f91a219e111b5f4",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4136: uniform commutation gap",
+        "evidence": "research/p104-uniform-commutation-gap/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "281ce601a8be9db470de630759179c23e1dfaa88",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4140: uniform encoding gap",
+        "evidence": "research/p104-uniform-encoding-gap/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "de25c6525aa866962309df5d107b32d55e6e5628",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4153: source-chart shortcut exhausts its optimistic allowance",
+        "evidence": "research/p104-source-chart-shortcut/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "9123241fea53df77e51ffe30d9aca1625d4bf3a8",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4154: fiber-tag seam mismatch",
+        "evidence": "research/p104-fiber-tag-seam/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "4ffcdaee5d6255a9cea1fe53a5424435068089d0",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "Selected PR5599: complete helper-subspace construction and independent caller replay; five framework assumptions remain.",
+        "evidence": "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md",
+        "remaining": "The next experiment must identify uncovered source-specific work. Successor archive intake does not transfer this admission.",
+        "status": "reviewed",
+        "source_commit": "09dd0965711ca7eeb169057a420abab1c9052137",
+        "selected_record_sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5"
+      }
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Construct an integral connected rho=1 L18 root extending the retained L3 mask pattern, emit and exactly replay its Q4 caller, and state its complete unbundled native price gate.",
+  "scope_change_reason": "The L3 sector normalization and source single-chain header permit a new connected eighteen-stage mask geometry. This is a caller result with an unimplemented resonant native contract.",
+  "bottleneck_link": "Resolves the connected root/caller obligation and supplies an exact native demand; no complete supplier or new kappa.",
+  "budget_minutes": 70,
+  "stop_rule": "Freeze exact root and emitted caller with independent checks and explicit missing native/ordinary/outer obligations.",
+  "outcome": "completed",
+  "evidence": "generate.py, replay.py, cost.py, independent root/tariff/formal replay, exact root and caller JSONs.",
+  "author": "Integer-multiplication research session",
+  "ai_assistance": "Substantial OpenAI Codex assistance with separate-agent independent exact checks; no human review.",
+  "selected_frontier_changed": false,
+  "open_questions": [
+    {
+      "question": "Can a resonant native meet the complete signed gate?",
+      "why_it_matters": "HOST(t=-1) is still supplied algebra.",
+      "first_step": "Emit its physical word, source/target maps, helpers and owned lifetimes, then apply NATIVE.md substitution.",
+      "blocked_by": "No profitable native supplied."
+    },
+    {
+      "question": "Can separate idles be legally fused?",
+      "why_it_matters": "181 separate H8 jobs set the actual native allowance.",
+      "first_step": "Emit a shared carrier/basis schedule and exact replay before repricing.",
+      "blocked_by": "No fused caller supplied."
+    },
+    {
+      "question": "What complete raw tariff and precision supports this caller?",
+      "why_it_matters": "Ordinary dyadic operations and LAMBDA counts are not a multiplier cost certificate.",
+      "first_step": "Combine native prefix bounds, child errors, compiler and outer inequalities.",
+      "blocked_by": "Physical native and framework admissions remain open."
+    }
+  ]
+}
diff --git a/research/connected-l18-root-caller/VALIDATION.md b/research/connected-l18-root-caller/VALIDATION.md
new file mode 100644
index 0000000000..216600cf37
--- /dev/null
+++ b/research/connected-l18-root-caller/VALIDATION.md
@@ -0,0 +1,53 @@
+# Publication validation
+
+Canonical base: `7c49fe32c55de02c2c873655c804b16e4c3fef0a`.
+Python 3.12; standard library; source exports authenticated locally.
+
+```sh
+python3 -B scripts/research_package.py --package research/connected-l18-root-caller
+```
+
+The original six registered commands passed in the publication worktree. The 44
+frozen author files exactly matched their prepublication SHA256 manifest
+after replay; none was rewritten. The lead then added the separately verified uniform-window extension
+and its seventh registered command. The tests cover:
+
+- Exact deterministic L3/L9/L18 root and caller regeneration, byte-bound
+  predecessor controls and all stage-mask commutators.
+- Formal D variables at all four Q characters, with deletion controls.
+- Actual scalar/native/idle/query census and conditional native price gates.
+- Separately implemented root, mask and all-D sector replay, chronological
+  scalar bounds, and the complete all-input native remix screen.
+- Independently implemented reverse Q4 quotient-ring replay of all 1,444
+  caller coefficients, retaining repeated D powers; eight adverse controls.
+- The exact eligibility-compression optimum and independently corroborated
+  rational full-bill intervals. Three malformed incidence/host controls reject.
+
+The lead separately reviewed the sign-Gram endpoint derivation, the hosted
+pair factorization and Q4 lift, the source/frame applicability of the remix
+obstruction, and the concavity/compression proof. These are model-assisted
+checks, not external human review or a formal proof-kernel certificate.
+
+The original five assertion-based entry points were executed under `-O` and all
+explicitly rejected that mode. The coalescing checker, which uses explicit
+exceptions, passed an isolated optimized replay against its retained receipt.
+No optimized-mode pass is claimed for the entire package. Source-independent
+temporary-directory execution was also checked by the checker authors.
+
+Whitespace and committed-byte/mode preflights precede publication. The
+remote whole-tree SHA is required to match the tested base-plus-package tree;
+no sparse-checkout omission is a deletion. The optional full-history source
+preflight was not run in this shallow repository. No hosted CI or unrelated
+repository-wide baseline run is claimed.
+
+The positive result is the finite connected root geometry and exact caller
+with a specified HOST interface. The native remains unbuilt. The negative
+result concerns the pinned F+H1 profile and fixed coordinate-role idle
+coalescing, excluding noncoordinate idle decompositions, changed roots,
+different native words and larger coupled constructions. **No new κ.**
+
+The uniform-window extension uses the unchanged public interval engine; only
+its source pin and read-only receipt/control interface were adapted for this
+package. Its complete histogram and numerical enclosure match the independent
+review after the engine-hash provenance update. The added entry point rejects
+optimized execution; paid-adapter omission and reversed-interval controls fail.
diff --git a/research/connected-l18-root-caller/VERIFY.json b/research/connected-l18-root-caller/VERIFY.json
new file mode 100644
index 0000000000..c6528a6374
--- /dev/null
+++ b/research/connected-l18-root-caller/VERIFY.json
@@ -0,0 +1,97 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/generate.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Exact source hashes, root/caller regeneration and source controls"
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/replay.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Formal D at all four Q characters and deletion controls"
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/cost.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Actual unbundled census and conditional native gates"
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/review.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Independent root and dyadic tariff checks"
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/independent.py",
+        "--package",
+        "{package}",
+        "--out",
+        "{package}/INDEPENDENT.json"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Independent reverse replay of all1444 formal Q4/D coefficients and eight rejection controls."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/idle_coalescing.py",
+        "--package-root",
+        "{package}",
+        "--receipt",
+        "{package}/IDLE-COALESCING.json"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Exact coordinate-role idle-compression optimum, source-bound full invoice intervals and three rejection controls."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/review/coalescing_window.py",
+        "--root",
+        "{package}/root_L18.json",
+        "--caller",
+        "{package}/caller_L18.json",
+        "--invoice",
+        "{package}/inputs/base_invoice.json",
+        "--engine",
+        "{package}/review/interval_engine.py",
+        "--receipt",
+        "{package}/COALESCING-WINDOW.json"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Independent complete-profile uniform negativity on kappa [.00362701882,.01], exact interval derivative bound and two negative controls."
+    }
+  ]
+}
diff --git a/research/connected-l18-root-caller/caller_L18.json b/research/connected-l18-root-caller/caller_L18.json
new file mode 100644
index 0000000000..2830c0096b
--- /dev/null
+++ b/research/connected-l18-root-caller/caller_L18.json
@@ -0,0 +1 @@
+{"roles": 38, "stages": 18, "masks": [262143, 511, 255, 255, 510, 254, 254, 508, 252, 252, 496, 240, 240, 480, 224, 224, 384, 128, 128, 1792, 1536, 1536, 3840, 3584, 3584, 16128, 15872, 15872, 32512, 32256, 32256, 130816, 130560, 130560, 261888, 261632, 261632, 256], "events": [["ADD", 1, 3, "1"], ["ADD", 0, 3, "1"], ["SCALE", 3, "-1"], ["ADD", 0, 2, "-1"], ["SWAP", 3, 2], ["ADD", 0, 1, "-1"], ["SWAP", 2, 1], ["SWAP", 1, 0], ["ADD", 0, 1, "-1"], ["LAMBDA", 1, 1], ["QUERY", 0, 1, 1], ["LAMBDA", 1, -1], ["ADD", 1, 3, "1"], ["ADD", 0, 2, "1"], ["SWAP", 3, 2], ["ADD", 3, 1, "1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["ADD", 3, 0, "-1"], ["ADD", 1, 0, "1"], ["ADD", 1, 3, "1"], ["SCALE", 3, "-1"], ["ADD", 1, 2, "-1"], ["ADD", 0, 2, "-1"], ["ADD", 3, 1, "1"], ["ADD", 0, 1, "-1"], ["SWAP", 2, 1], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "-1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["LAMBDA", 0, -1], ["HOST", 0, 1, 0, "1", "-1"], ["LAMBDA", 0, 1], ["ADD", 1, 0, "1"], ["SCALE", 1, "-1"], ["IDLE_ONE", 2, [0]], ["IDLE_ONE", 3, [0]], ["ADD", 1, 3, "-1"], ["ADD", 0, 3, "1"], ["ADD", 3, 2, "-1"], ["ADD", 1, 2, "2"], ["ADD", 0, 2, "-1"], ["SCALE", 2, "-1"], ["ADD", 0, 1, "1"], ["SWAP", 3, 1], ["ADD", 3, 0, "-1"], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "1"], ["ADD", 5, 6, "1"], ["ADD", 4, 6, "1"], ["ADD", 1, 6, "2"], ["ADD", 0, 6, "1"], ["SCALE", 6, "-1"], ["ADD", 4, 5, "1"], ["SCALE", 5, "-1"], ["SWAP", 6, 5], ["ADD", 6, 4, "1"], ["ADD", 0, 4, "-1"], ["SWAP", 5, 3], ["SWAP", 4, 2], ["SWAP", 3, 1], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "-1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["LAMBDA", 0, -1], ["HOST", 0, 1, 1, "1", "-1"], ["LAMBDA", 0, 1], ["ADD", 1, 0, "1"], ["SCALE", 1, "-1"], ["IDLE_ONE", 2, [1]], ["IDLE_ONE", 3, [1]], ["IDLE_ONE", 4, [1]], ["IDLE_ONE", 5, [1]], ["IDLE_ONE", 6, [1]], ["ADD", 3, 6, "-2"], ["ADD", 2, 6, "-1"], ["ADD", 0, 6, "1"], ["SWAP", 5, 3], ["ADD", 6, 2, "1"], ["ADD", 5, 2, "-2"], ["ADD", 1, 2, "1"], ["SCALE", 2, "-1"], ["SWAP", 4, 2], ["ADD", 0, 1, "1"], ["SWAP", 5, 1], ["ADD", 6, 0, "-1"], ["ADD", 4, 0, "1"], ["ADD", 1, 0, "2"], ["ADD", 7, 9, "1"], ["ADD", 6, 9, "-1"], ["ADD", 4, 9, "2"], ["ADD", 1, 9, "2"], ["ADD", 0, 9, "1"], ["ADD", 5, 8, "-1"], ["ADD", 4, 8, "-1"], ["ADD", 1, 8, "-2"], ["ADD", 0, 8, "-1"], ["SWAP", 9, 8], ["ADD", 5, 7, "-1"], ["ADD", 4, 7, "-1"], ["ADD", 1, 7, "-2"], ["ADD", 0, 7, "-1"], ["SWAP", 8, 7], ["ADD", 7, 6, "1"], ["ADD", 4, 6, "1"], ["SCALE", 6, "-1"], ["ADD", 6, 5, "-1"], ["ADD", 1, 5, "-2"], ["SCALE", 5, "-1"], ["ADD", 6, 4, "1"], ["SWAP", 5, 4], ["SWAP", 5, 3], ["SWAP", 4, 2], ["SWAP", 3, 1], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "-1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["LAMBDA", 0, -1], ["HOST", 0, 1, 2, "1", "-1"], ["LAMBDA", 0, 1], ["ADD", 1, 0, "1"], ["SCALE", 1, "-1"], ["IDLE_ONE", 2, [2]], ["IDLE_ONE", 3, [2]], ["IDLE_ONE", 4, [2]], ["IDLE_ONE", 5, [2]], ["IDLE_ONE", 6, [2]], ["IDLE_ONE", 7, [2]], ["IDLE_ONE", 8, [2]], ["IDLE_ONE", 9, [2]], ["ADD", 0, 9, "1"], ["ADD", 6, 8, "-2"], ["ADD", 3, 8, "-2"], ["ADD", 2, 8, "-1"], ["SWAP", 9, 8], ["ADD", 1, 7, "-1"], ["ADD", 9, 6, "1/2"], ["ADD", 3, 6, "-1"], ["ADD", 2, 6, "-1/2"], ["ADD", 