Record an independent scalar audit of the four PR6349 input lifts.

research/p104-input-lift-direction-audit/README.md

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+# Independent audit of four helper-input lifts
+
+This package checks the scalar schedule in Ali Romman's merged
+[PR #6349](https://github.com/CrocSwap/integer-mult-bounds/pull/6349),
+head `af7cb6c67f8fc7d82a2e4aee2dd2f07481bf6690`, archived on canonical main
+`7c49fe32c55de02c2c873655c804b16e4c3fef0a`. It answers the review requested in
+[discussion #1166 comment 19341394](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19341394).
+
+No new kappa is claimed. The selected frontier stays
+`781451/250000000`. The reported conditional value `0.003129111` is not
+re-derived here.
+
+## What was checked
+
+On the pinned PR6314 source word and the pinned lifted word, a separate
+replay agrees with the proof's local invoice:
+
+- All 799 scalar columns of both words end at the identity. Owned lifetimes
+  are 32 and peak ownership is 13.
+- The only initial-chart changes are roles 496, 649, 663 and 508, from frame
+  3 to frames 595, 597, 105 and 1093. Final frames are unchanged.
+- Each input direction `h` has a unit primary coordinate, disjoint support,
+  and an inverse `I - (h - e_p) e_p^T`. Replaying `h` through the source
+  chronology reproduces the stated departure response.
+- The new chart is contained in every nonzero departure frame of that
+  response. Frame 1093, basis `[30, 42, 384]`, is the GF(2) span intersection
+  of frames 118 and 733.
+- The two dirty-carrier sandwiches leave the wide carrier short one primary
+  input and the narrow carrier short half a primary input, including the
+  intervening additions that do not use those carriers. The six trailing
+  output additions are the inverse basis.
+- Ten frame-3 reads of the four primaries are absent from the lifted word.
+  Role 649 is injected into 198 at frame 597, and role 663 into 179 at frame
+  105, with the stated carrier subtractions.
+- Helper rank is `dim(final) - dim(initial)` off the 208 main roles. The four
+  lifts change ranks `9→8`, `9→8`, `9→8` and `9→6`. The histograms therefore
+  move by paid `H1+H2+H3+2H4-4H5` and productive `H6+3H8-4H9`. Scalar
+  allowances are 127042 and 127088. Paid rank masses are 5952 and 5946.
+
+Four mutations fail closed: deleting the first carrier subtraction, deleting
+one output correction, reversing the 649 injection, and replacing frame 1093
+by `[1, 2, 4]`.
+
+## What was not checked
+
+Native Pauli images, absolute phases, the physical caller, both rational
+price engines, the compiler threshold and the 58 outer predicates were not
+run. The five framework assumptions remain. This audit does not accept
+PR6349 and does not cover PR6350 or PR6353.
+
+## Reproduce
+
+Python 3.12, standard library, from the repository root:
+
+```sh
+python3 -W error -B research/p104-input-lift-direction-audit/verify.py
+python3 -O -W error -B research/p104-input-lift-direction-audit/verify.py
+python3 scripts/research_package.py --package research/p104-input-lift-direction-audit --check-only
+python3 scripts/research_package.py --package research/p104-input-lift-direction-audit
+```
+
+The direct verifier hashes the three pinned inputs and does not need Git or
+network. The registered runner also checks provenance blobs. Each scientific
+command finishes in a few seconds. Status:
+`PASS_P104_INPUT_LIFT_DIRECTION_AUDIT`.
+
+## Open next questions
+
+The signed Pauli image of one changed helper normalizer is still unchecked.
+That is the smallest native gate for this word; the predecessor checker and
+`native_all_columns` are the blocker. Separately, PR6353's later word needs
+its own initial-frame reading before these four ranks are reused. [TASK.json](TASK.json)
+records both first steps.
+
+## Credit
+
+Audit: unpaidmoon, with substantial Cursor Grok assistance. Apache-2.0.
+
+Construction and author checks: Ali Romman, with substantial OpenAI Codex
+assistance, in PR6349. Source word: DreamingOfClouds, with Claude Opus 5.5
+assistance, in PR6314, retaining PR6167. The frame and endpoint rules follow
+the published scalar model of that chain; this package reimplements them and
+does not vendor the checker.

