probe(helix): the ruler reads the address as a NUMBER — intake blindness kills the residue sweep, and "stride 4 isn't golden" is refuted

.claude/board/EPIPHANIES.md

@@ -1,3 +1,21 @@
+## 2026-07-31 — E-THE-RULER-READS-THE-ADDRESS-AS-A-NUMBER-NOT-A-HIERARCHY-1 — the helix intake is structure-blind (kills the residue sweep before it ran), and the "stride 4 isn't golden" suspicion remains NOT CONFIRMED (the 4-ary-matching claim drawn from it is withdrawn)
+
+**Status:** FINDING (measured, 3/3 gates green). **Confidence:** High — pure integer arithmetic over the shipped `CurveRuler`, no sampling. Probe: `crates/helix/examples/probe_hhtl_intake_blindness.rs`; record: `.claude/board/exec-runs/hhtl-intake-blindness.md`.
+
+**Operator anchors:** *"and CLAM to calculate, that's established"* / *"alternative is using HHTL+ helix residue"* / *"exact address, exact spacial location / perturbation"* / *"4x4 usually only helps with an irrational stride as Pythagorean comma"*.
+
+**The queued sweep did NOT run, and not running it is the result.** `PROBE-CLAM-VS-HELIX-RESIDUE` was to test whether a finer address shifts work from stored RESIDUE to deterministic PLACE. Two failure modes were pre-registered before any measurement. Running them first was decisive.
+
+**H1 — the carving cannot reach the ruler (confirmed; fatal to the sweep).** `from_hhtl(path: u64, depth: u8)` has no parameter that could carry a carving, so level structure has no channel into `from_place(p) = p % 17`. Measured: the whole difference between the two carvings is a **constant rotation of 2 across all 256 cells, variance 0**. ⊘ The first gate compared SORTED histograms — sorting discards which cell maps to which offset, and the unsorted histograms genuinely differ, so it passed while hiding that every cell had moved (codex P1 on #876). The ruler cannot distinguish the carvings, so a residue-vs-granularity sweep would return a null *for a reason unrelated to 4⁴*. **Reporting "4⁴ doesn't help the calculator" from that null would have been a false negative manufactured by the intake.** The 4⁴ ADDRESS result (`E-WORDNET-MAKES-THE-4-ARY-ADDRESS-SEMANTIC-1`, 24.71× out-of-cell band lift, 2.47-hop sub-nibble gap) is untouched — this is a finding about the CALCULATOR'S INTAKE.
+
+**H2 — my own "stride 4 isn't golden" suspicion is NOT CONFIRMED; the design claim I drew from that is WITHDRAWN (codex P1 on #876).** The worry: `gcd(4,17)=1` buys coverage, not low discrepancy — stride 4's first four steps `0,4,8,12` are one column of the 4×4 raster, while the φ stride over 17 is 11 (`17/φ = 10.51`; C5 pins 11/17). Since HHTL terminates early, short prefixes are what get consumed. Measured gap spread (lower = more uniform): n=2 → 9 vs **5**(φ); n=3 → 5 vs **1**(φ); **n=4 → 1 vs 5** (stride 4 wins decisively); n=5 → **3** vs 4; n=6 → **3** vs 4. **At n=4 — exactly the prefix a 4-ary tier consumes — stride 4 gives gaps `[4,4,4,5]`, near-perfect tiling, because `4·4 = 16 ≈ 17`.