0, 6, "-1/2"], ["SCALE", 6, "-1/2"], ["SWAP", 7, 6], ["ADD", 9, 3, "-1/2"], ["ADD", 7, 3, "1/2"], ["ADD", 2, 3, "-1/2"], ["ADD", 0, 3, "1/2"], ["SCALE", 3, "-1"], ["SWAP", 5, 3], ["ADD", 9, 2, "-1"], ["ADD", 7, 2, "1"], ["ADD", 5, 2, "-2"], ["ADD", 0, 2, "1"], ["SCALE", 2, "-2"], ["SWAP", 4, 2], ["ADD", 9, 1, "-1"], ["ADD", 7, 1, "1"], ["ADD", 5, 1, "-1"], ["ADD", 0, 1, "1"], ["SWAP", 4, 1], ["ADD", 5, 0, "1"], ["ADD", 4, 0, "1"], ["ADD", 1, 0, "2"], ["ADD", 7, 9, "1"], ["SCALE", 9, "-1"], ["ADD", 7, 8, "-1"], ["ADD", 4, 8, "-2"], ["ADD", 1, 8, "-2"], ["ADD", 0, 8, "-1"], ["ADD", 9, 7, "1"], ["ADD", 0, 7, "-1"], ["SWAP", 8, 7], ["SWAP", 8, 6], ["SWAP", 7, 5], ["SWAP", 6, 4], ["SWAP", 5, 3], ["SWAP", 4, 2], ["SWAP", 3, 1], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "-1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["LAMBDA", 0, -1], ["HOST", 0, 1, 3, "1", "-1"], ["LAMBDA", 0, 1], ["ADD", 1, 0, "1"], ["SCALE", 1, "-1"], ["IDLE_ONE", 2, [3]], ["IDLE_ONE", 3, [3]], ["IDLE_ONE", 4, [3]], ["IDLE_ONE", 5, [3]], ["IDLE_ONE", 6, [3]], ["IDLE_ONE", 7, [3]], ["IDLE_ONE", 8, [3]], ["IDLE_ONE", 9, [3]], ["ADD", 6, 9, "-2"], ["ADD", 3, 9, "-2"], ["ADD", 2, 9, "-1"], ["ADD", 1, 9, "1"], ["SCALE", 9, "-1"], ["SWAP", 9, 8], ["SWAP", 9, 7], ["ADD", 8, 6, "-1/2"], ["ADD", 3, 6, "-1"], ["ADD", 2, 6, "-1/2"], ["ADD", 1, 6, "1"], ["ADD", 0, 6, "-1/2"], ["SCALE", 6, "-1/2"], ["SWAP", 7, 6], ["SWAP", 9, 5], ["SWAP", 9, 3], ["ADD", 9, 2, "-2"], ["ADD", 8, 2, "-1"], ["ADD", 7, 2, "-1"], ["ADD", 1, 2, "2"], ["ADD", 0, 2, "-1"], ["SCALE", 2, "-2"], ["SWAP", 4, 2], ["ADD", 0, 1, "1"], ["SWAP", 9, 1], ["ADD", 9, 0, "-1"], ["ADD", 8, 0, "1"], ["ADD", 7, 0, "1"], ["ADD", 4, 0, "2"], ["ADD", 1, 0, "2"], ["ADD", 11, 12, "1"], ["ADD", 10, 12, "1"], ["ADD", 7, 12, "2"], ["ADD", 4, 12, "2"], ["ADD", 1, 12, "2"], ["ADD", 0, 12, "1"], ["SCALE", 12, "-1"], ["ADD", 10, 11, "1"], ["SCALE", 11, "-1"], ["SWAP", 12, 11], ["ADD", 12, 10, "1"], ["ADD", 0, 10, "-1"], ["SWAP", 11, 9], ["SWAP", 10, 8], ["SWAP", 9, 7], ["SWAP", 8, 6], ["SWAP", 7, 5], ["SWAP", 6, 4], ["SWAP", 5, 3], ["SWAP", 4, 2], ["SWAP", 3, 1], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "-1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["LAMBDA", 0, -1], ["HOST", 0, 1, 4, "1", "-1"], ["LAMBDA", 0, 1], ["ADD", 1, 0, "1"], ["SCALE", 1, "-1"], ["IDLE_ONE", 2, [4]], ["IDLE_ONE", 3, [4]], ["IDLE_ONE", 4, [4]], ["IDLE_ONE", 5, [4]], ["IDLE_ONE", 6, [4]], ["IDLE_ONE", 7, [4]], ["IDLE_ONE", 8, [4]], ["IDLE_ONE", 9, [4]], ["IDLE_ONE", 10, [4]], ["IDLE_ONE", 11, [4]], ["IDLE_ONE", 12, [4]], ["ADD", 9, 12, "-2"], ["ADD", 6, 12, "-2"], ["ADD", 3, 12, "-2"], ["ADD", 2, 12, "-1"], ["ADD", 0, 12, "1"], ["SWAP", 11, 10], ["ADD", 12, 9, "1/2"], ["ADD", 6, 9, "-1"], ["ADD", 3, 9, "-1"], ["ADD", 2, 9, "-1/2"], ["ADD", 1, 9, "1/2"], ["SCALE", 9, "-1/2"], ["SWAP", 10, 9], ["SWAP", 11, 8], ["SWAP", 11, 7], ["ADD", 12, 6, "1/2"], ["ADD", 10, 6, "-1/2"], ["ADD", 3, 6, "-1"], ["ADD", 2, 6, "-1/2"], ["ADD", 1, 6, "1/2"], ["SCALE", 6, "-1"], ["SWAP", 7, 6], ["SWAP", 11, 5], ["SWAP", 11, 3], ["ADD", 12, 2, "1"], ["ADD", 11, 2, "-2"], ["ADD", 10, 2, "-1"], ["ADD", 7, 2, "-2"], ["ADD", 1, 2, "1"], ["SCALE", 2, "-2"], ["SWAP", 4, 2], ["ADD", 0, 1, "1"], ["SWAP", 11, 1], ["ADD", 12, 0, "-1"], ["ADD", 10, 0, "1"], ["ADD", 7, 0, "2"], ["ADD", 4, 0, "2"], ["ADD", 1, 0, "2"], ["ADD", 13, 15, "1"], ["ADD", 12, 15, "-1"], ["ADD", 10, 15, "2"], ["ADD", 7, 15, "2"], ["ADD", 4, 15, "2"], ["ADD", 1, 15, "2"], ["ADD", 0, 15, "1"], ["ADD", 11, 14, "-1"], ["ADD", 10, 14, "-1"], ["ADD", 7, 14, "-2"], ["ADD", 4, 14, "-2"], ["ADD", 1, 14, "-2"], ["ADD", 0, 14, "-1"], ["SWAP", 15, 14], ["ADD", 11, 13, "-1"], ["ADD", 10, 13, "-1"], ["ADD", 7, 13, "-2"], ["ADD", 4, 13, "-2"], ["ADD", 1, 13, "-2"], ["ADD", 0, 13, "-1"], ["SWAP", 14, 13], ["ADD", 13, 12, "1"], ["ADD", 10, 12, "1"], ["SCALE", 12, "-1"], ["ADD", 12, 11, "-1"], ["ADD", 7, 11, "-2"], ["ADD", 4, 11, "-2"], ["ADD", 1, 11, "-2"], ["SCALE", 11, "-1"], ["ADD", 12, 10, "1"], ["SWAP", 11, 10], ["SWAP", 11, 9], ["SWAP", 10, 8], ["SWAP", 9, 7], ["SWAP", 8, 6], ["SWAP", 7, 5], ["SWAP", 6, 4], ["SWAP", 5, 3], ["SWAP", 4, 2], ["SWAP", 3, 1], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "-1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["LAMBDA", 0, -1], ["HOST", 0, 1, 5, "1", "-1"], ["LAMBDA", 0, 1], ["ADD", 1, 0, "1"], ["SCALE", 1, "-1"], ["IDLE_ONE", 2, [5]], ["IDLE_ONE", 3, [5]], ["IDLE_ONE", 4, [5]], ["IDLE_ONE", 5, [5]], ["IDLE_ONE", 6, [5]], ["IDLE_ONE", 7, [5]], ["IDLE_ONE", 8, [5]], ["IDLE_ONE", 9, [5]], ["IDLE_ONE", 10, [5]], ["IDLE_ONE", 11, [5]], ["IDLE_ONE", 12, [5]], ["IDLE_ONE", 13, [5]], ["IDLE_ONE", 14, [5]], ["IDLE_ONE", 15, [5]], ["ADD", 0, 15, "1"], ["ADD", 12, 14, "-2"], ["ADD", 9, 14, "-2"], ["ADD", 6, 14, "-2"], ["ADD", 3, 14, "-2"], ["ADD", 2, 14, "-1"], ["SWAP", 15, 14], ["ADD", 1, 13, "-1"], ["ADD", 15, 12, "1/2"], ["ADD", 9, 12, "-1"], ["ADD", 6, 12, 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diff --git a/research/connected-l18-root-caller/caller_L3.json b/research/connected-l18-root-caller/caller_L3.json
new file mode 100644
index 0000000000..93a6a7231d
--- /dev/null
+++ b/research/connected-l18-root-caller/caller_L3.json
@@ -0,0 +1 @@
+{"roles": 8, "stages": 3, "masks": [7, 3, 1, 1, 6, 4, 4, 2], "events": [["ADD", 1, 3, "1"], ["ADD", 0, 3, "1"], ["SCALE", 3, "-1"], ["ADD", 0, 2, "-1"], ["SWAP", 3, 2], ["ADD", 0, 1, "-1"], ["SWAP", 2, 1], ["SWAP", 1, 0], ["ADD", 0, 1, "-1"], ["LAMBDA", 1, 1], ["QUERY", 0, 1, 1], ["LAMBDA", 1, -1], ["ADD", 1, 3, "1"], ["ADD", 0, 2, "1"], ["SWAP", 3, 2], ["ADD", 3, 1, "1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["ADD", 3, 0, "-1"], ["ADD", 1, 0, "1"], ["ADD", 1, 3, "1"], ["SCALE", 3, "-1"], ["ADD", 1, 2, "-1"], ["ADD", 0, 2, "-1"], ["ADD", 3, 1, "1"], ["ADD", 0, 1, "-1"], ["SWAP", 2, 1], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "-1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["LAMBDA", 0, -1], ["HOST", 0, 1, 0, "1", "-1"], ["LAMBDA", 0, 1], ["ADD", 1, 0, "1"], ["SCALE", 1, "-1"], ["IDLE_ONE", 2, [0]], ["IDLE_ONE", 3, [0]], ["ADD", 1, 3, "-1"], ["ADD", 0, 3, "1"], ["ADD", 3, 2, "-1"], ["ADD", 1, 2, "2"], ["ADD", 0, 2, "-1"], ["SCALE", 2, "-1"], ["ADD", 0, 1, "1"], ["SWAP", 3, 1], ["ADD", 3, 0, "-1"], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "1"], ["ADD", 4, 7, "-1"], ["ADD", 1, 7, "-2"], ["SWAP", 7, 6], ["SWAP", 6, 5], ["ADD", 5, 4, "1"], ["ADD", 1, 4, "-1"], ["SCALE", 4, "1/2"], ["SWAP", 5, 3], ["SWAP", 4, 2], ["ADD", 3, 1, "1"], ["ADD", 2, 1, "1/2"], ["ADD", 0, 1, "-1/2"], ["SCALE", 1, "-1/2"], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "-1"], ["SCALE", 0, "2"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["LAMBDA", 0, -1], ["HOST", 0, 1, 1, "1", "-1"], ["LAMBDA", 0, 1], ["ADD", 1, 0, "1"], ["SCALE", 1, "-1"], ["IDLE_ONE", 2, [1]], ["IDLE_ONE", 3, [1]], ["SWAP", 7, 6], ["SWAP", 7, 5], ["ADD", 2, 3, "-1/2"], ["ADD", 0, 3, "1"], ["SCALE", 3, "-1"], ["SWAP", 7, 3], ["ADD", 0, 2, "-2"], ["SCALE", 2, "2"], ["SWAP", 4, 2], ["ADD", 4, 1, "2"], ["SCALE", 1, "-1"], ["ADD", 7, 0, "1"], ["ADD", 4, 0, "1"], ["SWAP", 1, 0], ["ADD", 4, 7, "2"], ["ADD", 0, 7, "-1"], ["SCALE", 7, "-1"], ["SWAP", 7, 6], ["SWAP", 6, 5], ["ADD", 0, 4, "2/3"], ["SWAP", 5, 4], ["SWAP", 4, 3], ["SWAP", 3, 2], ["ADD", 0, 1, "-2/3"], ["SWAP", 2, 1], ["SCALE", 0, "3"], ["SWAP", 1, 0], ["ADD", 0, 1, "-1"], ["LAMBDA", 1, 1], ["QUERY", 0, 1, 1], ["LAMBDA", 1, -1], ["SWAP", 7, 6], ["ADD", 1, 5, "-1/2"], ["ADD", 0, 5, "1/2"], ["SCALE", 5, "1/2"], ["SWAP", 7, 5], ["SWAP", 4, 3], ["ADD", 1, 2, "2"], ["SWAP", 4, 2], ["ADD", 7, 1, "-1/3"], ["ADD", 0, 1, "-1/3"], ["SCALE", 1, "2/3"], ["SWAP", 4, 1], ["ADD", 7, 0, "-1"], ["ADD", 4, 0, "2"], ["SCALE", 0, "-1"], ["ADD", 5, 6, "1"], ["ADD", 4, 6, "-1"], ["ADD", 0, 6, "1"], ["ADD", 4, 5, "1"], ["SCALE", 5, "-1"], ["SWAP", 6, 5], ["ADD", 6, 4, "1"], ["ADD", 0, 4, "1"], ["SCALE", 4, "-1"], ["SWAP", 5, 4], ["SWAP", 6, 3], ["SWAP", 5, 2], ["SWAP", 4, 1], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "-1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["LAMBDA", 0, -1], ["HOST", 0, 1, 2, "1", "-1"], ["LAMBDA", 0, 1], ["ADD", 1, 0, "1"], ["SCALE", 1, "-1"], ["IDLE_ONE", 2, [2]], ["IDLE_ONE", 3, [2]], ["SWAP", 5, 4], ["ADD", 2, 3, "1"], ["ADD", 0, 3, "1"], ["SCALE", 3, "-1"], ["SWAP", 6, 3], ["ADD", 6, 2, "1"], ["ADD", 1, 2, "1"], ["ADD", 0, 2, "-2"], ["SWAP", 4, 2], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["SWAP", 5, 1], ["ADD", 6, 0, "1"], ["ADD", 4, 0, "1"], ["SCALE", 0, "-1"], ["ADD", 0, 6, "1"], ["ADD", 4, 5, "1"], ["ADD", 0, 5, "-1"], ["SCALE", 5, "-1"], ["ADD", 0, 4, "1"], ["SWAP", 5, 4], ["SWAP", 4, 3], ["SWAP", 3, 2], ["SWAP", 2, 1], ["SWAP", 1, 0], ["ADD", 0, 1, "-1"], ["LAMBDA", 1, 1], ["QUERY", 0, 1, 1], ["LAMBDA", 1, -1], ["ADD", 1, 6, "-1"], ["ADD", 0, 5, "1"], ["SWAP", 4, 3], ["SWAP", 4, 2], ["ADD", 5, 1, "-1"], ["ADD", 0, 1, "-1"], ["SWAP", 4, 1], ["ADD", 5, 0, "-1"], ["ADD", 4, 0, "1"], ["SCALE", 0, "-1"], ["LAMBDA", 0, -1], ["LAMBDA", 1, -1], ["LAMBDA", 2, -1], ["LAMBDA", 3, -1], ["LAMBDA", 4, -1], ["LAMBDA", 5, -1], ["LAMBDA", 6, -1], ["LAMBDA", 7, -1]], "central_relation": "Q^4=1; R=Lambda Q; R^2=1"}
diff --git a/research/connected-l18-root-caller/caller_L9.json b/research/connected-l18-root-caller/caller_L9.json
new file mode 100644
index 0000000000..e35b166bdd
--- /dev/null
+++ b/research/connected-l18-root-caller/caller_L9.json
@@ -0,0 +1 @@
+{"roles": 20, "stages": 9, "masks": [511, 31, 15, 15, 30, 14, 14, 28, 12, 12, 112, 96, 96, 240, 224, 224, 496, 480, 480, 16], "events": [["ADD", 1, 3, "1"], ["ADD", 0, 3, "1"], ["SCALE", 3, "-1"], ["ADD", 0, 2, "-1"], ["SWAP", 3, 2], ["ADD", 0, 1, "-1"], ["SWAP", 2, 1], ["SWAP", 1, 0], ["ADD", 0, 1, "-1"], ["LAMBDA", 1, 1], ["QUERY", 0, 1, 1], ["LAMBDA", 1, -1], ["ADD", 1, 3, "1"], ["ADD", 0, 2, "1"], ["SWAP", 3, 2], ["ADD", 3, 1, "1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["ADD", 3, 0, "-1"], ["ADD", 1, 0, "1"], ["ADD", 1, 3, "1"], ["SCALE", 3, "-1"], ["ADD", 1, 2, "-1"], ["ADD", 0, 2, "-1"], ["ADD", 3, 1, "1"], ["ADD", 0, 1, "-1"], ["SWAP", 2, 1], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "-1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["LAMBDA", 0, -1], ["HOST", 0, 1, 0, "1", "-1"], ["LAMBDA", 0, 1], ["ADD", 1, 0, "1"], ["SCALE", 1, "-1"], ["IDLE_ONE", 2, [0]], ["IDLE_ONE", 3, [0]], ["ADD", 1, 3, "-1"], ["ADD", 0, 3, "1"], ["ADD", 3, 2, "-1"], ["ADD", 1, 2, "2"], ["ADD", 0, 2, "-1"], ["SCALE", 2, "-1"], ["ADD", 0, 1, "1"], ["SWAP", 3, 1], ["ADD", 3, 0, "-1"], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "1"], ["ADD", 5, 6, "1"], ["ADD", 4, 6, "1"], ["ADD", 1, 6, "2"], ["ADD", 0, 6, "1"], ["SCALE", 6, "-1"], ["ADD", 4, 5, "1"], ["SCALE", 5, "-1"], ["SWAP", 6, 5], ["ADD", 6, 4, "1"], ["ADD", 0, 4, "-1"], ["SWAP", 5, 3], ["SWAP", 4, 2], ["SWAP", 3, 1], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "-1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["LAMBDA", 0, -1], ["HOST", 0, 1, 1, "1", "-1"], ["LAMBDA", 0, 1], ["ADD", 1, 0, "1"], ["SCALE", 1, "-1"], ["IDLE_ONE", 2, [1]], ["IDLE_ONE", 3, [1]], ["IDLE_ONE", 4, [1]], ["IDLE_ONE", 5, [1]], ["IDLE_ONE", 6, [1]], ["ADD", 3, 6, "-2"], ["ADD", 2, 6, "-1"], ["ADD", 0, 6, "1"], ["SWAP", 5, 3], ["ADD", 6, 2, "1"], ["ADD", 5, 2, "-2"], ["ADD", 1, 2, "1"], ["SCALE", 2, "-1"], ["SWAP", 4, 2], ["ADD", 0, 1, "1"], ["SWAP", 5, 1], ["ADD", 6, 0, "-1"], ["ADD", 4, 0, "1"], ["ADD", 1, 0, "2"], ["ADD", 7, 9, "1"], ["ADD", 6, 9, "-1"], ["ADD", 4, 9, "2"], ["ADD", 1, 9, "2"], ["ADD", 0, 9, "1"], ["ADD", 5, 8, "-1"], ["ADD", 4, 8, "-1"], ["ADD", 1, 8, "-2"], ["ADD", 0, 8, "-1"], ["SWAP", 9, 8], ["ADD", 5, 7, "-1"], ["ADD", 4, 7, "-1"], ["ADD", 1, 7, "-2"], ["ADD", 0, 7, "-1"], ["SWAP", 8, 7], ["ADD", 7, 6, "1"], ["ADD", 4, 6, "1"], ["SCALE", 6, "-1"], ["ADD", 6, 5, "-1"], ["ADD", 1, 5, "-2"], ["SCALE", 5, "-1"], ["ADD", 6, 4, "1"], ["SWAP", 5, 4], ["SWAP", 5, 3], ["SWAP", 4, 2], ["SWAP", 3, 1], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "-1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["LAMBDA", 0, -1], ["HOST", 0, 1, 2, "1", "-1"], ["LAMBDA", 0, 1], ["ADD", 1, 0, "1"], ["SCALE", 1, "-1"], ["IDLE_ONE", 2, [2]], ["IDLE_ONE", 3, [2]], ["IDLE_ONE", 4, [2]], ["IDLE_ONE", 5, [2]], ["IDLE_ONE", 6, [2]], ["IDLE_ONE", 7, [2]], ["IDLE_ONE", 8, [2]], ["IDLE_ONE", 9, [2]], ["ADD", 0, 9, "1"], ["ADD", 6, 8, "-2"], ["ADD", 3, 8, "-2"], ["ADD", 2, 8, "-1"], ["SWAP", 9, 8], ["ADD", 1, 7, "-1"], ["ADD", 9, 6, "1/2"], ["ADD", 3, 6, "-1"], ["ADD", 2, 6, "-1/2"], ["ADD", 0, 6, "-1/2"], ["SCALE", 6, "-1/2"], ["SWAP", 7, 6], ["ADD", 9, 3, "-1/2"], ["ADD", 7, 3, "1/2"], ["ADD", 2, 3, "-1/2"], ["ADD", 0, 3, "1/2"], ["SCALE", 3, "-1"], ["SWAP", 5, 3], ["ADD", 9, 2, "-1"], ["ADD", 7, 2, "1"], ["ADD", 5, 2, "-2"], ["ADD", 0, 2, "1"], ["SCALE", 2, "-2"], ["SWAP", 