research/p104-input-lift-direction-audit/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a",
+      "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec",
+      "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81"
+    },
+    {
+      "path": "research/p104-frontier-compression-2/WORD.json.gz",
+      "usage": "input",
+      "git_blob": "cb3aed1d5604eb290f18759b37becaad428ac27a",
+      "sha256": "889f0f5d193d993dabee1e20dcfbcf63f9d88cfe5bd6973d564276c744d1e190"
+    },
+    {
+      "path": "research/p104-native-input-lifting/PROOF.md",
+      "usage": "input",
+      "git_blob": "85499c9eb7b6413f460ef0e77430957ec94e6620",
+      "sha256": "7207c047aa18aa97f304df99057978c37f612ef710f35354216b9956f906fe81"
+    },
+    {
+      "path": "research/p104-native-input-lifting/WORD.json.gz",
+      "usage": "input",
+      "git_blob": "f21f7ac451c3f2e1ae8d5ca1dcad839a0b0d844f",
+      "sha256": "1415a62059ed62d0b4657db91f7ec01b23c117f5f2744746d93c880bd777be92"
+    }
+  ]
+}

research/p104-input-lift-direction-audit/TASK.json

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+{
+  "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": "Independent scalar audit of PR6349 four delayed helper-input lifts: directions, inverse output basis, two dirty-carrier subtractions, and the local native target debit on the PR6314 word.",
+  "scope_change_reason": "The card asks for one uncovered helper cut on a pinned source word. This package does not build a new cut of selected #5599. It audits the published PR6349 lifts, whose source is the PR6314 compression of PR6167, because discussion 1166 comment 19341394 requests that review.",
+  "bottleneck_link": "The local signed target debit H6+3H8-4H9 and paid change H1+H2+H3+2H4-4H5 are necessary for PR6349's reported kappa increase. Confirming them does not admit the outer compiler, native phases, or a new selected frontier.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop if a direction, carrier sandwich, endpoint row, frame inclusion, or the paid/target histogram disagrees with the pinned word. Do not extend the audit into the native Clifford checker or a new lift search.",
+  "outcome": "completed",
+  "evidence": "verify.py endpoint replays, carrier sandwiches, and four failure controls",
+  "author": "unpaidmoon",
+  "ai_assistance": "Substantial Cursor Grok assistance. The predecessor construction and author checks are not this audit.",
+  "open_questions": [
+    {
+      "question": "Do the four changed helper normalizers keep their signed Pauli images and absolute phases at the new charts?",
+      "why_it_matters": "The scalar endpoint and target debit do not discharge native_all_columns. PR6349's kappa claim stays conditional until that gate, the caller, and the other four framework assumptions are checked.",
+      "first_step": "Pin PR6349 head af7cb6c67f8fc7d82a2e4aee2dd2f07481bf6690 and compare one changed helper normalizer, including its absolute phase, against an independent Pauli multiplication on every column of that chart.",
+      "blocked_by": "This package does not run the predecessor native or caller checkers. Those checks remain author-side."
+    },
+    {
+      "question": "Do these four input charts still account for the same target debit after PR6353's nine output contractions?",
+      "why_it_matters": "PR6353 reports a higher conditional kappa on a later word. An input-lift audit of PR6349 does not transfer to that head.",
+      "first_step": "On the frozen PR6353 word, read the initial frames of roles 496, 649, 663 and 508 and recompute only their dim(final)-dim(initial) ranks.",
+      "blocked_by": "PR6353 is a different construction and a separate handoff. Its physical-contact gate is not this package."
+    }
+  ]
+}

research/p104-input-lift-direction-audit/VERIFY.json

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+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/p104-frontier-compression-2/WORD.json.gz",
+    "research/p104-native-input-lifting/PROOF.md",
+    "research/p104-native-input-lifting/WORD.json.gz"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-W",
+        "error",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 60,
+      "checks": "SHA256 pins; four directions and inverses; carrier sandwiches; endpoint rows; paid and target histograms; four failure controls."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-O",
+        "-W",
+        "error",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 60,
+      "checks": "Repeat the same explicit checks with assertion-stripping enabled."
+    }
+  ]
+}