** The comma IS what makes the 4-step prefix uniform. The operator's Pythagorean-comma framing is confirmed in mechanism: stride 4 over **16** covers only 4/16 and retraces one column forever; `17 = 4²+1` is what turns the raster into a sweep. **⊘ But "matched to the 4-ary use case" is withdrawn:** the premise that a 4-ary tier consumes 4 ruler steps is not wired into anything that ships — `ResidueEncoder::encode` reads only `start_offset` (n=1, `residue.rs:157`), `index`/`arc` appear solely in `walk_spectrum` and crate tests, and the shipped `NiblePath` is `FAN_OUT = 16`. The n=4 result is a property of a HYPOTHETICAL consumer. This RETRACTS a suspicion; it does not vindicate a design.
+
+**H3 — the blindness is fixable, so this is a direction, not a dead end.** Per-tier seeding (one ruler per 2-bit group, folded with its level) preserves ancestry by construction: EXHAUSTIVE over all 256·255/2 = 32,640 cell pairs; eligible population **8,064** sharing ≥1 address level; flat intake preserves ancestry in **360/8,064 = 4.4643 %** against a base rate of **1,800/32,640 = 5.5147 %** over ALL pairs — **Δ = −1.05 pp, so no ancestry lift at all**, and in fact mildly ancestry-AVERSE (prefix-sharing cells are numerically close, hence less likely to be congruent mod 17); per-tier **8,064/8,064 = 100 % by construction** (a construction check, not evidence). The criterion is a **declared null model** (H0 = the flat seed carries no ancestry information ⇒ eligible rate must not exceed base rate), replacing a hand-tuned `< 0.25` that 24.9 % would have passed (CodeRabbit). Its first formulation — "the rates coincide" — FAILED on contact and was itself corrected: they diverge, so the gate now asserts only the true, weaker claim. ⊘ **The denominator was wrong TWICE:** first "4,662" (counter incremented before the eligibility check — codex P2), then "1,152" (the eligible *thinned sample* mislabelled as the *population* — CodeRabbit). Root cause of both: a `(a+b) % 7` thinning that bought nothing. Removing it eliminates the class of error, and the reviewer independently reproduced 360/8,064. The unblock is to feed the ruler the address's HIERARCHY, not its integer value — a helix API change that needs its own review.
+
+**The transferable rule:** *a calculator's INTAKE can silently discard the very structure a probe is trying to measure.* Check what the consumer actually reads before running a sweep over what the producer emits — otherwise a null measures the seam, not the hypothesis. This is the same shape as the falsifier-defect pattern (four instances now: the non-falsifying shuffle, the hair-wide twin window, the inert cover guard, and — self-caught here — an H3 loop that sampled 0 pairs because `256 as u8 == 0` and correctly FAILED rather than passing on zero evidence).
+
+**Boundaries:** properties of the RULER only (integer arithmetic over 17). No residue encoded, no CLAM comparison, no cost measured. Brief-gates AGREEMENT and COST remain NOT RUN — blocked on H1, not skipped. H2 compares two strides on gap-spread; it does not claim stride 4 is optimal, only that it is not the defect suspected.
+
 ## 2026-07-30 — E-WORDNET-MAKES-THE-4-ARY-ADDRESS-SEMANTIC-1 — the 4⁴ fold turns HHTL adjacency into a *semantic* prior, and the sub-nibble rung is load-bearing (2.47 hops the 16-ary router cannot address)
 