4, 2], ["ADD", 9, 1, "-1"], ["ADD", 7, 1, "1"], ["ADD", 5, 1, "-1"], ["ADD", 0, 1, "1"], ["SWAP", 4, 1], ["ADD", 5, 0, "1"], ["ADD", 4, 0, "1"], ["ADD", 1, 0, "2"], ["ADD", 7, 9, "1"], ["SCALE", 9, "-1"], ["ADD", 7, 8, "-1"], ["ADD", 4, 8, "-2"], ["ADD", 1, 8, "-2"], ["ADD", 0, 8, "-1"], ["ADD", 9, 7, "1"], ["ADD", 0, 7, "-1"], ["SWAP", 8, 7], ["SWAP", 8, 6], ["SWAP", 7, 5], ["SWAP", 6, 4], ["SWAP", 5, 3], ["SWAP", 4, 2], ["SWAP", 3, 1], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "-1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["LAMBDA", 0, -1], ["HOST", 0, 1, 3, "1", "-1"], ["LAMBDA", 0, 1], ["ADD", 1, 0, "1"], ["SCALE", 1, "-1"], ["IDLE_ONE", 2, [3]], ["IDLE_ONE", 3, [3]], ["IDLE_ONE", 4, [3]], ["IDLE_ONE", 5, [3]], ["IDLE_ONE", 6, [3]], ["IDLE_ONE", 7, [3]], ["IDLE_ONE", 8, [3]], ["IDLE_ONE", 9, [3]], ["ADD", 6, 9, "-2"], ["ADD", 3, 9, "-2"], ["ADD", 2, 9, "-1"], ["ADD", 1, 9, "1"], ["SCALE", 9, "-1"], ["SWAP", 9, 8], ["SWAP", 9, 7], ["ADD", 8, 6, "-1/2"], ["ADD", 3, 6, "-1"], ["ADD", 2, 6, "-1/2"], ["ADD", 1, 6, "1"], ["ADD", 0, 6, "-1/2"], ["SCALE", 6, "-1/2"], ["SWAP", 7, 6], ["SWAP", 9, 5], ["SWAP", 9, 3], ["ADD", 9, 2, "-2"], ["ADD", 8, 2, "-1"], ["ADD", 7, 2, "-1"], ["ADD", 1, 2, "2"], ["ADD", 0, 2, "-1"], ["SCALE", 2, "-2"], ["SWAP", 4, 2], ["ADD", 0, 1, "1"], ["SWAP", 9, 1], ["ADD", 9, 0, "-1"], ["ADD", 8, 0, "1"], ["ADD", 7, 0, "1"], ["ADD", 4, 0, "2"], ["ADD", 1, 0, "2"], ["ADD", 7, 19, "-1"], ["ADD", 4, 19, "-1"], ["ADD", 1, 19, "-1"], ["SCALE", 19, "-1/2"], ["SWAP", 19, 18], ["SWAP", 18, 17], ["ADD", 17, 16, "1/2"], ["ADD", 13, 16, "-1"], ["SCALE", 16, "-1"], ["SWAP", 17, 15], ["SWAP", 16, 14], ["ADD", 14, 13, "1"], ["ADD", 10, 13, "-1"], ["SWAP", 15, 12], ["SWAP", 14, 11], ["ADD", 11, 10, "1"], ["ADD", 7, 10, "-1"], ["SWAP", 13, 9], ["SWAP", 12, 8], ["ADD", 10, 7, "1"], ["ADD", 1, 7, "1"], ["SCALE", 7, "-1"], ["SWAP", 9, 7], ["SWAP", 11, 6], ["SWAP", 10, 5], ["ADD", 9, 4, "1"], ["ADD", 1, 4, "-1"], ["SWAP", 9, 3], ["SWAP", 8, 2], ["ADD", 3, 1, "1"], ["ADD", 2, 1, "1/2"], ["ADD", 0, 1, "-1/2"], ["SCALE", 1, "-1/2"], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "-1"], ["SCALE", 0, "2"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["LAMBDA", 0, -1], ["HOST", 0, 1, 4, "1", "-1"], ["LAMBDA", 0, 1], ["ADD", 1, 0, "1"], ["SCALE", 1, "-1"], ["IDLE_ONE", 2, [4]], ["IDLE_ONE", 3, [4]], ["IDLE_ONE", 4, [4]], ["IDLE_ONE", 5, [4]], ["IDLE_ONE", 6, [4]], ["IDLE_ONE", 7, [4]], ["SWAP", 19, 18], ["SWAP", 19, 17], ["SWAP", 19, 15], ["SWAP", 16, 14], ["SWAP", 16, 13], ["SWAP", 19, 12], ["SWAP", 13, 11], ["SWAP", 19, 10], ["SWAP", 16, 9], ["SWAP", 10, 8], ["ADD", 6, 7, "-1"], ["ADD", 2, 7, "1/2"], ["ADD", 0, 7, "1"], ["SCALE", 7, "-1"], ["SWAP", 16, 7], ["ADD", 16, 6, "-1"], ["ADD", 2, 6, "1/2"], ["SCALE", 6, "-1"], ["SWAP", 13, 6], ["ADD", 4, 5, "-1"], ["ADD", 3, 5, "-1"], ["ADD", 2, 5, "-1/2"], ["ADD", 0, 5, "1"], ["SCALE", 5, "-1"], ["SWAP", 19, 5], ["ADD", 19, 4, "-1"], ["ADD", 3, 4, "-1"], ["ADD", 2, 4, "-1/2"], ["SCALE", 4, "-1"], ["SWAP", 7, 4], ["ADD", 19, 3, "-1"], ["ADD", 7, 3, "-1"], ["ADD", 2, 3, "-1/2"], ["ADD", 0, 3, "1"], ["SCALE", 3, "-1"], ["SWAP", 4, 3], ["ADD", 16, 2, "2"], ["ADD", 13, 2, "2"], ["ADD", 0, 2, "-2"], ["SCALE", 2, "2"], ["SWAP", 10, 2], ["ADD", 16, 1, "2"], ["ADD", 13, 1, "2"], ["ADD", 10, 1, "2"], ["SCALE", 1, "-1"], ["ADD", 19, 0, "1"], ["ADD", 16, 0, "1"], ["ADD", 13, 0, "1"], ["ADD", 10, 0, "1"], ["ADD", 7, 0, "1"], ["ADD", 4, 0, "1"], ["SWAP", 1, 0], ["ADD", 16, 19, "2"], ["ADD", 13, 19, "2"], ["ADD", 10, 19, "2"], ["ADD", 0, 19, "-1"], ["SCALE", 19, "-1"], ["SWAP", 19, 18], ["SWAP", 18, 17], ["ADD", 0, 16, "2/3"], ["SWAP", 17, 16], ["SWAP", 16, 15], ["SWAP", 15, 14], ["ADD", 0, 13, "-2/3"], ["SWAP", 14, 13], ["SWAP", 13, 12], ["SWAP", 12, 11], ["ADD", 0, 10, "2/3"], ["SWAP", 11, 10], ["SWAP", 10, 9], ["SWAP", 9, 8], ["ADD", 0, 7, "-2/3"], ["SWAP", 8, 7], ["SWAP", 7, 6], ["SWAP", 6, 5], ["ADD", 0, 4, "2/3"], ["SWAP", 5, 4], ["SWAP", 4, 3], ["SWAP", 3, 2], ["ADD", 0, 1, "-2/3"], ["SWAP", 2, 1], ["SCALE", 0, "3"], ["SWAP", 1, 0], ["ADD", 0, 1, "-1"], ["LAMBDA", 1, 1], ["QUERY", 0, 1, 1], ["LAMBDA", 1, -1], ["SWAP", 19, 18], ["ADD", 14, 17, "-1"], ["ADD", 11, 17, "-1"], ["ADD", 1, 17, "-1/2"], ["ADD", 0, 17, "1/2"], ["SCALE", 17, "1/2"], ["SWAP", 19, 17], ["SWAP", 16, 15], ["ADD", 19, 14, "1/2"], ["ADD", 11, 14, "-1"], ["ADD", 1, 14, "3/2"], ["ADD", 0, 14, "1/2"], ["SCALE", 14, "-1"], ["SWAP", 16, 14], ["SWAP", 13, 12], ["ADD", 19, 11, "1/2"], ["ADD", 16, 11, "-1"], ["ADD", 1, 11, "-1/2"], ["ADD", 0, 11, "1/2"], ["SCALE", 11, "-1"], ["SWAP", 13, 11], ["SWAP", 10, 9], ["ADD", 1, 8, "2"], ["SWAP", 10, 8], ["SWAP", 10, 7], ["SWAP", 10, 6], ["ADD", 1, 5, "-2"], ["SWAP", 10, 5], ["SWAP", 10, 4], ["SWAP", 10, 3], ["ADD", 1, 2, "2"], ["SWAP", 10, 2], ["ADD", 19, 1, "-1/3"], ["ADD", 16, 1, "2/3"], ["ADD", 13, 1, "2/3"], ["ADD", 0, 1, "-1/3"], ["SCALE", 1, "2/3"], ["SWAP", 10, 1], ["ADD", 19, 0, "-1"], ["ADD", 16, 0, "2"], ["ADD", 13, 0, "2"], ["ADD", 10, 0, "2"], ["SCALE", 0, "-1"], ["ADD", 13, 16, "-1"], ["ADD", 10, 16, "-1/2"], ["ADD", 0, 16, "1/2"], ["SCALE", 16, "-1/2"], ["SWAP", 16, 15], ["SWAP", 15, 14], ["SWAP", 14, 13], ["ADD", 13, 12, "1"], ["ADD", 11, 12, "1"], ["ADD", 10, 11, "1"], ["SCALE", 11, "-1"], ["SWAP", 12, 11], ["ADD", 12, 10, "1"], ["ADD", 0, 10, "1"], ["SCALE", 10, "-1"], ["SWAP", 11, 10], ["SWAP", 18, 9], ["SWAP", 17, 8], ["SWAP", 16, 7], ["SWAP", 15, 6], ["SWAP", 14, 5], ["SWAP", 13, 4], ["SWAP", 12, 3], ["SWAP", 11, 2], ["SWAP", 10, 1], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "-1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["LAMBDA", 0, -1], ["HOST", 0, 1, 5, "1", "-1"], ["LAMBDA", 0, 1], ["ADD", 1, 0, "1"], ["SCALE", 1, "-1"], ["IDLE_ONE", 2, [5]], ["IDLE_ONE", 3, [5]], ["IDLE_ONE", 4, [5]], ["IDLE_ONE", 5, [5]], ["IDLE_ONE", 6, [5]], ["IDLE_ONE", 7, [5]], ["IDLE_ONE", 8, [5]], ["IDLE_ONE", 9, [5]], ["SWAP", 16, 15], ["SWAP", 16, 14], ["SWAP", 11, 10], ["SWAP", 18, 9], ["SWAP", 17, 8], ["SWAP", 15, 7], ["SWAP", 14, 6], ["ADD", 4, 5, "-1/2"], ["ADD", 3, 5, "-1/2"], ["ADD", 2, 5, "1/2"], ["SCALE", 5, "-1"], ["SWAP", 16, 5], ["ADD", 16, 4, "-2"], ["ADD", 3, 4, "-1"], ["ADD", 2, 4, "1"], ["SCALE", 4, "-2"], ["SWAP", 13, 4], ["ADD", 16, 3, "-2"], ["ADD", 13, 3, "-2"], ["ADD", 2, 3, "1"], ["ADD", 0, 3, "1"], ["SCALE", 3, "-1"], ["SWAP", 12, 3], ["ADD", 16, 2, "2"], ["ADD", 13, 2, "2"], ["ADD", 12, 2, "1"], ["ADD", 1, 2, "1"], ["ADD", 0, 2, "-2"], ["SWAP", 10, 2], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["SWAP", 11, 1], ["ADD", 16, 0, "2"], ["ADD", 13, 0, "2"], ["ADD", 12, 0, "1"], ["ADD", 10, 0, "1"], ["SCALE", 0, "-1"], ["ADD", 14, 16, "1/2"], ["ADD", 13, 16, "-1"], ["ADD", 11, 16, "1/2"], ["ADD", 10, 16, "-1/2"], ["ADD", 0, 16, "1/2"], ["SCALE", 16, "-1/2"], ["ADD", 16, 15, "1"], ["ADD", 14, 15, "-1"], ["ADD", 13, 15, "1"], ["ADD", 12, 15, "-1"], ["ADD", 11, 15, "-1"], ["ADD", 10, 15, "1"], ["ADD", 16, 14, "1"], ["ADD", 13, 14, "1"], ["SCALE", 14, "-1"], ["SWAP", 15, 14], ["ADD", 15, 13, "1"], ["ADD", 14, 13, "1"], ["ADD", 12, 13, "-1"], ["ADD", 0, 13, "1"], ["SCALE", 13, "-1"], ["ADD", 14, 12, "1"], ["ADD", 10, 12, "1"], ["SCALE", 12, "-1"], ["SWAP", 13, 11], ["ADD", 12, 10, "1"], ["SCALE", 10, "-1"], ["SWAP", 18, 9], ["SWAP", 17, 8], ["SWAP", 16, 7], ["SWAP", 15, 6], ["SWAP", 14, 5], ["SWAP", 13, 4], ["SWAP", 12, 3], ["SWAP", 11, 2], ["SWAP", 10, 1], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "-1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["LAMBDA", 0, -1], ["HOST", 0, 1, 6, "1", "-1"], ["LAMBDA", 0, 1], ["ADD", 1, 0, "1"], ["SCALE", 1, "-1"], ["IDLE_ONE", 2, [6]], ["IDLE_ONE", 3, [6]], ["IDLE_ONE", 4, [6]], ["IDLE_ONE", 5, [6]], ["IDLE_ONE", 6, [6]], ["IDLE_ONE", 7, [6]], ["IDLE_ONE", 8, [6]], ["IDLE_ONE", 9, [6]], ["SWAP", 16, 15], ["SWAP", 15, 14], ["SWAP", 15, 13], ["SWAP", 13, 12], ["SWAP", 13, 11], ["SWAP", 18, 9], ["SWAP", 17, 8], ["ADD", 0, 7, "-1"], ["SWAP", 14, 7], ["ADD", 4, 6, "1/2"], ["ADD", 3, 6, "-1/2"], ["ADD", 2, 6, "1/2"], ["SCALE", 6, "-1"], ["SWAP", 16, 6], ["ADD", 1, 5, "1"], ["SWAP", 12, 5], ["ADD", 16, 4, "-2"], ["ADD", 3, 4, "1"], ["ADD", 2, 4, "1"], ["SCALE", 4, "-2"], ["SWAP", 15, 4], ["ADD", 16, 3, "2"], ["ADD", 15, 3, "2"], ["ADD", 2, 3, "-1"], ["SWAP", 11, 3], ["ADD", 16, 2, "2"], ["ADD", 15, 2, "1"], ["ADD", 0, 2, "-1"], ["SWAP", 13, 2], ["ADD", 15, 1, "1"], ["ADD", 13, 1, "-1"], ["ADD", 11, 1, "1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["SWAP", 10, 1], ["ADD", 16, 0, "2"], ["ADD", 13, 0, "2"], ["ADD", 11, 0, "-1"], ["ADD", 10, 0, "1"], ["SCALE", 0, "-1"], ["ADD", 13, 16, "-1/2"], ["ADD", 0, 16, "1/2"], ["SCALE", 16, "1/2"], ["ADD", 13, 15, "1"], ["SCALE", 15, "-1"], ["ADD", 16, 14, "1"], ["SCALE", 14, "-1"], ["ADD", 15, 13, "1"], ["ADD", 0, 13, "1"], ["SCALE", 13, "-1"], ["SWAP", 14, 13], ["SWAP", 18, 12], ["SWAP", 17, 11], ["SWAP", 16, 10], ["SWAP", 15, 9], ["SWAP", 14, 8], ["SWAP", 13, 7], ["SWAP", 12, 6], ["SWAP", 11, 5], ["SWAP", 10, 4], ["SWAP", 9, 3], ["SWAP", 8, 2], ["SWAP", 7, 1], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "-1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["LAMBDA", 0, -1], ["HOST", 0, 1, 7, "1", "-1"], ["LAMBDA", 0, 1], ["ADD", 1, 0, "1"], ["SCALE", 1, "-1"], ["IDLE_ONE", 2, [7]], ["IDLE_ONE", 3, [7]], ["IDLE_ONE", 4, [7]], ["IDLE_ONE", 5, [7]], ["IDLE_ONE", 6, [7]], ["SWAP", 15, 14], ["SWAP", 15, 13], ["SWAP", 18, 12], ["SWAP", 17, 11], ["SWAP", 16, 10], ["SWAP", 14, 9], ["SWAP", 13, 8], ["SWAP", 15, 7], ["SWAP", 18, 6], ["SWAP", 17, 5], ["ADD", 3, 4, "1"], ["ADD", 2, 4, "-1"], ["SCALE", 4, "2"], ["SWAP", 16, 4], ["ADD", 16, 3, "-2"], ["ADD", 2, 3, "1"], ["ADD", 1, 3, "1"], ["SWAP", 14, 3], ["ADD", 16, 2, "2"], ["ADD", 14, 2, "-1"], ["ADD", 0, 2, "-1"], ["SWAP", 13, 2], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["SWAP", 15, 1], ["ADD", 16, 0, "2"], ["ADD", 15, 0, "1"], ["ADD", 14, 0, "-1"], ["ADD", 13, 0, "1"], ["SCALE", 0, "-1"], ["ADD", 17, 18, "1"], ["ADD", 16, 18, "-1"], ["ADD", 0, 18, "1"], ["ADD", 16, 17, "1"], ["SCALE", 17, "-1"], ["SWAP", 18, 17], ["ADD", 18, 16, "1"], ["ADD", 0, 16, "1"], ["SCALE", 16, "-1"], ["SWAP", 17, 16], ["SWAP", 18, 15], ["SWAP", 17, 14], ["SWAP", 16, 13], ["SWAP", 15, 12], ["SWAP", 14, 11], ["SWAP", 13, 10], ["SWAP", 12, 9], ["SWAP", 11, 8], ["SWAP", 10, 7], ["SWAP", 9, 6], ["SWAP", 8, 5], ["SWAP", 7, 4], ["SWAP", 6, 3], ["SWAP", 5, 2], ["SWAP", 4, 1], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "-1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["LAMBDA", 0, -1], ["HOST", 0, 1, 8, "1", "-1"], ["LAMBDA", 0, 1], ["ADD", 1, 0, "1"], ["SCALE", 1, "-1"], ["IDLE_ONE", 2, [8]], ["IDLE_ONE", 3, [8]], ["SWAP", 17, 16], ["SWAP", 18, 15], ["SWAP", 16, 14], ["SWAP", 17, 13], ["SWAP", 18, 12], ["SWAP", 16, 11], ["SWAP", 17, 10], ["SWAP", 18, 9], ["SWAP", 16, 8], ["SWAP", 17, 7], ["SWAP", 18, 6], ["SWAP", 16, 5], ["SWAP", 17, 4], ["ADD", 2, 3, "1"], ["ADD", 0, 3, "1"], ["SCALE", 3, "-1"], ["SWAP", 18, 3], ["ADD", 18, 2, "1"], ["ADD", 1, 2, "1"], ["ADD", 0, 2, "-2"], ["SWAP", 16, 2], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["SWAP", 17, 1], ["ADD", 18, 0, "1"], ["ADD", 16, 0, "1"], ["SCALE", 0, "-1"], ["ADD", 0, 18, "1"], ["ADD", 16, 17, "1"], ["ADD", 0, 17, "-1"], ["SCALE", 17, "-1"], ["ADD", 0, 16, "1"], ["SWAP", 17, 16], ["SWAP", 16, 15], ["SWAP", 15, 14], ["SWAP", 14, 13], ["SWAP", 13, 12], ["SWAP", 12, 11], ["SWAP", 11, 10], ["SWAP", 10, 9], ["SWAP", 9, 8], ["SWAP", 8, 7], ["SWAP", 7, 6], ["SWAP", 6, 5], ["SWAP", 5, 4], ["SWAP", 4, 3], ["SWAP", 3, 2], ["SWAP", 2, 1], ["SWAP", 1, 0], ["ADD", 0, 1, "-1"], ["LAMBDA", 1, 1], ["QUERY", 0, 1, 1], ["LAMBDA", 1, -1], ["ADD", 1, 18, "-1"], ["ADD", 0, 17, "1"], ["SWAP", 16, 15], ["SWAP", 16, 14], ["SWAP", 16, 13], ["SWAP", 16, 12], ["SWAP", 16, 11], ["SWAP", 16, 10], ["SWAP", 16, 9], ["SWAP", 16, 8], ["SWAP", 16, 7], ["SWAP", 16, 6], ["SWAP", 16, 5], ["SWAP", 16, 4], ["SWAP", 16, 3], ["SWAP", 16, 2], ["ADD", 17, 1, "-1"], ["ADD", 0, 1, "-1"], ["SWAP", 16, 1], ["ADD", 17, 0, "-1"], ["ADD", 16, 0, "1"], ["SCALE", 0, "-1"], ["LAMBDA", 0, -1], ["LAMBDA", 1, -1], ["LAMBDA", 2, -1], ["LAMBDA", 3, -1], ["LAMBDA", 4, -1], ["LAMBDA", 5, -1], ["LAMBDA", 6, -1], ["LAMBDA", 7, -1], ["LAMBDA", 8, -1], ["LAMBDA", 9, -1], ["LAMBDA", 10, -1], ["LAMBDA", 11, -1], ["LAMBDA", 12, -1], ["LAMBDA", 13, -1], ["LAMBDA", 14, -1], ["LAMBDA", 15, -1], ["LAMBDA", 16, -1], ["LAMBDA", 17, -1], ["LAMBDA", 18, -1], ["LAMBDA", 19, -1]], "central_relation": "Q^4=1; R=Lambda Q; R^2=1"}
diff --git a/research/connected-l18-root-caller/cost.py b/research/connected-l18-root-caller/cost.py
new file mode 100644
index 0000000000..58c4b13697
--- /dev/null
+++ b/research/connected-l18-root-caller/cost.py
@@ -0,0 +1,34 @@
+"""Actual emitted census and conditional native gates, never a kappa certificate."""
+from pathlib import Path
+from fractions import Fraction as F
+from decimal import Decimal as D,getcontext
+from collections import Counter
+import json,math
+if not __debug__:raise RuntimeError('Cost check requires assertions')
+HERE=Path(__file__).resolve().parent;getcontext().prec=60
+
+def value(h,k):return sum(D(c)*D(r)**(1-k)for r,c in h.items())
+def census(g):
+ C=json.loads((HERE/f'caller_L{g}.json').read_text());counts=Counter(e[0]for e in C['events']);n=C['roles'];T=Counter(1+8*m.bit_count()for m in C['masks']);P={8:counts['IDLE_ONE'],1:counts['QUERY']};sc=[F(e[-1])for e in C['events']if e[0]in['ADD','SCALE']]
+ assert counts['HOST']==g and counts['QUERY']==3 and counts['LAMBDA']==2*g+6+n
+ assert all(m>0 for m in C['masks'])
+ if g==18:assert counts==Counter({'ADD':1041,'SCALE':189,'SWAP':858,'LAMBDA':80,'QUERY':3,'HOST':18,'IDLE_ONE':181})
+ gates={}
+ for label,k in [('selected_complex',D('.003125804')),('pending_complex_6936',D('.00362701882')),('ordinary_BIT_6726',D('.00376669'))]:
+  gate=(value(T,k)-value(P,k))/g
+  baseline={8:P[8]+2*g,1:3+2*g}
+  gates[label]={'comparison_kappa':str(k),'max_native_signed_cost_per_port_per_call_before_ordinary_outer':str(gate),'allowance_above_two_H8':str(gate-2*D(8)**(1-k)),'direct_baseline_signed_moment':str(value(T,k)-value(baseline,k))}
+  assert value(T,k)-value(baseline,k)<0
+ source=json.loads((HERE/'inputs/base_invoice.json').read_text());fp={int(r):c for r,c in source['local_paid'].items()};ft={int(r):c for r,c in source['helpers'].items()}
+ if g==18:
+  for label,z in gates.items():
+   k=D(z['comparison_kappa']);fprice=(value(fp,k)-value(ft,k))/104+1
+   z['retained_F_plus_H1_cost_per_port']=str(fprice)
+   z['retained_F_plus_H1_excess']=str(fprice-D(z['max_native_signed_cost_per_port_per_call_before_ordinary_outer']))
+   assert fprice>D(z['max_native_signed_cost_per_port_per_call_before_ordinary_outer'])
+ return {'roles':n,'stages':g,'events':len(C['events']),'event_counts':dict(counts),'ordinary_events':sum(counts[x]for x in['ADD','SCALE','SWAP','LAMBDA']),'target_histogram':dict(sorted(T.items())),'target_rank_mass':sum(r*c for r,c in T.items()),'paid_outside_native':P,'paid_outside_native_mass':sum(r*c for r,c in P.items()),'ordinary_scalar_denominator_lcm':str(math.lcm(*(x.denominator for x in sc))),'max_abs_ordinary_scalar':str(max(map(abs,sc))),'native_gates':gates}
+if __name__=='__main__':
+ out={str(g):census(g)for g in[3,9,18]};out=json.loads(json.dumps(out))
+ p=HERE/'COST.json'
+ if p.exists():assert out==json.loads(p.read_text())
+ print(json.dumps(out,indent=2));print('PASS_EMITTED_CENSUS')
diff --git a/research/connected-l18-root-caller/generate.py b/research/connected-l18-root-caller/generate.py
new file mode 100644
index 0000000000..cfb35ad6f9
--- /dev/null
+++ b/research/connected-l18-root-caller/generate.py
@@ -0,0 +1,119 @@
+import json,sys
+from pathlib import Path
+from fractions import Fraction as Q
+sys.path.insert(0,str(Path(__file__).resolve().parent))
+import matrix as v
+if not __debug__:raise RuntimeError('Exact generator requires assertions')
+def construct(g):
+ assert g in (3,9,18)
+ n=2*g+2;N=2*g+3;X=[];Y=[]
+ for i in range(g):
+  x=[Q(0)]*n;y=x[:];x[0]=1;x[1+i]=1;y[0]=1;y[1+i]=-1
+  for j in range(i):x[1+j]=2
+  X.append(x);Y.append(y)
+ for a,ss,p,q in [(0,1,0,1),(-1,0,1,0),(-1,-1,1,-1)]:
+  u=2-ss if g%2 else ss;x=[Q(0)]*n;y=x[:];x[0]=a;y[0]=u;x[-1]=q;y[-1]=p
+  for i in range(g):x[1+i]=a+1;y[1+i]=(1-u)*(-1)**i
+  for m in range(g):x[g+1+m]=1-a;y[g+1+m]=(u-1)*(-1)**(g-1-m)
+  X.append(x);Y.append(y)
+ for m in range(g):
+  x=[Q(0)]*n;y=x[:];x[0]=-1;x[g+1+m]=1;y[0]=1;y[g+1+m]=1
+  for j in range(m+1,g):x[g+1+j]=2
+  X.append(x);Y.append(y)
+ B=v.eye(n)
+ for start in list(range(1,g+1,3))+list(range(g+1,2*g+1,3)):
+  block=[[1,1,0],[1,1,1],[1,0,1]]
+  for i in range(3):
+   for j in range(3):B[start+i][start+j]=Q(block[i][j])
+ Bi=v.inverse(B);X=[list(r) for r in zip(*v.mul(Bi,list(zip(*X))))];Y=v.mul(Y,B);stages=[]
+ for u in range(1,g-1,2):
+  e=u+1;end=3*((e+3)//3);stages.append(dict(units=[u,e],mask=[0]+list(range(1,1+end))))
+ stages.append(dict(units=[g,g+1],mask=[0,n-1]+list(range(1,g+1,3))+list(range(g+1,2*g+1,3))))
+ for m in range(0,g-1,2):
+  start=3*(m//3);stages.append(dict(units=[g+3+m,g+4+m],mask=[0]+list(range(g+1+start,2*g+1))))
+ pref=v.prefixes(X,Y,Q(-2));assert pref[-1]==v.scale(v.eye(n),Q(-1))
+ assert all(v.dot(Y[i],X[j])==((i>j)-(i<j)) for i in range(N) for j in range(N))
+ for st in stages:
+  mask=set(st['mask']);assert all(not X[u][c] and not Y[u][c] for u in st['units'] for c in range(n) if c not in mask)
+  for k in [min(st['units']),max(st['units'])+1]:assert all(not pref[k][i][j] for i in range(n) for j in range(n) if (i in mask)!=(j in mask))
+ return dict(n=n,N=N,X=[[str(x) for x in r] for r in X],Y=[[str(x) for x in r] for r in Y],stages=stages)
+
+def basis(candidates,n):
+ cols=[]
+ for c in candidates:
+  if v.rank(list(map(list,zip(*(cols+[c])))))>len(cols):cols.append(c)
+  if len(cols)==n:return list(map(list,zip(*cols)))
+ raise ValueError('not a basis')
+def synth(M):
+ A=[r[:] for r in M];n=len(M);ops=[]
+ for c in range(n):
+  p=next(i for i in range(c,n) if A[i][c])
+  if p!=c:A[p],A[c]=A[c],A[p];ops.append(['SWAP',p,c])
+  q=A[c][c]
+  if q!=1:A[c]=[x/q for x in A[c]];ops.append(['SCALE',c,str(1/q)])
+  for i in range(n):
+   if i!=c and A[i][c]:
+    q=-A[i][c];A[i]=[x+q*y for x,y in zip(A[i],A[c])];ops.append(['ADD',i,c,str(q)])
+ out=[]
+ for op in reversed(ops):
+  op=op[:]
+  if op[0]=='SCALE':op[2]=str(1/Q(op[2]))
+  if op[0]=='ADD':op[3]=str(-Q(op[3]))
+  out.append(op)
+ return out
+
+def compile_root(R):
+ n=R['n'];X=[[Q(x)for x in r]for r in R['X']];Y=[[Q(x)for x in r]for r in R['Y']];ST=R['stages'];events=[];skip=set();at={s['units'][0]:k for k,s in enumerate(ST)}
+ for u in range(R['N']):
+  if u in skip:continue
+  if u in at:
+   k=at[u];w=u+1;skip.add(w);mask=ST[k]['mask'];H=v.add(v.outer(X[u],Y[w]),v.outer(X[w],Y[u]),Q(-1));E=v.zero(n)
+   for c in mask:E[c][c]=Q(1)
+   residual=v.add(E,H,Q(-1));outside=[v.eye(n)[c]for c in range(n)if c not in mask]
+   B=basis([X[u],X[w]]+list(map(list,zip(*residual)))+outside,n);Bi=v.inverse(B)
+   assert v.mul(v.mul(Bi,E),B)==[[Q(i==j and i<len(mask))for j in range(n)]for i in range(n)]
+   assert v.mul([Y[u],Y[w]],B)==[[Q(-1 if j==1 else 0)for j in range(n)],[Q(1 if j==0 else 0)for j in range(n)]]
+   events+=synth(Bi)+[['ADD',0,1,'1'],['SCALE',1,'-1'],['LAMBDA',0,-1],['HOST',0,1,k,'1','-1'],['LAMBDA',0,1],['ADD',1,0,'1'],['SCALE',1,'-1']]
+   events += [['IDLE_ONE',j,[k]]for j in range(2,len(mask))]
+   events+=synth(B)
+  else:
+   a,b=X[u],Y[u];j=next(i for i,z in enumerate(b)if z);q=[Q(0)]*n;q[j]=1/b[j];K=v.add(v.eye(n),v.outer(q,b),Q(-1));B=basis([a,q]+list(map(list,zip(*K))),n)
+   events+=synth(v.inverse(B))+[['ADD',0,1,'-1'],['LAMBDA',1,1],['QUERY',0,1,1],['LAMBDA',1,-1]]+synth(B)
+ events += [['LAMBDA',r,-1]for r in range(n)]
+ return dict(roles=n,stages=len(ST),masks=[sum(1<<k for k,s in enumerate(ST)if c in s['mask'])for c in range(n)],events=events,central_relation='Q^4=1; R=Lambda Q; R^2=1')
+
+if __name__=='__main__':
+ import argparse,hashlib
+ parser=argparse.ArgumentParser();parser.add_argument('--write',action='store_true');args=parser.parse_args();here=Path(__file__).resolve().parent
+ for pin in json.loads((here/'INPUT-PINS.json').read_text())['inputs']:
+  assert hashlib.sha256((here/pin['local_path']).read_bytes()).hexdigest()==pin['sha256']
+ from collections import Counter
+ for name in ['tHHtHt','tHtHHt']:
+  data=json.loads((here/f'inputs/root_L3_{name}.json').read_text())
+  a,b,plus,parts,es=v.reconstruct(data,Q(1));_,_,minus,_,ems=v.reconstruct(data,Q(-1))
+  assert minus[-1]==v.scale(plus[-1],Q(-1)) and es==ems
+  dims={}
+  for mask in range(8):
+   J=v.eye(8)
+   for k,E in enumerate(es):J=v.mul(J,E if mask>>k&1 else v.add(v.eye(8),E,Q(-1)))
+   if v.rank(J):dims[mask]=v.rank(J)
+  assert dims=={1:2,2:1,3:1,4:2,6:1,7:1}
+ for g in [3,9,18]:
+  root=construct(g);caller=compile_root(root)
+  assert v.rank([[Q(x)for x in r]for r in root['X']])==root['n']
+  assert v.rank([[Q(x)for x in r]for r in root['Y']])==root['n']
+  for name,data in [(f'root_L{g}.json',root),(f'caller_L{g}.json',caller)]:
+   if args.write:(here/name).write_text(json.dumps(data)+'\n')
+   else:assert data==json.loads((here/name).read_text()),name
+  if g==9:
+   B=v.eye(20);block=[[1,1,0],[1,1,1],[1,0,1]]
+   for start in list(range(1,10,3))+list(range(10,19,3)):
+    for i in range(3):
+     for j in range(3):B[start+i][start+j]=Q(block[i][j])
+   XX=[[Q(x)for x in r]for r in root['X']]
+   rawX=list(map(list,zip(*v.mul(B,list(zip(*XX))))))
+   rawY=v.mul([[Q(x)for x in r]for r in root['Y']],v.inverse(B))
+   retained=json.loads((here/'inputs/root_A.json').read_text())
+   assert rawX==[[Q(x)for x in retained['X'][2*i][:20]]for i in range(21)]
+   assert rawY==[[Q(x)for x in retained['Y'][2*i][:20]]for i in range(21)]
+  print('PASS_ROOT_CALLER',g,len(caller['events']))
diff --git a/research/connected-l18-root-caller/idle_coalescing.py b/research/connected-l18-root-caller/idle_coalescing.py
new file mode 100644
index 0000000000..66091e8538
--- /dev/null
+++ b/research/connected-l18-root-caller/idle_coalescing.py
@@ -0,0 +1,192 @@
+#!/usr/bin/env python3
+"""Exact eligibility-compression certificate for the optimistic L18 idle bill.
+Standard library; rational transcendental bounds; checks stay active under -O.
+"""
+from fractions import Fraction as Q
+from functools import lru_cache
+from itertools import combinations
+from pathlib import Path
+from hashlib import sha256
+from decimal import Decimal, localcontext, ROUND_FLOOR, ROUND_CEILING
+from collections import Counter
+import json
+import argparse
+
+HERE=Path(__file__).resolve().parent
+PIN_DIGESTS={
+ 'root_L18.json':'be4a2beed3a40de6d2c5dcc6e4f25f3c2a4375551b70e63fb0e9a03041db6a34',
+ 'caller_L18.json':'f4090329f219edd493b4ca592128521e867a355fb528556b15201e759783568b',
+ 'inputs/base_invoice.json':'87a41b13bdd9248d538805f76a970f51335567845dfc0070698b6979a08b70d6',
+}
+K=Q('0.00362701882')
+REQUIRED=Q('10.081828') # Checked below against the source-bound rational full bill.
+
+
+def need(ok,label):
+    if not ok:raise ValueError(label)
+
+
+def log_series(z,terms=40):
+    """2atanh(z), z in[0,1/3], exact positive-series lower/tail upper."""
+    need(0<=z<=Q(1,3),'log range reduction')
+    lo=sum((2*z**(2*j+1)/Q(2*j+1) for j in range(terms)),Q(0))
+    tail=2*z**(2*terms+1)/(Q(2*terms+1)*(1-z*z))
+    return lo,lo+tail
+
+
+@lru_cache(None)
+def log_bounds(n):
+    e=n.bit_length()-1;p=2**e
+    a,b=log_series(Q(1,3));c,d=log_series(Q(n-p,n+p))
+    return e*a+c,e*b+d
+
+
+def exp_neg_bounds(x):
+    """Alternating Taylor series bounds for exp(-x), 0<=x<1."""
+    need(0<=x<1,'exponential alternating-series range')
+    term=Q(1);s=term
+    for j in range(1,31):term*=(-x)/j;s+=term
+    hi=s # even partial sum is an upper bound
+    term*=(-x)/31
+    return s+term,hi
+
+
+@lru_cache(None)
+def power_bounds(n):
+    if not n:return Q(0),Q(0)
+    need(isinstance(n,int) and n>0,'positive integral child rank')
+    ll,lu=log_bounds(n)
+    low=exp_neg_bounds(K*lu)[0];high=exp_neg_bounds(K*ll)[1]
+    return n*low,n*high
+
+
+def cost_bounds(degree):
+    return power_bounds(8*degree)
+
+
+def histogram_bounds(histogram):
+    need(all(int(r)>0 and isinstance(c,int) and c>=0 for r,c in histogram.items()),'nonnegative invoice counts')
+    return (sum((c*power_bounds(int(r))[0] for r,c in histogram.items()),Q(0)),
+            sum((c*power_bounds(int(r))[1] for r,c in histogram.items()),Q(0)))
+
+
+def required_savings_bounds(caller,invoice):
+    counts=Counter(e[0] for e in caller['events'])
+    need(counts['HOST']==18 and counts['IDLE_ONE']==181 and counts['QUERY']==3,'source-bound recursive census')
+    target=Counter(1+8*m.bit_count() for m in caller['masks'])
+    tl,tu=histogram_bounds(target)
+    pl,pu=histogram_bounds(invoice['local_paid'])
+    hl,hu=histogram_bounds(invoice['helpers'])
+    fl,fu=(pl-hu)/104+1,(pu-hl)/104+1
+    el,eu=power_bounds(8)
+    return 18*fl-tu+181*el+3,18*fu-tl+181*eu+3
+
+
+def savings_bounds(degrees):
+    l1,u1=cost_bounds(1);D=sum(degrees)
+    return D*l1-sum(cost_bounds(d)[1] for d in degrees),D*u1-sum(cost_bounds(d)[0] for d in degrees)
+
+
+def decimal(q,rounding=ROUND_FLOOR):
+    with localcontext() as c:
+        c.prec=45;c.rounding=rounding
+        return str(Decimal(q.numerator)/Decimal(q.denominator))
+
+
+def allowed_host_pairs(mask,eligibility):
+    # Compression-stable idle sets imply that a host set is downward closed
+    # under STRICT eligibility inclusion. Equal-eligibility roles need no tie.
+    return [list(h) for h in combinations(mask,2)
+            if all(not (eligibility[j]<eligibility[i] and i in h and j not in h)
+                   for i in mask for j in mask)]
+
+
+def degrees_from_hosts(masks,hosts):
+    need(len(hosts)==len(masks),'stage count')
+    for m,h in zip(masks,hosts):need(len(h)==2 and len(set(h))==2 and set(h)<=set(m),'two eligible host roles')
+    idle=[[role for role in m if role not in h] for m,h in zip(masks,hosts)]
+    return validate_idle_assignment(masks,idle)
+
+
+def validate_idle_assignment(masks,idle):
+    need(len(idle)==len(masks),'idle-stage count')
+    for m,fields in zip(masks,idle):
+        need(len(fields)==len(set(fields)),'independent idle incidences are distinct')
+        need(set(fields)<=set(m),'every idle role is eligible at that stage')
+        need(len(fields)==len(m)-2,'exact stage idle count must be retained')
+    degrees=[sum(role in fields for fields in idle) for role in range(38)]
+    need(sum(degrees)==181,'all181 idle actions are retained')
+    return degrees
+
+
+def validate_compressed_hosts(hosts,allowed):
+    need(len(hosts)==len(allowed),'compressed stage count')
+    for pair,possibilities in zip(hosts,allowed):
+        need(set(pair) in [set(p) for p in possibilities],'hostset must be downward-closed under eligibility inclusion')
+
+
+def main():
+    parser=argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--package-root',type=Path,default=HERE)
+    parser.add_argument('--receipt',type=Path,help='Optional retained JSON receipt to compare; never written')
+    args=parser.parse_args();base=args.package_root.resolve()
+    for name,digest in PIN_DIGESTS.items():
+        need(sha256((base/name).read_bytes()).hexdigest()==digest,'source hash '+name)
+    root=json.loads((base/'root_L18.json').read_text())
+    caller=json.loads((base/'caller_L18.json').read_text())
+    invoice=json.loads((base/'inputs/base_invoice.json').read_text())
+    required_lo,required_hi=required_savings_bounds(caller,invoice)
+    need(required_lo>REQUIRED,'source-bound invoice certifies conservative required saving')
+    masks=[s['mask'] for s in root['stages']]
+    need(root['n']==38 and len(masks)==18,'L18 source dimensions')
+    need(all(len(set(m))==len(m) for m in masks),'mask roles are independent and distinct')
+    eligibility=[{s for s,m in enumerate(masks) if r in m} for r in range(38)]
+    need([sum(1<<s for s in e) for e in eligibility]==caller['masks'],'caller/root mask binding')
+    caps=list(map(len,eligibility));need(sum(caps)==217 and sum(len(m)-2 for m in masks)==181,'exact idle mass')
+    allowed=[allowed_host_pairs(m,eligibility) for m in masks]
+    need([len(x) for x in allowed]==[1]*8+[2]+[1]*9,'compression forces17 stages and2 bridge cases')
+    need({tuple(sorted(x)) for x in allowed[8]}=={(16,37),(19,37)},'two bridge host pairs')
+    host0=[x[0] for x in allowed];host1=[x[0] for x in allowed]
+    host0[8]=[16,37];host1[8]=[19,37]
+    validate_compressed_hosts(host0,allowed);validate_compressed_hosts(host1,allowed)
+    d0=degrees_from_hosts(masks,host0);d1=degrees_from_hosts(masks,host1)
+    need(all(d0[r]==d1[r] for r in range(38) if r not in(16,19)),'only two bridge degrees differ')
+    need((d0[16],d0[19],d1[16],d1[19])==(1,3,2,2),'concavity comparison is(1,3)vs(2,2)')
+    # Since0<1-K<1, concavity gives f(1)+f(3)<=2f(2), selecting d0.
+    need(0<K<1,'strict concavity parameter')
+    lo,hi=savings_bounds(d0)
+    need(hi<REQUIRED,'even optimum coalescing is below required full-bill saving')
+    need(hi-lo<Q(1,10**30),'rational interval precision')
+    # Controls: illegal host role, omitted idle action, and an optimistic
+    # degree-only allocation that cannot satisfy the stage incidence rules.
+    bad=[h[:] for h in host0];bad[0]=[2,37]
+    try:degrees_from_hosts(masks,bad)
+    except ValueError:pass
+    else:raise ValueError('ineligible host mutation accepted')
+    bad_idle=[[role for role in m if role not in h] for m,h in zip(masks,host0)]
+    bad_idle[0].pop() # Delete one real idle incidence from the certified optimum.
+    try:validate_idle_assignment(masks,bad_idle)
+    except ValueError:pass
+    else:raise ValueError('omitted idle incidence mutation accepted')
+    bad_closed=[h[:] for h in host0];bad_closed[0]=[0,1]
+    degrees_from_hosts(masks,bad_closed) # Valid ordinary assignment; compression alone excludes it.
+    try:validate_compressed_hosts(bad_closed,allowed)
+    except ValueError:pass
+    else:raise ValueError('non-downward-closed hostset mutation accepted')
+    left=181;relaxed=[]
+    for cap in sorted(caps,reverse=True):v=min(cap,left);relaxed.append(v);left-=v
+    rlo,rhi=savings_bounds(relaxed)
+    need(rlo>REQUIRED,'degree-only relaxation must remain visibly insufficient')
+    report={'status':'OPTIMISTIC_COALESCING_ONLY_ROUTE_CLOSED','kappa_probe':str(K),'independent_roles':38,'stages':18,'idle_actions':181,
+            'host_roles_by_stage':host0,'optimal_degrees':d0,'optimal_degree_histogram':dict(sorted(Counter(d0).items())),
+            'optimal_savings_interval':[decimal(lo),decimal(hi,ROUND_CEILING)],
+            'required_saving_interval':[decimal(required_lo),decimal(required_hi,ROUND_CEILING)],
+            'required_saving_lower':decimal(REQUIRED),'shortfall_lower':decimal(required_lo-hi),
+            'degree_only_upper_interval':[decimal(rlo),decimal(rhi,ROUND_CEILING)],'candidate_native_per_stage':'17.69144246035','uncoalesced_gate_per_stage':'17.13134090285',
+            'proof':'eligibility union/intersection compression plus two exact bridge cases; rational ln/exp enclosures','scope':'fixed38 coordinate roles;181 idles;two coordinate hosts perstage;free all-occurrence same-role merging;no noncoordinate or general native obstruction;no supplier or kappa claim'}
+    if args.receipt:
+        need(json.loads(json.dumps(report))==json.loads(args.receipt.read_text()),'retained receipt matches recomputation')
+    print(json.dumps(report,sort_keys=True))
+    print('PASS_L18_IDLE_COALESCING_BOUND optimum_savings_lt_9.707290 required_gt_10.081828 independent_roles=38 controls=3_REJECT degree_only_relaxation=DISTINGUISHED')
+
+if __name__=='__main__':main()
diff --git a/research/connected-l18-root-caller/independent.py b/research/connected-l18-root-caller/independent.py
new file mode 100644
index 0000000000..de7a5afb80
--- /dev/null
+++ b/research/connected-l18-root-caller/independent.py
@@ -0,0 +1,106 @@
+#!/usr/bin/env python3
+"""Independent reverse formal Q4/Gaussian-rational review of the emitted connected L18 caller.
+OpenAI Codex-assisted review; no imports from the primary builder/replayer.
+"""
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+import argparse,copy,hashlib,json,time
+if not __debug__:raise RuntimeError('Independent replay requires assertions')
+ONE=(F(1),F(0));ZERO=(F(0),F(0))
+def cadd(a,b):return(a[0]+b[0],a[1]+b[1])
+def cmul(a,b):return(a[0]*b[0]-a[1]*b[1],a[0]*b[1]+a[1]*b[0])
+def add(a,b):
+ out=a.copy()
+ for mon,v in b.items():
+  z=cadd(out.get(mon,ZERO),v)
+  if z!=ZERO:out[mon]=z
+  elif mon in out:del out[mon]
+ return out
+def scale(a,c):return{m:z for m,v in a.items()if(z:=cmul(v,c))!=ZERO}
+def shift(a,qe=0,ds=(),modulus=4):
+ out={}
+ for mon,v in a.items():
+  m=list(mon);m[0]=(m[0]+qe)%modulus
+  for d in ds:m[d+1]+=1
+  m=tuple(m);z=cadd(out.get(m,ZERO),v)
+  if z!=ZERO:out[m]=z
+  elif m in out:del out[m]
+ return out
+
+def replay(w,modulus=4,wrong_host_index=None,stop_on_failure=False):
+ zero=(0,)*(w['stages']+1);bad=[];peak=0;checks=0
+ for output in range(w['roles']):
+  a=[{}for _ in range(w['roles'])];a[output]={zero:ONE}
+  for event_index,e in reversed(list(enumerate(w['events']))):
+   op=e[0]
+   if op=='ADD':a[e[2]]=add(a[e[2]],scale(a[e[1]],(F(e[3]),F(0))))
+   elif op=='SCALE':a[e[1]]=scale(a[e[1]],(F(e[2]),F(0)))
+   elif op=='SWAP':a[e[1]],a[e[2]]=a[e[2]],a[e[1]]
+   elif op=='QUERY':a[e[2]]=add(a[e[2]],shift(a[e[1]],qe=e[3],modulus=modulus))
+   elif op=='LAMBDA':
+    z=a[e[1]];s=e[2];assert s in(-1,1)
+    a[e[1]]=add(scale(z,(F(1,2),F(s,2))),shift(scale(z,(F(1,2),F(-s,2))),qe=2,modulus=modulus))
+   elif op=='IDLE_ONE':a[e[1]]=shift(a[e[1]],ds=e[2],modulus=modulus)
+   elif op=='HOST':
+    x,y,d=e[1:4];left,right=a[x],a[y]
+    a[x]=shift(add(left,scale(shift(right,qe=-1,modulus=modulus),(F(1 if event_index==wrong_host_index else -1),F(0)))),ds=(d,),modulus=modulus)
+    a[y]=shift(left,qe=1,ds=(d,),modulus=modulus)
+   else:raise ValueError(op)
+   peak=max(peak,sum(len(p)for p in a))
+  expected=(1,)+tuple(int(w['masks'][output]>>d&1)for d in range(w['stages']))
+  for j,z in enumerate(a):
+   checks+=1
+   if z!=({expected:ONE}if output==j else{}):
+    bad.append([output,j])
+    if stop_on_failure:return dict(bad=bad,coefficients=checks,peak_terms=peak)
+ return dict(bad=bad,coefficients=checks,peak_terms=peak)
+
+def factor(n):
+ out=[];d=2
+ while d*d<=n:
+  if n%d==0:
+   out.append(d)
+   while n%d==0:n//=d
+  d+=1
+ if n>1:out.append(n)
+ return out
+
+def main():
+ ap=argparse.ArgumentParser();ap.add_argument('--package',required=True);ap.add_argument('--out',required=True);ap.add_argument('--write',action='store_true');args=ap.parse_args();h=Path(args.package);started=time.monotonic()
+ p=h/'caller_L18.json';blob=p.read_bytes();w=json.loads(blob);root_blob=(h/'root_L18.json').read_bytes();root=json.loads(root_blob)
+ caller_sha=hashlib.sha256(blob).hexdigest();root_sha=hashlib.sha256(root_blob).hexdigest()
+ assert caller_sha=='f4090329f219edd493b4ca592128521e867a355fb528556b15201e759783568b'
+ assert root_sha=='be4a2beed3a40de6d2c5dcc6e4f25f3c2a4375551b70e63fb0e9a03041db6a34'
+ assert(w['roles'],w['stages'],root['n'],len(root['stages']))==(38,18,38,18)
+ masks=[sum(1<<j for j,s in enumerate(root['stages'])if r in s['mask'])for r in range(38)];assert w['masks']==masks
+ result=replay(w);assert not result['bad'],result;assert result['coefficients']==1444
+ print('PASS_ALL_1444_FORMAL_COEFFICIENTS',result['peak_terms'],flush=True)
+ controls={}
+ for op in('HOST','QUERY','IDLE_ONE','LAMBDA'):
+  bad=copy.deepcopy(w);at=next(i for i,e in enumerate(bad['events'])if e[0]==op);del bad['events'][at];r=replay(bad,stop_on_failure=True);assert r['bad'],op;controls['missing_'+op]=dict(event=at,witness=r['bad'][0]);print('REJECT',op,flush=True)
+ at=next(i for i,e in enumerate(w['events'])if e[0]=='HOST');r=replay(w,wrong_host_index=at,stop_on_failure=True);assert r['bad'];controls['wrong_HOST_lower_left_sign']=dict(event=at,witness=r['bad'][0])
+ for op in('QUERY','LAMBDA','IDLE_ONE'):
+  bad=copy.deepcopy(w);at=next(i for i,e in enumerate(bad['events'])if e[0]==op)
+  if op=='QUERY':bad['events'][at][3]*=-1
+  elif op=='LAMBDA':bad['events'][at][2]*=-1
+  else:bad['events'][at][2].append(bad['events'][at][2][0])
+  r=replay(bad,stop_on_failure=True);assert r['bad'],('wrong',op);controls['wrong_'+op]=dict(event=at,witness=r['bad'][0])
+ counts=Counter(e[0]for e in w['events']);assert counts==Counter({'ADD':1041,'SCALE':189,'SWAP':858,'LAMBDA':80,'HOST':18,'QUERY':3,'IDLE_ONE':181})
+ assert[e[3]for e in w['events']if e[0]=='HOST']==list(range(18));assert all(len(e[2])==1 for e in w['events']if e[0]=='IDLE_ONE')
+ targets=Counter(1+8*m.bit_count()for m in masks);paid=Counter({1:3,8:181});assert sum(r*c for r,c in targets.items())==1774
+ fractions=[F(e[-1])for e in w['events']if e[0]in('ADD','SCALE')];assert max(q.denominator for q in fractions)==2 and max(abs(q)for q in fractions)==F(5,2)
+ ordinary=sum(counts[op]for op in('ADD','SCALE','SWAP','LAMBDA'));assert ordinary==2168
+ report=dict(status='PASS_INDEPENDENT_CONNECTED_L18_CALLER',caller_sha256=caller_sha,root_sha256=root_sha,
+  formal_ring='Q(i)[Q,D0,...,D17]/(Q^4-1); unrestricted tuple D powers; direct reverse covectors, no evaluation of Q or D',
+  coefficients=result['coefficients'],peak_reverse_polynomial_terms=result['peak_terms'],event_counts=dict(counts),ordinary_events=ordinary,
+  target_histogram=dict(sorted(targets.items())),target_rank_mass=1774,paid_non_native=dict(paid),native_contract_calls=18,
+  native_contract='HOST(x,y,s): D_s*(x+Q*y,-Q^-1*x), t=-1; supplied macro only, no native implementation or tariff verified',
+  scalar_max_denominator=2,scalar_max_magnitude='5/2',controls=controls,
+  scope='Exact finite caller and root-mask binding, event and symbolic profile audit only. No HOST native construction, physical/routing or ordinary-tariff admission, finite supplier, kappa or general root theorem.',seconds=time.monotonic()-started)
+ report=json.loads(json.dumps(report));out=Path(args.out)
+ if args.write:out.write_text(json.dumps(report,indent=2)+'\n')
+ else:
+  frozen=json.loads(out.read_text());assert{k:v for k,v in frozen.items()if k!='seconds'}=={k:v for k,v in report.items()if k!='seconds'},'frozen review differs'
+ print(json.dumps(report,indent=2))
+if __name__=='__main__':main()
diff --git a/research/connected-l18-root-caller/inputs/NATIVE-NOTICE b/research/connected-l18-root-caller/inputs/NATIVE-NOTICE
new file mode 100644
index 0000000000..a3687d65a0
--- /dev/null
+++ b/research/connected-l18-root-caller/inputs/NATIVE-NOTICE
@@ -0,0 +1,9 @@
+New shared-wire composition, seventeenth wire, and two enabling splits: developed with substantial OpenAI assistance, 2026. Apache-2.0.
+
+Frozen predecessor native words and odd verifier: DreamingOfClouds, with Claude Opus 5.5 (Anthropic), from #6936 and #6937.
+
+Retained Clifford compiler and exact native interpreter retain their original headers and lineage from #6833: native source by DreamingOfClouds; independent-helper mechanism by Ali Romman; inventory, retiming and helper-retirement extensions by Jerry Chen / @CubeJerry with OpenAI assistance.
+
+Helper-split lemma: Ali Romman (#5599). Shared native applications: CubeJerry (#6916). Caller blocks: CubeJerry (#6912). Owned-rise argument: CubeJerry (#6914). Width-2 phase convention: unpaidmoon (#6930). Odd-grid precedent: icekylinx (#104).
+
+The higher-level caller and BIT integration require their own source attribution and pins.
diff --git a/research/connected-l18-root-caller/inputs/base_invoice.json b/research/connected-l18-root-caller/inputs/base_invoice.json
new file mode 100644
index 0000000000..f2a6958ee2
--- /dev/null
+++ b/research/connected-l18-root-caller/inputs/base_invoice.json
@@ -0,0 +1,61 @@
+{
+ "helpers": {
+  "1": 14,
+  "2": 8,
+  "3": 4,
+  "4": 109,
+  "5": 17,
+  "6": 3,
+  "7": 10,
+  "8": 40,
+  "9": 359
+ },
+ "kappa_literal": "0.00337180047549672",
+ "local_paid": {
+  "1": 2234,
+  "2": 454,
+  "3": 489,
+  "4": 110,
+  "5": 152,
+  "6": 7,
+  "7": 9,
+  "8": 1
+ },
+ "paid": {
+  "1": 40524,
+  "16": 208,
+  "2": 8172,
+  "24": 208,
+  "3": 8802,
+  "32": 208,
+  "4": 1980,
+  "40": 208,
+  "48": 208,
+  "5": 2736,
+  "56": 208,
+  "6": 126,
+  "64": 208,
+  "7": 162,
+  "8": 226
+ },
+ "targets": {
+  "1": 356,
+  "145": 104,
+  "17": 208,
+  "2": 144,
+  "25": 208,
+  "3": 72,
+  "33": 208,
+  "4": 1962,
+  "41": 208,
+  "49": 208,
+  "5": 306,
+  "57": 208,
+  "6": 54,
+  "65": 208,
+  "7": 180,
+  "73": 208,
+  "8": 720,
+  "9": 6670
+ }
+}
\ No newline at end of file
diff --git a/research/connected-l18-root-caller/inputs/final_native.json.gz b/research/connected-l18-root-caller/inputs/final_native.json.gz
new file mode 100644
index 0000000000..74563a7867
Binary files /dev/null and b/research/connected-l18-root-caller/inputs/final_native.json.gz differ
diff --git a/research/connected-l18-root-caller/inputs/root_A.json b/research/connected-l18-root-caller/inputs/root_A.json
new file mode 100644
index 0000000000..1f8c2e3152
--- /dev/null
+++ b/research/connected-l18-root-caller/inputs/root_A.json
@@ -0,0 +1 @@
+{"n": 40, "N": 42, "X": [["1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"], ["0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"], ["1", "2", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"], ["0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "2", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"], ["1", "2", "2", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", 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\ No newline at end of file
diff --git a/research/connected-l18-root-caller/inputs/root_L3_tHHtHt.json b/research/connected-l18-root-caller/inputs/root_L3_tHHtHt.json
new file mode 100644
index 0000000000..15071c325b
--- /dev/null
+++ b/research/connected-l18-root-caller/inputs/root_L3_tHHtHt.json
@@ -0,0 +1 @@
+{"types": "tHHtHt", "a": [["1", "0", "0", "0", "0", "0", "0", "0"], ["0", "1", "0", "0", "0", "0", "0", "0"], ["0", "0", "1", "0", "0", "0", "0", "0"], ["0", "0", "0", "1", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "0"], ["0", "0", "0", "0", "0", "1", "0", "0"], ["0", "0", "0", "0", "0", "0", "1", "0"], ["0", "0", "0", "0", "0", "0", "0", "1"], ["-1", "0", "-1", "0", "-1", "0", "-1", "0"]], "b": [["0", "1", "0", "0", "0", "0", "0", "0"], ["-1", "0", "1", "0", "0", "0", "0", "0"], ["0", "-1", "0", "1", "0", "0", "0", "0"], ["0", "0", "-1", "0", "1", "0", "0", "0"], ["0", "0", "0", "-1", "0", "1", "0", "0"], ["0", "0", "0", "0", "-1", "0", "1", "0"], ["0", "0", "0", "0", "0", "-1", "0", "1"], ["0", "0", "0", "0", "0", "0", "-1", "0"], ["0", "0", "0", "0", "0", "0", "0", "-1"]], "stages": [{"block": ["H", [1, 2]], "idle_slots": [2, 2]}, {"block": ["H", [3, 4]], "idle_slots": [5, 5]}, {"block": ["H", [6, 7]], "idle_slots": [7, 8]}], "params": ["4", "-4", "4", "-4", "-9", "-1/13", "0", "0", "24/13", "0", "0", "8", "-6/13", "6", "-18/13", "0", "-8", "48/23", "-8", "48/23", "108/23", "12/299", "0", "0", "-4", "0", "0", "-6", "1", "-13", "3", "0", "5/3", "0", "5/3", "3", "5/3", "3", "0", "0", "0", "0", "-7", "0", "0", "-2", "7", "0", "-12/7", "0", "-12/7", "6", "-12/7", "6", "0", "0", "0", "0", "-9", "0", "0", "5", "9", "0", "2379/287", "0", "2379/287", "312/287", "9", "780/287", "0", "780/287", "0", "0", "-6/13", "3/13", "-3", "-9", "0", "0", "-9", "0", "-9", "9/7", "-1485/182", "45/14", "0", "45/14", "0", "0", "-8/13", "4/13", "-4", "15", "0", "0"]}
\ No newline at end of file
diff --git a/research/connected-l18-root-caller/inputs/root_L3_tHtHHt.json b/research/connected-l18-root-caller/inputs/root_L3_tHtHHt.json
new file mode 100644
index 0000000000..67ea062843
--- /dev/null
+++ b/research/connected-l18-root-caller/inputs/root_L3_tHtHHt.json
@@ -0,0 +1 @@
+{"types": "tHtHHt", "a": [["1", "0", "0", "0", "0", "0", "0", "0"], ["0", "1", "0", "0", "0", "0", "0", "0"], ["0", "0", "1", "0", "0", "0", "0", "0"], ["0", "0", "0", "1", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "0"], ["0", "0", "0", "0", "0", "1", "0", "0"], ["0", "0", "0", "0", "0", "0", "1", "0"], ["0", "0", "0", "0", "0", "0", "0", "1"], ["-1", "0", "-1", "0", "-1", "0", "-1", "0"]], "b": [["0", "1", "0", "0", "0", "0", "0", "0"], ["-1", "0", "1", "0", "0", "0", "0", "0"], ["0", "-1", "0", "1", "0", "0", "0", "0"], ["0", "0", "-1", "0", "1", "0", "0", "0"], ["0", "0", "0", "-1", "0", "1", "0", "0"], ["0", "0", "0", "0", "-1", "0", "1", "0"], ["0", "0", "0", "0", "0", "-1", "0", "1"], ["0", "0", "0", "0", "0", "0", "-1", "0"], ["0", "0", "0", "0", "0", "0", "0", "-1"]], "stages": [{"block": ["H", [1, 2]], "idle_slots": [1, 3]}, {"block": ["H", [4, 5]], "idle_slots": [6, 6]}, {"block": ["H", [6, 7]], "idle_slots": [7, 8]}], "params": ["-13", "3042/509", "-13", "3042/509", "676/509", "0", "0", "0", "-198/415", "0", "0", "-11", "99/830", "-253/830", "297/830", "0", "23", "-1", "23", "-1", "-2/9", "0", "0", "0", "-13", "0", "0", "-29", "13/4", "-299/36", "39/4", "0", "12", "0", "12", "22/3", "0", "22/3", "0", "0", "0", "0", "-3", "-27", "0", "0", "3", "0", "26", "0", "26", "-26/9", "0", "-26/9", "0", "0", "0", "0", "11", "-18", "0", "0", "-11", "0", "768/89", "0", "768/89", "646/89", "24", "950/89", "0", "950/89", "0", "0", "-2", "9", "-23", "21", "0", "0", "-6", "0", "-6", "17", "30", "25", "0", "25", "0", "0", "-38/23", "171/23", "-19", "39", "0", "0"]}
\ No newline at end of file
diff --git a/research/connected-l18-root-caller/matrix.py b/research/connected-l18-root-caller/matrix.py
new file mode 100644
index 0000000000..f7dd034102
--- /dev/null
+++ b/research/connected-l18-root-caller/matrix.py
@@ -0,0 +1,77 @@
+"""Exact rational matrix helpers and explicit L3 projector decoder."""
+from fractions import Fraction as F
+
+def eye(n):
+    return [[F(i == j) for j in range(n)] for i in range(n)]
+
+def zero(n):
+    return [[F(0) for _ in range(n)] for _ in range(n)]
+
+def add(a, b, c=F(1)):
+    return [[x+c*y for x,y in zip(r,s)] for r,s in zip(a,b)]
+
+def scale(a, c):
+    return [[c*x for x in r] for r in a]
+
+def mul(a,b):
+    bt=list(zip(*b))
+    return [[sum((x*y for x,y in zip(r,s) if x and y), F(0)) for s in bt] for r in a]
+
+def outer(a,b):
+    return [[x*y for y in b] for x in a]
+
+def dot(a,b):
+    return sum((x*y for x,y in zip(a,b)), F(0))
+
+def rank(a):
+    a=[r[:] for r in a]; pivot=0
+    for c in range(len(a[0])):
+        p=next((i for i in range(pivot,len(a)) if a[i][c]),None)
+        if p is None: continue
+        a[pivot],a[p]=a[p],a[pivot]; q=a[pivot][c]
+        a[pivot]=[x/q for x in a[pivot]]
+        for i in range(pivot+1,len(a)):
+            q=a[i][c]
+            if q: a[i]=[x-q*y for x,y in zip(a[i],a[pivot])]
+        pivot+=1
+        if pivot==len(a): break
+    return pivot
+
+def inverse(a):
+    n=len(a); b=[r[:]+s for r,s in zip(a,eye(n))]
+    for c in range(n):
+        p=next(i for i in range(c,n) if b[i][c]); b[c],b[p]=b[p],b[c]
+        q=b[c][c]; b[c]=[x/q for x in b[c]]
+        for i in range(n):
+            if i!=c:
+                q=b[i][c]; b[i]=[x-q*y for x,y in zip(b[i],b[c])]
+    return [r[n:] for r in b]
+
+def prefixes(a,b,coefficient):
+    out=[eye(len(a[0]))]
+    for x,y in zip(a,b):
+        out.append(mul(add(eye(len(x)),outer(x,y),coefficient),out[-1]))
+    return out
+
+def reconstruct(data,coefficient=F(1)):
+    """Recovered interpretation; not claimed to reproduce unpublished author code.
+    Six (p,q) pairs normalize to p q/(q p). Slot s is after s units.
+    Prefix conjugation transports every projector to initial coordinates.
+    """
+    a=[[F(v) for v in r] for r in data['a']]
+    b=[[F(v) for v in r] for r in data['b']]
+    n=len(a[0]); v=list(map(F,data['params']))
+    pref=prefixes(a,b,coefficient); inv=[inverse(p) for p in pref]
+    es=[]; pieces=[]
+    for k,st in enumerate(data['stages']):
+        u,w=st['block'][1]
+        host=add(outer(a[w],b[u]),outer(a[u],b[w]),F(-1))
+        ps=[mul(mul(inv[w+1],host),pref[w+1])]
+        for j,slot in enumerate(st['idle_slots']):
+            off=4*n*k+2*n*j; p,q=v[off:off+n],v[off+n:off+2*n]
+            idle=scale(outer(p,q),1/dot(q,p))
+            ps.append(mul(mul(inv[slot],idle),pref[slot]))
+        pieces.append(ps); e=zero(n)
+        for p in ps: e=add(e,p)
+        es.append(e)
+    return a,b,pref,pieces,es
diff --git a/research/connected-l18-root-caller/replay.py b/research/connected-l18-root-caller/replay.py
new file mode 100644
index 0000000000..26a0267be0
--- /dev/null
+++ b/research/connected-l18-root-caller/replay.py
@@ -0,0 +1,74 @@
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+import json,math
+HERE=Path(__file__).resolve().parent
+if not __debug__: raise RuntimeError('Exact replay requires assertions enabled')
+ZERO=(F(0),F(0));ONE=(F(1),F(0))
+def ga(a,b):return(a[0]+b[0],a[1]+b[1])
+def gm(a,b):return(a[0]*b[0]-a[1]*b[1],a[0]*b[1]+a[1]*b[0])
+def gp(q,n):
+ out=ONE
+ for _ in range(n%4):out=gm(out,q)
+ return out
+
+def padd(a,b,c):
+ out=a.copy()
+ for m,x in b.items():
+  z=ga(out.get(m,ZERO),gm(c,x))
+  if z!=ZERO:out[m]=z
+  elif m in out:del out[m]
+ return out
+
+def radd(a,b,c):return[padd(x,y,c) for x,y in zip(a,b)]
+def rscale(a,c):return[{m:gm(c,x) for m,x in p.items() if gm(c,x)!=ZERO} for p in a]
+def rd(a,k):
+ out=[]
+ for p in a:
+  q={}
+  for m,x in p.items():
+   assert(m//4**k)%4<3
+   q[m+4**k]=x
+  out.append(q)
+ return out
+
+def replay(C,q,check=True):
+ n=C['roles'];R=[[{0:ONE} if i==j else {} for j in range(n)] for i in range(n)];peak=0;den=1;mag=F(0)
+ for e in C['events']:
+  op=e[0]
+  if op=='ADD':R[e[1]]=radd(R[e[1]],R[e[2]],(F(e[3]),F(0)))
+  elif op=='SCALE':R[e[1]]=rscale(R[e[1]],(F(e[2]),F(0)))
+  elif op=='SWAP':R[e[1]],R[e[2]]=R[e[2]],R[e[1]]
+  elif op=='QUERY':R[e[1]]=radd(R[e[1]],R[e[2]],gp(q,e[3]))
+  elif op=='LAMBDA':R[e[1]]=rscale(R[e[1]],ONE if q[1]==0 else(F(0),F(e[2])))
+  elif op=='IDLE_ONE':
+   for k in e[2]:R[e[1]]=rd(R[e[1]],k)
+  elif op=='HOST':
+   x,y,k=e[1:4];old=R[x];R[x]=rd(radd(old,R[y],gp(q,1)),k);R[y]=rd(rscale(old,gm((F(-1),F(0)),gp(q,-1))),k)
+  else:raise ValueError(op)
+  peak=max(peak,sum(len(p) for row in R for p in row))
+  for row in R:
+   mass=F(0)
+   for p in row:
+    for z in p.values():
+     mass+=abs(z[0])+abs(z[1]);den=math.lcm(den,z[0].denominator,z[1].denominator)
+   mag=max(mag,mass)
+ target=[[{sum(4**k for k in range(C['stages']) if C['masks'][i]>>k&1):q} if i==j else{} for j in range(n)] for i in range(n)]
+ if check:assert R==target
+ return dict(ok=R==target,peak_monomials=peak,common_denominator=str(den),denominator_bits=den.bit_length(),max_coefficient_row_l1=str(mag))
+
+
+if __name__=='__main__':
+ result={}
+ for g in [3,9,18]:
+  C=json.loads((HERE/f'caller_L{g}.json').read_text())
+  chars=[ONE,(-F(1),F(0)),(F(0),F(1)),(F(0),-F(1))]
+  result[str(g)]=dict(characters=[replay(C,q)for q in chars])
+  controls={}
+  for op in ['HOST','QUERY','IDLE_ONE','LAMBDA','ADD']:
+   bad=json.loads(json.dumps(C));idx=next(i for i,e in enumerate(bad['events'])if e[0]==op);del bad['events'][idx]
+   controls['drop_'+op]=any(not replay(bad,q,False)['ok']for q in chars)
+  assert all(controls.values());result[str(g)]['controls']=controls
+ expected=HERE/'REPLAY.json'
+ if expected.exists():assert result==json.loads(expected.read_text())
+ print(json.dumps(result,indent=2));print('PASS_FOUR_CHARACTER_CALLER')
diff --git a/research/connected-l18-root-caller/review.py b/research/connected-l18-root-caller/review.py
new file mode 100644
index 0000000000..e2cfbd6db5
--- /dev/null
+++ b/research/connected-l18-root-caller/review.py
@@ -0,0 +1,22 @@
+"""Read-only adapter for separately authored exact checks."""
+from pathlib import Path
+import importlib.util,json,hashlib
+if not __debug__:raise RuntimeError('Assertions required')
+HERE=Path(__file__).resolve().parent
+
+def module(name):
+ spec=importlib.util.spec_from_file_location('independent_'+name,HERE/'review'/f'{name}.py');m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m
+if __name__=='__main__':
+ for f,h in json.loads((HERE/'review/PINS.json').read_text()).items():assert hashlib.sha256((HERE/'review'/f).read_bytes()).hexdigest()==h
+ root=module('root');tariff=module('tariff')
+ for g in[3,9,18]:
+  got=json.loads(json.dumps(root.audit(HERE/f'root_L{g}.json')));assert got==json.loads((HERE/f'review/ROOT-L{g}.json').read_text())
+ got=json.loads(json.dumps(tariff.audit(HERE/'root_L18.json',HERE/'caller_L18.json')));assert got==json.loads((HERE/'review/TARIFF-L18.json').read_text())
+ import sys,io,contextlib
+ native=module('native_screen');before=sys.argv[:];buf=io.StringIO()
+ try:
+  sys.argv=['native_screen','--word',str(HERE/'inputs/final_native.json.gz'),'--caller',str(HERE/'caller_L18.json'),'--base-invoice',str(HERE/'inputs/base_invoice.json')]
+  with contextlib.redirect_stdout(buf):native.main()
+ finally:sys.argv=before
+ assert json.loads(buf.getvalue())==json.loads((HERE/'review/NATIVE-SCREEN.json').read_text())
+ print('PASS_INDEPENDENT_CONNECTED_ROOT')
diff --git a/research/connected-l18-root-caller/review/COALESCING-CORROBORATION.json b/research/connected-l18-root-caller/review/COALESCING-CORROBORATION.json
new file mode 100644
index 0000000000..4d14491fc3
--- /dev/null
+++ b/research/connected-l18-root-caller/review/COALESCING-CORROBORATION.json
@@ -0,0 +1,58 @@
+{
+  "status": "PASS_SCOPED_COORDINATE_RELAXATION",
+  "degrees": [
+    18,
+    9,
+    7,
+    7,
+    8,
+    6,
+    6,
+    7,
+    4,
+    4,
+    5,
+    3,
+    3,
+    4,
+    1,
+    1,
+    1,
+    0,
+    0,
+    3,
+    0,
+    0,
+    4,
+    2,
+    2,
+    6,
+    3,
+    3,
+    7,
+    5,
+    5,
+    9,
+    6,
+    6,
+    10,
+    8,
+    8,
+    0
+  ],
+  "savings_interval": [
+    "3033528101617798656112890157815521712666569108366082250278978304720236523139057/312500000000000000000000000000000000000000000000000000000000000000000000000000",
+    "121341124064711946244515606312620868506662764334643290011159132188809460925586779/12500000000000000000000000000000000000000000000000000000000000000000000000000000"
+  ],
+  "savings_float": [
+    9.707289925176955,
+    9.707289925176955
+  ],
+  "required_interval": [
+    "252045700871891006117661147933138018225692366318310196499062699144282319103300381/25000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "25204570087189100611766114793313801822569236631831019649906269914428231910339183/2500000000000000000000000000000000000000000000000000000000000000000000000000000"
+  ],
+  "shortfall_lower": "9363452742467113628629935307896281212366837649023616476744434766663397252126823/25000000000000000000000000000000000000000000000000000000000000000000000000000000",
+  "shortfall_float": 0.37453810969868456,
+  "scope": "Fixed38 coordinate roles;181 idles;2coordinate hosts perstage;free all-occurrence same-role merging. No general noncoordinate/native obstruction."
+}
diff --git a/research/connected-l18-root-caller/review/NATIVE-SCREEN.json b/research/connected-l18-root-caller/review/NATIVE-SCREEN.json
new file mode 100644
index 0000000000..50efbb519b
--- /dev/null
+++ b/research/connected-l18-root-caller/review/NATIVE-SCREEN.json
@@ -0,0 +1,106 @@
+{
+  "F_plus_H1_flux": 1824,
+  "F_plus_H1_total_surplus": 760,
+  "decimal_diagnostics": [
+    {
+      "F_plus_H1_excess": "0.56010155749309112470591366207364004050153859181846710333125044254283",
+      "F_plus_owned_H1": "17.69144246034742374374226766005918882596302205588672118282217165847194",
+      "direct_2H8_2H1": "17.87977915542244729685245179385024283436296335935575119145603373117512",
+      "kappa": "0.00362701882",
+      "optimistic_200_pair_average": "16.69183303860612547832196639740589905469059016993397237884018706223357",
+      "root_native_gate": "17.13134090285433261903635399798554878546148346406825407949092121592911",
+      "source_F": "16.69144246034742374374226766005918882596302205588672118282217165847194",
+      "two_plane_total": "3338.366607721225095664393279481179810938118033986794475768037412446714"
+    },
+    {
+      "F_plus_H1_excess": "0.56090360605116616032886342215277046550073736040002877275662354442563",
+      "F_plus_owned_H1": "17.69156997132560881744434535959819594850102165127698553460444813337146",
+      "direct_2H8_2H1": "17.87967879314305368469257668080959404075866024594087966633329031309724",
+      "kappa": "0.00363005817",
+      "optimistic_200_pair_average": "16.69194291954464571022790950055455399321534375977813713842975079698974",
+      "root_native_gate": "17.13066636527444265711548193744542548300028429087695676184782458894583",
+      "source_F": "16.69156997132560881744434535959819594850102165127698553460444813337146",
+      "two_plane_total": "3338.388583908929142045581900110910798643068751955627427685950159397947"
+    }
+  ],
+  "grouped_order": [
+    "X1",
+    "X2",
+    "Y1",
+    "Y2"
+  ],
+  "inputs": {
+    "base_invoice": "87a41b13bdd9248d538805f76a970f51335567845dfc0070698b6979a08b70d6",
+    "caller": "f4090329f219edd493b4ca592128521e867a355fb528556b15201e759783568b",
+    "word": "2b94953dc14a122e3ef089633f05b58ec689ec5156feb7c784ed3e137dc01883"
+  },
+  "native_public_inputs": 1480,
+  "native_type_A_exact_ports": 96,
+  "root_outside_paid": {
+    "1": 3,
+    "8": 181
+  },
+  "root_targets": {
+    "9": 3,
+    "17": 3,
+    "25": 5,
+    "33": 4,
+    "41": 3,
+    "49": 5,
+    "57": 4,
+    "65": 5,
+    "73": 4,
+    "81": 1,
+    "145": 1
+  },
+  "scope": "Same-frame invertible input/output remix of two main planes only; excludes paid cross-frame mixing, feedback, helper mixing and larger rewrites. CLEAR uses inherited owned erasure. No Clifford/all-width replay newly claimed.",
+  "source_F_flux": 1720,
+  "source_F_helpers": {
+    "1": 14,
+    "2": 8,
+    "3": 4,
+    "4": 109,
+    "5": 17,
+    "6": 3,
+    "7": 10,
+    "8": 40,
+    "9": 359
+  },
+  "source_F_paid": {
+    "1": 2234,
+    "2": 454,
+    "3": 489,
+    "4": 110,
+    "5": 152,
+    "6": 7,
+    "7": 9,
+    "8": 1
+  },
+  "status": "SCOPED_OBSTRUCTIONS_ONLY_NO_NEW_NATIVE",
+  "type_A_matrix": [
+    [
+      1,
+      0,
+      0,
+      0
+    ],
+    [
+      0,
+      1,
+      0,
+      -1
+    ],
+    [
+      1,
+      0,
+      1,
+      0
+    ],
+    [
+      0,
+      0,
+      0,
+      1
+    ]
+  ]
+}
diff --git a/research/connected-l18-root-caller/review/PINS.json b/research/connected-l18-root-caller/review/PINS.json
new file mode 100644
index 0000000000..f427774796
--- /dev/null
+++ b/research/connected-l18-root-caller/review/PINS.json
@@ -0,0 +1,10 @@
+{
+  "ROOT-L3.json": "ed168e53a67b4e9c85969c2f80074807c39483bdf2d065b449c46b7d2a0b8be0",
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diff --git a/research/connected-l18-root-caller/review/ROOT-L18.json b/research/connected-l18-root-caller/review/ROOT-L18.json
new file mode 100644
index 0000000000..cfaac7e877
--- /dev/null
+++ b/research/connected-l18-root-caller/review/ROOT-L18.json
@@ -0,0 +1,502 @@
+{
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+  "unbundled_nonnative_mass": 1451,
+  "hypothetical_ideal_mass": 1739,
+  "hypothetical_ideal_surplus": 35,
+  "unbuilt_obligations": [
+    "18 resonant t=-1 HOST supplier calls with their actual full T/P invoice",
+    "all scalar basis/gauge/wrapper operations and exact alphabet checks",
+    "native all-width correctness, rounding, finite compiler and outer admission; no kappa claim"
+  ]
+}
diff --git a/research/connected-l18-root-caller/review/ROOT-L3.json b/research/connected-l18-root-caller/review/ROOT-L3.json
new file mode 100644
index 0000000000..5f03ba2d4c
--- /dev/null
+++ b/research/connected-l18-root-caller/review/ROOT-L3.json
@@ -0,0 +1,109 @@
+{
+  "status": "PASS",
+  "root_sha256": "cdc6535c3d5927915ce622fb2b71b15b9a98f65c0759222e487dcd558fd8ee59",
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+  "connected_header": "every offdiagonal Gram entry is nonzero",
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+  "minus_endpoint": "-I",
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+  "hypothetical_ideal_surplus": 5,
+  "unbuilt_obligations": [
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+    "all scalar basis/gauge/wrapper operations and exact alphabet checks",
+    "native all-width correctness, rounding, finite compiler and outer admission; no kappa claim"
+  ]
+}
diff --git a/research/connected-l18-root-caller/review/ROOT-L9.json b/research/connected-l18-root-caller/review/ROOT-L9.json
new file mode 100644
index 0000000000..946d90e1a1
--- /dev/null
+++ b/research/connected-l18-root-caller/review/ROOT-L9.json
@@ -0,0 +1,242 @@
+{
+  "status": "PASS",
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+  "integral_header": true,
+  "connected_header": "every offdiagonal Gram entry is nonzero",
+  "connected_masks": "all masks share coordinate0 and their union covers all n fields",
+  "complete_sign_Gram_entries": 441,
+  "minus_endpoint": "-I",
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+  "hypothetical_ideal_surplus": 17,
+  "unbuilt_obligations": [
+    "9 resonant t=-1 HOST supplier calls with their actual full T/P invoice",
+    "all scalar basis/gauge/wrapper operations and exact alphabet checks",
+    "native all-width correctness, rounding, finite compiler and outer admission; no kappa claim"
+  ]
+}
diff --git a/research/connected-l18-root-caller/review/TARIFF-L18.json b/research/connected-l18-root-caller/review/TARIFF-L18.json
new file mode 100644
index 0000000000..39a65a03af
--- /dev/null
+++ b/research/connected-l18-root-caller/review/TARIFF-L18.json
@@ -0,0 +1,58 @@
+{
+  "status": "PASS",
+  "root_sha256": "be4a2beed3a40de6d2c5dcc6e4f25f3c2a4375551b70e63fb0e9a03041db6a34",
+  "caller_sha256": "f4090329f219edd493b4ca592128521e867a355fb528556b15201e759783568b",
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+  "event_census": {
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+    "HOST": 18,
+    "IDLE_ONE": 181,
+    "LAMBDA": 80,
+    "QUERY": 3,
+    "SCALE": 189,
+    "SWAP": 858
+  },
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+    "-1/2": 101,
+    "-2": 126,
+    "-5/2": 3,
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+  },
+  "scalar_denominators": {
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+  },
+  "scalar_max_abs": "5/2",
+  "coefficient_l1_majorant": "347424048600207422608405048958225038000101861270",
+  "coefficient_l1_strict_power_2_bound": 158,
+  "dyadic_denominator_height_bound": 51,
+  "root_target_per_port": {
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+    "25": 5,
+    "33": 4,
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+  "unbundled_outer_paid_per_port": {
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+  },
+  "native_calls": 18,
+  "supplier_substitution": {
+    "T": "p*Troot + 18*Thelp",
+    "P": "p*(181 H8 + 3 H1) + 18*Pnative",
+    "p": "simultaneous root ports in one supplier call",
+    "general_surplus": "323*p - 18*sum_r r*(Pnative[r]-Thelp[r])",
+    "conditional_example": "if supplier signed rank flux is 16*p, surplus is 35*p"
+  },
+  "scope": "Algebraic interface and scalar census only. Supplier, full ordinary price, compiler and outer admission remain open."
+}
diff --git a/research/connected-l18-root-caller/review/coalescing_window.py b/research/connected-l18-root-caller/review/coalescing_window.py
new file mode 100644
index 0000000000..daae8ac6c8
--- /dev/null
+++ b/research/connected-l18-root-caller/review/coalescing_window.py
@@ -0,0 +1,68 @@
+#!/usr/bin/env python3
+"""Independent fixed-invoice negativity over an interval; no author imports."""
+import argparse,hashlib,importlib.util,json
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+from itertools import combinations
+if not __debug__:raise RuntimeError('Assertions required')
+
+def certify(v,T,P,lo,hi):
+ assert 0<lo<hi<1
+ endpoint=v.sub(v.moment(T,lo),v.moment(P,lo));upper=(0,0)
+ for r in T.keys()|P.keys():
+  c=T[r]-P[r]
+  # Positive c has negative derivative, largest at hi; negative c has
+  # positive derivative, largest at lo. Sum interval upper endpoints.
+  term=v.mul(v.power(r,hi if c>=0 else lo),v.log(r))
+  upper=v.add(upper,v.smul(term,-c))
+ assert endpoint[1]<0 and upper[1]<0,'Nonnegative endpoint or derivative bound'
+ return endpoint,upper
+
+def audit(root,caller,invoice,engine):
+ spec=importlib.util.spec_from_file_location('iv',engine);v=importlib.util.module_from_spec(spec);spec.loader.exec_module(v)
+ raw=Path(root).read_bytes();native_raw=Path(invoice).read_bytes();caller_raw=Path(caller).read_bytes();R=json.loads(raw);N=json.loads(native_raw);C=json.loads(caller_raw)
+ assert hashlib.sha256(raw).hexdigest()=='be4a2beed3a40de6d2c5dcc6e4f25f3c2a4375551b70e63fb0e9a03041db6a34'
+ assert hashlib.sha256(native_raw).hexdigest()=='87a41b13bdd9248d538805f76a970f51335567845dfc0070698b6979a08b70d6'
+ assert hashlib.sha256(Path(engine).read_bytes()).hexdigest()=='60a743d13f668ef86db4b8215b4d5d04430a671ba6f1fe06d9c1c4c3dfe86da5'
+ assert hashlib.sha256(caller_raw).hexdigest()=='f4090329f219edd493b4ca592128521e867a355fb528556b15201e759783568b'
+ masks=[set(s['mask'])for s in R['stages']];assert len(masks)==18 and R['n']==38
+ eligibility=[{s for s,m in enumerate(masks)if r in m}for r in range(38)]
+ assert C['roles']==38 and C['stages']==18 and C['masks']==[sum(1<<s for s in E)for E in eligibility]
+ census=Counter(e[0]for e in C['events']);assert census['HOST']==18 and census['IDLE_ONE']==181 and census['QUERY']==3
+ allowed=[[set(h)for h in combinations(sorted(m),2)if all(not(eligibility[j]<eligibility[i])or j in h for i in h for j in m)]for m in masks]
+ assert [len(z)for z in allowed]==[1]*8+[2]+[1]*9 and allowed[8]==[{16,37},{19,37}]
+ degrees=[]
+ for bridge in allowed[8]:
+  host=[z[0]for z in allowed];host[8]=bridge
+  degrees.append([sum(r in m-h for m,h in zip(masks,host))for r in range(38)])
+ d,e=degrees;assert sum(d)==sum(e)==181
+ assert [(r,d[r],e[r])for r in range(38)if d[r]!=e[r]]==[(16,1,2),(19,3,2)]
+ # For every 0<k<1, strict concavity gives f(1)+f(3)<2f(2).
+ # Eligibility union/intersection compression and its finite increasing
+ # potential establish that these are the only compressed optimum cases.
+ ports=104;calls=18;T=Counter();P=Counter()
+ for E in eligibility:T[1+8*len(E)]+=ports
+ for degree in d:
+  if degree:P[8*degree]+=ports
+ P[1]+=3*ports+calls*ports
+ for r,c in N['helpers'].items():T[int(r)]+=calls*c
+ for r,c in N['local_paid'].items():P[int(r)]+=calls*c
+ lo=F('.00362701882');hi=F('.01')
+ endpoint,upper=certify(v,T,P,lo,hi)
+ assert endpoint[1]<-F('38.95')*v.B and upper[1]<-198383*v.B
+ surplus=sum(r*(T[r]-P[r])for r in T.keys()|P.keys());assert surplus==760
+ bad=P.copy();bad[1]-=calls*ports
+ for label,args in [('omitted_paid_adapter',(T,bad,lo,hi)),('reversed_interval',(T,P,hi,lo))]:
+  try:certify(v,*args)
+  except AssertionError:pass
+  else:raise AssertionError('Negative control accepted: '+label)
+ return dict(status='PASS_UNIFORM_NEGATIVITY',root_sha256=hashlib.sha256(raw).hexdigest(),native_invoice_sha256=hashlib.sha256(native_raw).hexdigest(),engine_sha256=hashlib.sha256(Path(engine).read_bytes()).hexdigest(),interval=[str(lo),str(hi)],T=dict(sorted(T.items())),P=dict(sorted(P.items())),rank_surplus=surplus,optimal_degrees=d,left_endpoint_margin=v.show(endpoint),left_endpoint_margin_float=v.value(endpoint),uniform_derivative_upper_interval=v.show(upper),uniform_derivative_upper_float=v.value(upper),scope='Fixed104-port F+H1 supplier,18 full paid/helper invoices,3thinH1 perport,and181 idle incidences optimally coalesced in the fixed38 coordinate-role relaxation. Ordinary implementation work is optimistically free. Not a general root/native obstruction.')
+
+if __name__=='__main__':
+ if not __debug__:raise RuntimeError('Assertions required')
+ p=argparse.ArgumentParser();p.add_argument('--root',required=True);p.add_argument('--caller',required=True);p.add_argument('--invoice',required=True);p.add_argument('--engine',required=True);p.add_argument('--out',default='-');p.add_argument('--receipt');a=p.parse_args();result=audit(a.root,a.caller,a.invoice,a.engine);s=json.dumps(result,indent=2)+'\n'
+ if a.receipt:assert json.loads(Path(a.receipt).read_text())==json.loads(s),'Frozen interval receipt differs'
+ if a.out!='-':Path(a.out).write_text(s)
+ print(s)
+ print('PASS_UNIFORM_NEGATIVITY_AND_TWO_CONTROLS')
diff --git a/research/connected-l18-root-caller/review/interval_engine.py b/research/connected-l18-root-caller/review/interval_engine.py
new file mode 100644
index 0000000000..e24dc46079
--- /dev/null
+++ b/research/connected-l18-root-caller/review/interval_engine.py
@@ -0,0 +1,128 @@
+#!/usr/bin/env python3
+"""Independent certified fixed-grid intervals (80 decimal places).
+ln via 2 atanh after binary range reduction; exp(-x) via alternating
+Taylor brackets. Uses only integer floor/ceiling, not Decimal transcendents.
+"""
+from fractions import Fraction as F
+from functools import lru_cache
+from pathlib import Path
+import json,argparse
+if not __debug__: raise RuntimeError('Run without -O; assertions are proof checks.')
+B=10**80
+
+def ceildiv(a,b):return -((-a)//b)
+def exact(q):
+ q=F(q);return q.numerator*B//q.denominator,ceildiv(q.numerator*B,q.denominator)
+def add(a,b):return a[0]+b[0],a[1]+b[1]
+def sub(a,b):return a[0]-b[1],a[1]-b[0]
+def mul(a,b):
+ p=[a[i]*b[j] for i in (0,1) for j in (0,1)];return min(p)//B,ceildiv(max(p),B)
+def div(a,b):
+ assert b[0]>0
+ p=[F(a[i]*B,b[j]) for i in (0,1) for j in (0,1)]
+ return min(p).__floor__(),max(p).__ceil__()
+def smul(a,q):return mul(a,exact(q))
+def atanh_log(y):
+ yi=exact(y);yy=mul(yi,yi);p=yi;s=(0,0)
+ for j in range(100):s=add(s,smul(p,F(2,2*j+1)));p=mul(p,yy)
+ # 0 <= tail <= 2 y^201/[201(1-y^2)] < 3*(1/3)^201.
+ return s[0],s[1]+ceildiv(3*B,3**201)
+@lru_cache(None)
+def log(r):
+ assert r>=1
+ k=r.bit_length()-1;y=F(r-2**k,r+2**k)
+ a=atanh_log(y);b=atanh_log(F(1,3));return add(a,smul(b,k))
+def expminus(x):
+ assert 0<=x[0]<=x[1]<B
+ # Lower odd truncation at larger x, upper even truncation at smaller x.
+ term=exact(1);s=exact(1);lower=upper=None
+ for j in range(1,62):
+  term=smul(mul(term,x),F(1,j));s=sub(s,term) if j%2 else add(s,term)
+  if j==60:upper=s[1]
+  if j==61:lower=s[0]
+ return lower,upper
+@lru_cache(None)
+def power(r,k):return smul(expminus(smul(log(r),F(k))),r)
+def moment(hist,k):
+ out=(0,0)
+ for r,c in hist.items():out=add(out,smul(power(int(r),F(k)),c))
+ return out
+def show(x):return [str(F(t,B)) for t in x]
+def value(x):return [float(F(t,B)) for t in x]
+def gate(invoice,claim,tested,lo,hi,bit_pin='.00376669'):
+ T=invoice['T'];P=invoice['P'];claim,tested,lo,hi=map(F,(claim,tested,lo,hi));cap=F(bit_pin)
+ assert 0<claim<tested<lo<hi and tested<cap
+ margins={str(k):sub(moment(T,k),moment(P,k)) for k in (lo,hi,tested)}
+ assert margins[str(lo)][0]>0 and margins[str(hi)][1]<0 and margins[str(tested)][0]>0
+ target=moment(T,tested);paid=moment(P,tested)
+ alpha=div(paid,target)
+ # Tail exponent = 1-tested+1/7; argument exp may not be negative.
+ # r^(1-tested+1/7)=r^(1-tested)* exp(log(r)/7).
+ def exppos(x):
+  assert 0<=x[0]<=x[1]<B
+  return div(exact(1),expminus(x))
+ def shifted(hist):
+  out=(0,0)
+  for rr,c in hist.items():
+   r=int(rr);out=add(out,smul(mul(power(r,tested),exppos(smul(log(r),F(1,7)))),c))
+  return out
+ gamma=div(shifted(P),mul(exppos(smul(log(11),F(1,7))),target))
+ delta=div(exact(sum(T.values())*12),mul(exppos(smul(log(11),tested)),target))
+ reserve=F(1,10**27);decay=F(31,32);v=1920
+ assert F(alpha[1],B)<1-reserve and F(gamma[1],B)<decay and F(delta[1],B)<decay
+ assert 1/(1+v*reserve)+4*decay**v<1
+ # exp(v*k*ln153) is large; apply repeated squaring of small factor.
+ unit=exppos(smul(log(153),tested));factor=exact(1);z=unit;n=v
+ while n:
+  if n&1:factor=mul(factor,z)
+  n//=2
+  if n:z=mul(z,z)
+ eta=div(exact(1-tested),factor);lp=1
+ while F(eta[0],B)<=F(63,64)**lp:lp+=1
+ written=lp+1
+ assert F(factor[1],B)<2**written and 11**64<12**63 and 2*(11**v)**64 <= (153**v)**63
+ gap=(tested-claim)/7;assert gap>0 and gap.numerator==1;step=gap.denominator
+ wins=lambda j:(step*j+1)**written<2**j
+ l,h=1,2
+ while not wins(h):l,h=h,2*h
+ while h-l>1:
+  m=(l+h)//2
+  if wins(m):h=m
+  else:l=m
+ assert wins(h) and not wins(h-1)
+ # Monotonicity: upper derivative bound on [0, cap].
+ derivative=(0,0)
+ for rr in T.keys()|P.keys():
+  c=T.get(rr,0)-P.get(rr,0);r=int(rr)
+  term=mul(power(r,cap if c>=0 else 0),log(r));derivative=add(derivative,smul(term,-c))
+ assert derivative[1]<0
+ result=dict(claim=str(claim),tested=str(tested),raw_bracket=[str(lo),str(hi)],moment_margins={k:show(v) for k,v in margins.items()},moment_margin_float={k:value(v) for k,v in margins.items()},derivative_upper=float(F(derivative[1],B)),alpha=value(alpha),gamma=value(gamma),delta=value(delta),minimum_log_power=lp,written_log_power=written,compiler_gap=str(gap),H=str(step*h),BIT_pin=str(cap),BIT_margin=str(cap-tested))
+ # Outer formulas evaluated independently after algebraically substituting
+ # b=k+5g,a=k+4g,q=k+3g,epsilon=1-g,beta=1-3g.
+ k=claim;g=gap;b=k+5*g;a=k+4*g;q=k+3*g;ep=1-g;be=1-3*g;r0=g/10;stop=layout=g
+ sig=1-b;tau=1-a;internal=tau+(1-stop)*max(sig-tau,0);leaf=sig+stop*(1-sig);lam=1-(q+a)/2;xi=ep*(1+q)-F(3,32)+layout;key=be+1-ep
+ M=[ep*q,a,1-ep+q*be,1-ep+a*be,1-ep+be,F(3,32)+xi-ep,xi+F(1,2)-ep,ep,1-(ep+be+48-128+2)]
+ checks=[cap-a,b-a,q,b-q,a-q,stop,1-stop,(1-stop)*b-a,1-internal-q,1-leaf-q,lam-tau,lam-sig,lam-internal,1-q-lam,1-q-leaf,ep,1-ep,xi-F(1,2),ep-xi,be,ep-be,1-be,1-(2*xi-2)-r0-be,1-(2*xi-2)-be,1-ep-r0,1-ep,r0,1-key,1-be-2*(1-ep),128-48-be,layout,ep-a,F(1,32)-b,F(2**45-7**16),F(2),2-xi,F(5),1-be,1-be,1-ep,M[2]-M[0],g,k-F('.001730970419199163702738'),1-ep,F(11,2)]+[x-k for x in M]
+ functional=[1-be,be*(1-F(3,1000)),128-48-ep-be-1,be*(1-F(1,250))]
+ assert len(checks)==54 and len(functional)==4 and min(checks+functional)>0
+ result['outer']=dict(strict_count=54,functional_count=4,minimum_margin=str(min(checks+functional)),BIT_just_below_effective_rejected=(a-F(1,10**12))-a<0)
+ # Input-lift is only needed on [1-tested_complex,1]. A stronger BIT
+ # pin is irrelevant to this interval; the source's crude BIT-wide bound
+ # is not imported beyond its valid range.
+ pos={7:1,3:1,5:1};neg={9:1,4:1,1:2};d1=(0,0);curvature=(0,0)
+ for hist,sign in ((pos,1),(neg,-1)):
+  for r,c in hist.items():
+   d1=add(d1,smul(log(r),sign*c*r))
+   curvature=add(curvature,smul(mul(log(r),log(r)),c*r))
+ lift_cap=cap if cap<=F('.00376669') else tested
+ assert tested<=lift_cap and F(d1[1],B)+lift_cap*F(curvature[1],B)<0
+ lifts={}
+ for price in (claim,tested):
+  lift=sub(moment(pos,price),moment(neg,price));assert lift[0]>0
+  assert price*(-F(d1[1],B))-price*price*F(curvature[1],B)/2>0
+  lifts[str(price)]=show(lift)
+ result['input_lift']=dict(margins=lifts,interval_kappa_cap=str(lift_cap),derivative_upper_on_required_interval=str(F(d1[1],B)+lift_cap*F(curvature[1],B)),source_BIT_wide_crude_bound_would_be=str(F(d1[1],B)+cap*F(curvature[1],B)))
+ return result
+if __name__=='__main__':
+ p=argparse.ArgumentParser();p.add_argument('audit');p.add_argument('--claim',default='.00362852408');p.add_argument('--tested',default='.00362852408007');p.add_argument('--lower',default='.00362852408398727978896072723289');p.add_argument('--upper',default='.00362852408398727978896072723290');p.add_argument('--out',required=True);p.add_argument('--bit-pin',default='.00376669');a=p.parse_args()
+ r=gate(json.loads(Path(a.audit).read_text())['invoice'],a.claim,a.tested,a.lower,a.upper,a.bit_pin);Path(a.out).write_text(json.dumps(r,indent=2)+'\n');print(json.dumps(r,indent=2))
diff --git a/research/connected-l18-root-caller/review/native_screen.py b/research/connected-l18-root-caller/review/native_screen.py
new file mode 100644
index 0000000000..9e92a9f0d1
--- /dev/null
+++ b/research/connected-l18-root-caller/review/native_screen.py
@@ -0,0 +1,129 @@
+#!/usr/bin/env python3
+"""Exact two-plane replay and optimistic budget screen; no new supplier claim."""
+import argparse
+import gzip
+import hashlib
+import json
+from collections import Counter
+from decimal import Decimal, localcontext
+from fractions import Fraction as Q
+from pathlib import Path
+
+def read(p):
+    raw=p.read_bytes()
+    return json.loads(gzip.decompress(raw) if p.suffix=='.gz' else raw)
+
+def mm(a,b):
+    return [[sum(x*y for x,y in zip(r,c)) for c in zip(*b)] for r in a]
+
+def replay(w):
+    n=len(w['initial']); current=w['initial'][:]+[None]*w['owned_fields']
+    rows=[{r:Q(1)} for r in range(n)]+[{} for _ in range(w['owned_fields'])]
+    dim=list(map(len,w['frames'])); spans=[]
+    for f in w['frames']:
+        s={0}
+        for v in f:
+            assert v not in s
+            s|={x^v for x in tuple(s)}
+        spans.append(s)
+    owned=set(); paid=Counter()
+    for i,e in enumerate(w['program']):
+        op,r=e[:2]
+        if op=='MOVE':
+            _,_,a,b,private=e
+            assert current[r]==a and bool(private)==(r in owned),i
+            assert spans[a]<spans[b] or (private and spans[b]<spans[a]),i
+            current[r]=b; paid[abs(dim[b]-dim[a])]+=1
+        elif op=='INIT':
+            assert r>=n and r not in owned,i
+            owned.add(r); current[r]=e[2]; rows[r]={}
+        elif op=='CLEAR':
+            assert r in owned and current[r]==e[2],i
+            owned.remove(r); current[r]=None; rows[r]={}
+        elif op=='SCALE':
+            assert current[r]==e[3],i
+            q=Q(e[2]); assert q
+            rows[r]={k:q*v for k,v in rows[r].items()}
+        else:
+            assert op in ('ADD','COPY'),i
+            _,_,s,q,f=e
+            assert r!=s and current[r]==f==current[s],i
+            if op=='COPY': assert r in owned and not rows[r],i
+            q=Q(q)
+            for k,v in rows[s].items():
+                z=rows[r].get(k,Q(0))+q*v
+                if z: rows[r][k]=z
+                else: rows[r].pop(k,None)
+    assert not owned and current[:n]==w['final']
+    live=w['live']; h=w['hosted']; type_a=set(h['Dports'])
+    main=set(live)|{r+112 for r in live}|set(h['X2'])|set(h['Y2'])
+    checked=0
+    for i,x2,y2 in zip(h['Dports'],h['X2'],h['Y2']):
+        x,y=live[i],live[i]+112
+        assert rows[x]=={x:Q(1)}
+        assert rows[y]=={x:Q(1),y:Q(1)}
+        assert rows[x2]=={x2:Q(1),y2:Q(-1)}
+        assert rows[y2]=={y2:Q(1)}
+        for boundary in ('initial','final'):
+            f=w[boundary]
+            assert f[x]==f[x2] and f[y]==f[y2] and f[x]!=f[y]
+        checked+=1
+    for i,x in enumerate(live):
+        if i not in type_a:
+            y=x+112
+            assert rows[x]=={x:Q(1),y:Q(-1)}
+            assert rows[y]=={x:Q(1,2),y:Q(1,2)}
+    helpers=Counter()
+    for r in range(n):
+        if r not in main:
+            assert rows[r]=={r:Q(1)}
+            a,b=w['initial'][r],w['final'][r]
+            assert spans[a]<spans[b]
+            helpers[dim[b]-dim[a]]+=1
+    return checked,paid,helpers
+
+def main():
+    p=argparse.ArgumentParser()
+    for flag in ('word','caller','base-invoice'): p.add_argument('--'+flag,type=Path,required=True)
+    args=p.parse_args(); paths=[args.word,args.caller,args.base_invoice]
+    w,c,base=map(read,paths); checked,paid,helpers=replay(w)
+    target=Counter(1+8*int(m).bit_count() for m in c['masks']); outside=Counter()
+    for e in c['events']:
+        if e[0]=='QUERY': outside[1]+=1
+        elif e[0]=='IDLE_ONE': outside[8*len(e[2])]+=1
+    assert c['stages']==18 and outside=={1:3,8:181}
+    fpaid=Counter({int(k):v for k,v in base['local_paid'].items()})
+    fhel=Counter({int(k):v for k,v in base['helpers'].items()})
+    flux=sum(r*(fpaid[r]-fhel[r]) for r in set(fpaid)|set(fhel))
+    U,F,J=[[1,-1],[0,1]],[[1,0],[1,1]],[[1,0],[0,-1]]
+    assert mm(F,U)==[[1,-1],[1,0]]
+    assert mm(J,mm(mm(F,U),J))==[[1,1],[-1,0]]
+    half=[[Q(1),Q(-1)],[Q(1,2),Q(1,2)]]
+    assert half[1][1] and mm(F,U)[1][1]==0
+    assert sum(half[i][i] for i in range(2))!=1
+    records=[]
+    with localcontext() as ctx:
+        ctx.prec=70
+        for k in map(Decimal,('.00362701882','.00363005817')):
+            def moment(h): return sum(Decimal(v)*Decimal(r)**(1-k) for r,v in h.items())
+            gate=(moment(target)-moment(outside))/18
+            fcost=(moment(fpaid)-moment(fhel))/104
+            full=moment(paid)-moment(helpers)
+            records.append(dict(kappa=str(k),root_native_gate=str(gate),source_F=str(fcost),
+                F_plus_owned_H1=str(fcost+1),F_plus_H1_excess=str(fcost+1-gate),
+                direct_2H8_2H1=str(2*Decimal(8)**(1-k)+2),two_plane_total=str(full),
+                optimistic_200_pair_average=str(full/200)))
+    out=dict(status='SCOPED_OBSTRUCTIONS_ONLY_NO_NEW_NATIVE',
+        inputs={key:hashlib.sha256(path.read_bytes()).hexdigest() for key,path in zip(('word','caller','base_invoice'),paths)},
+        native_type_A_exact_ports=checked,native_public_inputs=len(w['initial']),
+        grouped_order=['X1','X2','Y1','Y2'],
+        type_A_matrix=[[1,0,0,0],[0,1,0,-1],[1,0,1,0],[0,0,0,1]],
+        root_targets=dict(sorted(target.items())),root_outside_paid=dict(sorted(outside.items())),
+        source_F_paid=dict(sorted(fpaid.items())),source_F_helpers=dict(sorted(fhel.items())),
+        source_F_flux=flux,F_plus_H1_flux=flux+104,
+        F_plus_H1_total_surplus=104*sum(r*(target[r]-outside[r]) for r in set(target)|set(outside))-18*(flux+104),
+        decimal_diagnostics=records,
+        scope='Same-frame invertible input/output remix of two main planes only; excludes paid cross-frame mixing, feedback, helper mixing and larger rewrites. CLEAR uses inherited owned erasure. No Clifford/all-width replay newly claimed.')
+    print(json.dumps(out,indent=2,sort_keys=True))
+
+if __name__=='__main__': main()
diff --git a/research/connected-l18-root-caller/review/root.py b/research/connected-l18-root-caller/review/root.py
new file mode 100644
index 0000000000..8dda1d932e
--- /dev/null
+++ b/research/connected-l18-root-caller/review/root.py
@@ -0,0 +1,101 @@
+#!/usr/bin/env python3
+"""Independent exact sector-root audit. Imports no construction/author checker."""
+import argparse,hashlib,json
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+
+def ident(n):return [{i:F(1)} for i in range(n)]
+def add(a,b,c=F(1)):
+ d=a.copy()
+ for k,v in b.items():
+  z=d.get(k,F(0))+c*v
+  if z:d[k]=z
+  else:d.pop(k,None)
+ return d
+def scale(A,c):return [{j:c*v for j,v in r.items() if c*v} for r in A]
+def plus(A,B,c=F(1)):return [add(a,b,c) for a,b in zip(A,B)]
+def mul(A,B):
+ C=[]
+ for a in A:
+  r={}
+  for k,v in a.items():r=add(r,B[k],v)
+  C.append(r)
+ return C
+def outer(x,y):return [{j:a*b for j,b in enumerate(y) if a*b} for a in x]
+def dot(x,y):return sum((a*b for a,b in zip(x,y)),F(0))
+def rank(A):
+ A=[r.copy() for r in A];piv={}
+ for r in A:
+  while r:
+   k=min(r)
+   if k in piv:r=add(r,piv[k],-r[k])
+   else:
+    z=r[k];piv[k]={j:v/z for j,v in r.items()};break
+ return len(piv)
+def unit(rows,x,y,c):
+ r={}
+ for j,v in enumerate(y):
+  if v:r=add(r,rows[j],v)
+ return [add(row,r,c*x[i]) if x[i] else row.copy() for i,row in enumerate(rows)]
+def all_D(d,sign,drop_mask=False,wrong_order=False):
+ n=d['n'];X=[[F(x) for x in r] for r in d['X']];Y=[[F(x) for x in r] for r in d['Y']]
+ rows=[{(i,0):F(1)} for i in range(n)]
+ after={max(st['units']):j for j,st in enumerate(d['stages'])};assert len(after)==len(d['stages'])
+ # Every D occurs once, on one diagonal layer. Hence no lane exceeds degree 1.
+ assert len(after)<256
+ for k,(x,y) in enumerate(zip(X,Y)):
+  if wrong_order and k==0:x,y=X[1],Y[1]
+  rows=unit(rows,x,y,F(sign-1))
+  if k in after:
+   j=after[k];mask=d['stages'][j]['mask']
+   if drop_mask and j==0:mask=mask[1:]
+   for i in mask:
+    assert all(((pow>>(8*j))&255)==0 for src,pow in rows[i])
+    rows[i]={(src,pow+(1<<(8*j))):v for (src,pow),v in rows[i].items()}
+ expected=[]
+ for i in range(n):
+  mon=sum(1<<(8*j) for j,st in enumerate(d['stages']) if i in st['mask'])
+  expected.append({(i,mon):F(sign)})
+ return rows==expected,sum(map(len,rows)),len(set(k[1] for row in rows for k in row))
+def audit(path):
+ raw=Path(path).read_bytes();d=json.loads(raw);n=d['n'];N=d['N'];stages=d['stages'];L=len(stages)
+ X=[[F(x) for x in r] for r in d['X']];Y=[[F(x) for x in r] for r in d['Y']]
+ assert N==n+1==2*L+3 and len(X)==len(Y)==N and all(len(r)==n for r in X+Y)
+ assert all(x.denominator==1 for row in X+Y for x in row)
+ assert all(dot(Y[i],X[j])==F((i>j)-(i<j)) for i in range(N) for j in range(N))
+ pairs=[u for st in stages for u in st['units']];assert len(pairs)==len(set(pairs))==2*L
+ I=ident(n);zero=[{} for _ in range(n)];pref=[I]
+ for x,y in zip(X,Y):pref.append(unit(pref[-1],x,y,F(-2)))
+ assert pref[-1]==scale(I,F(-1))
+ details=[]
+ for j,st in enumerate(stages):
+  u,v=st['units'];mask=set(st['mask']);assert v==u+1 and len(mask)==len(st['mask'])
+  assert all(0<=i<n for i in mask)
+  assert all(not X[k][i] and not Y[k][i] for k in [u,v] for i in range(n) if i not in mask)
+  H=plus(outer(X[u],Y[v]),outer(X[v],Y[u]),F(-1));P=[{i:F(1)} if i in mask else {} for i in range(n)];R=plus(P,H,F(-1))
+  assert mul(H,H)==H and mul(R,R)==R and mul(H,R)==mul(R,H)==zero
+  assert plus(H,R)==P and rank(H)==2 and rank(R)==len(mask)-2
+  assert all(not dot(Y[k],[R[i].get(c,F(0)) for i in range(n)]) for k in [u,v] for c in range(n))
+  assert all(not sum((a*X[k][c] for c,a in row.items()),F(0)) for k in [u,v] for row in R)
+  for cut in [u,v+1]:assert mul(P,pref[cut])==mul(pref[cut],P)
+  M=unit(unit(I,X[u],Y[u],F(-2)),X[v],Y[v],F(-2))
+  assert mul(M,R)==R and mul(R,M)==R and mul(M,H)==mul(H,M)
+  details.append({'stage':j,'units':[u,v],'mask':sorted(mask),'host_rank':rank(H),'idle_rank':rank(R),'support_Y':sum(bool(Y[u][i] or Y[v][i]) for i in range(n))})
+ assert all(any(i in st['mask'] for st in stages) for i in range(n))
+ assert all(0 in st['mask'] for st in stages)
+ formal={str(s):all_D(d,s) for s in [1,-1]};assert all(z[0] for z in formal.values())
+ assert not all_D(d,-1,drop_mask=True)[0] and not all_D(d,-1,wrong_order=True)[0]
+ # A deliberate header change must invalidate at least one sign-Gram condition.
+ bad=[r[:] for r in X];bad[0][0]+=1
+ assert any(dot(Y[i],bad[j])!=F((i>j)-(i<j)) for i in range(N) for j in range(N))
+ membership=Counter(sum(i in st['mask'] for st in stages) for i in range(n))
+ target=Counter({1+8*k:v for k,v in membership.items()});idle=sum(len(st['mask'])-2 for st in stages);thin=N-2*L
+ paid=Counter({8:idle,1:thin});ideal=paid+Counter({8:2*L})
+ mass=lambda a:sum(k*v for k,v in a.items())
+ assert mass(target)-mass(ideal)==n-thin
+ if n==38:assert mass(target)-mass(ideal)==35
+ return {'status':'PASS','root_sha256':hashlib.sha256(raw).hexdigest(),'n':n,'N':N,'L':L,'sector_semantics':'I+(S-1) X_i Y_i; S^2=1','integral_header':True,'connected_header':'every offdiagonal Gram entry is nonzero','connected_masks':'all masks share coordinate0 and their union covers all n fields','complete_sign_Gram_entries':N*N,'minus_endpoint':'-I','mask_prefix_commutators':2*L,'stages':details,'formal_all_D':formal,'negative_controls':['first mask coordinate omitted','first unit replaced','one header coefficient changed'],'thin_units':sorted(set(range(N))-set(pairs)),'target_profile':dict(sorted(target.items())),'unbundled_paid_excluding_HOST':dict(sorted(paid.items())),'hypothetical_ideal_paid_with_2H8_per_HOST':dict(sorted(ideal.items())),'mask_incidence':sum(len(st['mask']) for st in stages),'target_mass':mass(target),'unbundled_nonnative_mass':mass(paid),'hypothetical_ideal_mass':mass(ideal),'hypothetical_ideal_surplus':mass(target)-mass(ideal),'unbuilt_obligations':[str(L)+' resonant t=-1 HOST supplier calls with their actual full T/P invoice','all scalar basis/gauge/wrapper operations and exact alphabet checks','native all-width correctness, rounding, finite compiler and outer admission; no kappa claim']}
+if __name__=='__main__':
+ if not __debug__:raise RuntimeError('Assertions required')
+ ap=argparse.ArgumentParser();ap.add_argument('--root',required=True);ap.add_argument('--out',required=True);a=ap.parse_args();r=audit(a.root);s=json.dumps(r,indent=2)+'\n';Path(a.out).write_text(s);print(s)
diff --git a/research/connected-l18-root-caller/review/tariff.py b/research/connected-l18-root-caller/review/tariff.py
new file mode 100644
index 0000000000..31b3fd32a1
--- /dev/null
+++ b/research/connected-l18-root-caller/review/tariff.py
@@ -0,0 +1,66 @@
+#!/usr/bin/env python3
+"""Independent unbundled root invoice and scalar majorant; no author imports."""
+import argparse, hashlib, json
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+
+def audit(rp, cp):
+    R=json.loads(Path(rp).read_bytes()); raw=Path(cp).read_bytes(); C=json.loads(raw)
+    n=R['n']; L=len(R['stages']); assert C['roles']==n and C['stages']==L
+    assert C['masks']==[sum(1<<k for k,s in enumerate(R['stages']) if i in s['mask']) for i in range(n)]
+    counts=Counter(e[0] for e in C['events']); idles=Counter(); hosts=Counter(); scalars=[]
+    mass=[F(1)]*n; height=[0]*n; maxmass=F(1); maxheight=0
+    for e in C['events']:
+        op=e[0]; r=e[1]; assert 0<=r<n
+        if op in ['ADD','SCALE']:
+            a=F(e[-1]); scalars.append(a); den=a.denominator; assert den&(den-1)==0
+            h=den.bit_length()-1
+            if op=='ADD':
+                s=e[2]; assert r!=s and 0<=s<n
+                mass[r]+=abs(a)*mass[s]; height[r]=max(height[r],height[s]+h)
+            else:
+                assert a
+                mass[r]*=abs(a); height[r]+=h
+        elif op=='SWAP':
+            s=e[2]; assert 0<=s<n and r!=s
+            mass[r],mass[s]=mass[s],mass[r]; height[r],height[s]=height[s],height[r]
+        elif op=='QUERY':
+            s=e[2]; assert 0<=s<n and r!=s and e[3] in [-1,1]
+            mass[r]+=mass[s]; height[r]=max(height[r],height[s])
+        elif op=='LAMBDA':
+            assert e[2] in [-1,1]
+            mass[r]*=2; height[r]+=1
+        elif op=='IDLE_ONE':
+            assert len(e[2])==1 and 0<=e[2][0]<L
+            idles.update(e[2])
+        elif op=='HOST':
+            s,k=e[2:4]; assert 0<=s<n and r!=s and 0<=k<L
+            assert list(map(F,e[4:]))==[F(1),F(-1)]
+            hosts[k]+=1; m,h=mass[r],height[r]
+            mass[r]+=mass[s]; height[r]=max(height[r],height[s]); mass[s]=m; height[s]=h
+        else: raise AssertionError(op)
+        maxmass=max(maxmass,*mass); maxheight=max(maxheight,*height)
+    assert hosts==Counter({k:1 for k in range(L)})
+    assert idles==Counter({k:len(s['mask'])-2 for k,s in enumerate(R['stages'])})
+    assert counts['QUERY']==R['N']-2*L
+    T=Counter(1+8*mask.bit_count() for mask in C['masks'])
+    P=Counter({1:counts['QUERY'],8:counts['IDLE_ONE']})
+    bits=0
+    while F(2)**bits<=maxmass: bits+=1
+    return dict(status='PASS',root_sha256=hashlib.sha256(Path(rp).read_bytes()).hexdigest(),
+        caller_sha256=hashlib.sha256(raw).hexdigest(),events=len(C['events']),
+        event_census=dict(sorted(counts.items())),scalar_census=dict(sorted(Counter(map(str,scalars)).items())),
+        scalar_denominators=dict(Counter(x.denominator for x in scalars)),
+        scalar_max_abs=str(max(map(abs,scalars))),coefficient_l1_majorant=str(maxmass),
+        coefficient_l1_strict_power_2_bound=bits,dyadic_denominator_height_bound=maxheight,
+        root_target_per_port=dict(sorted(T.items())),unbundled_outer_paid_per_port=dict(sorted(P.items())),
+        native_calls=L,supplier_substitution=dict(T='p*Troot + 18*Thelp',P='p*(181 H8 + 3 H1) + 18*Pnative',
+            p='simultaneous root ports in one supplier call',general_surplus='323*p - 18*sum_r r*(Pnative[r]-Thelp[r])',
+            conditional_example='if supplier signed rank flux is 16*p, surplus is 35*p'),
+        scope='Algebraic interface and scalar census only. Supplier, full ordinary price, compiler and outer admission remain open.')
+
+if __name__=='__main__':
+    if not __debug__: raise RuntimeError('Assertions required')
+    p=argparse.ArgumentParser(); p.add_argument('--root',required=True); p.add_argument('--caller',required=True); p.add_argument('--out',required=True)
+    a=p.parse_args(); r=audit(a.root,a.caller); s=json.dumps(r,indent=2)+'\n'; Path(a.out).write_text(s); print(s)
diff --git a/research/connected-l18-root-caller/root_L18.json b/research/connected-l18-root-caller/root_L18.json
new file mode 100644
index 0000000000..e2d43655b2
--- /dev/null
+++ b/research/connected-l18-root-caller/root_L18.json
@@ -0,0 +1 @@
+{"n": 38, "N": 39, "X": [["1", "1", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"], ["1", "1", "1", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"], ["1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"], ["1", "2", "0", "0", "1", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"], ["1", "2", "0", "0", "1", "1", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"], ["1", "2", 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diff --git a/research/connected-l18-root-caller/root_L3.json b/research/connected-l18-root-caller/root_L3.json
new file mode 100644
index 0000000000..6f48845dc7
--- /dev/null
+++ b/research/connected-l18-root-caller/root_L3.json
@@ -0,0 +1 @@
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diff --git a/research/connected-l18-root-caller/root_L9.json b/research/connected-l18-root-caller/root_L9.json
new file mode 100644
index 0000000000..bd43cc8231
--- /dev/null
+++ b/research/connected-l18-root-caller/root_L9.json
@@ -0,0 +1 @@
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