 **Status:** FINDING (measured, 5/5 gates green on real WordNet 3.1). **Confidence:** High for the structure claim; explicitly NOT extended to embedding-trained codebooks (see Boundaries). Probe: `crates/lance-graph-contract/examples/probe_wordnet_44_activation.rs`; record: `.claude/board/exec-runs/wordnet-44-activation.md`.

.claude/board/exec-runs/hhtl-intake-blindness.md

@@ -0,0 +1,145 @@
+# PROBE-HHTL-INTAKE-BLINDNESS (PROBE-CLAM-VS-HELIX-RESIDUE leg 0) — execution record
+
+Follows the merged `PROBE-WORDNET-44-ACTIVATION` (#875,
+`E-WORDNET-MAKES-THE-4-ARY-ADDRESS-SEMANTIC-1`). Operator ruling fixed the
+division of labour: the 4⁴ fold is the ADDRESS, **CLAM is the established
+CALCULATOR**, **HHTL + helix residue** is the alternative — *"exact address,
+exact spacial location / perturbation"*.
+
+## Files
+- NEW `crates/helix/examples/probe_hhtl_intake_blindness.rs` (3 gates).
+- Board: `EPIPHANIES.md` prepend, this file. Same commit (board-hygiene rule).
+
+## Core-First compliance
+CONSUMES `helix::curve_ruler::CurveRuler` — nothing re-derived. helix is in-tree
+at `crates/helix` (standalone crate, own workspace) and already ships the seam:
+`from_hhtl(path, depth)` → place; `index(k) = (start + STRIDE·k) mod MODULUS`
+regenerates the interior; `ResidueEdge`/`Signed360` are the stored residue.
+
+## The sweep was NOT RUN — and that is the finding
+
+The queued hypothesis (finer address ⇒ more deterministic place ⇒ less stored
+residue) was gated behind two PRE-REGISTERED failure modes. Both were run first,
+exactly as the brief required. One is fatal to the sweep; the other is NOT CONFIRMED (a suspicion retracted, not a hypothesis disproven).
+
+### H1 — the carving cannot reach the ruler (failure mode (a): CONFIRMED, fatal)
+
+Two halves. **Type-level (stated, not measured):** `from_hhtl(path: u64,
+depth: u8)` has no parameter that could carry a carving, so level structure has
+no channel into `from_place(p) = p % 17`. **Empirical (the gate):** the entire
+difference between the two carvings, as the ruler sees it, is a **constant
+rotation of 2 across all 256 cells, variance 0** — a cell-dependent shift is the
+falsifier. Unsorted histograms:
+
+```text
+4-ary  (depth 4): [15,15,15,15,16,15,15,15,15,15,15,15,15,15,15,15,15]
+16-ary (depth 2): [15,15,16,15,15,15,15,15,15,15,15,15,15,15,15,15,15]
+```
+
+> **⊘ Gate corrected pre-merge (codex P1 on #876).** The first version sorted
+> both histograms and compared multisets. Sorting discards which cell maps to
+> which offset, and the UNSORTED histograms genuinely differ — so the gate
+> passed while hiding that every cell had moved. An aggregate distribution does
+> not establish per-cell invariance; the constant-shift measurement does.
+
+**Consequence: a residue-vs-granularity sweep cannot carry signal.** Its null
+would have been a false negative caused entirely by the intake, and reporting
+"4⁴ doesn't help the calculator" from it would have been wrong. Reported as an
+INTAKE finding, per the pre-registration. The 4⁴ ADDRESS result is untouched.
+
+### H2 — stride 4 vs the φ stride 11 (failure mode (b): NOT CONFIRMED)
+
+The suspicion: `gcd(4,17)=1` buys coverage, not low discrepancy; stride 4's
+first four steps `0,4,8,12` are one column of the 4×4 raster, while the φ stride
+over 17 is 11 (`17/φ = 10.51`; C5 pins 11/17 as the golden step). Since HHTL
+terminates early, short prefixes are what get consumed.
+
+Measured gap spread (max−min gap; lower = more uniform):
+
+| n | stride 4 | gaps | stride 11 (φ) | gaps |
+|---|---|---|---|---|
+| 2 | 9 | [4,13] | **5** | [6,11] |
+| 3 | 5 | [4,4,9] | **1** | [5,6,6] |
+| **4** | **1** | **[4,4,4,5]** | 5 | [1,5,5,6] |
+| 5 | **3** | [1,4,4,4,4] | 4 | [1,1,5,5,5] |
+| 6 | **3** | [1,1,3,4,4,4] | 4 | [1,1,1,4,5,5] |
+
+At n=4 stride 4 is near-perfect (spread 1) and beats φ (spread 5); `4·4 = 16 ≈ 17`.
+
+> **⊘ DESIGN CLAIM WITHDRAWN (codex P1 on #876).** The first version concluded
+> "the shipped constants are MATCHED to the 4-ary use case". That premise — that
+> a 4-ary tier consumes 4 ruler steps — is **not wired into anything that
+> ships**: `ResidueEncoder::encode` reads only `start_offset` (n=1,
+> `residue.rs:157`); `index`/`arc` appear solely in `walk_spectrum` and this
+> crate's tests; the shipped `NiblePath` is `FAN_OUT = 16`. The n=4 comparison is
+> therefore a property of a HYPOTHETICAL consumer. What survives: the
+> pre-registered suspicion is **NOT CONFIRMED** — a retraction of a concern, not
+> a vindication of a design.
+
+Operator framing that produced this check: *"4x4 usually only helps with an
+irrational stride as Pythagorean comma."* Confirmed in mechanism — stride 4 over
+**16** covers only 4/16 (retraces one column forever); the `+1` is the comma.
+
+### H3 — the blindness is FIXABLE at the intake, not fundamental
+
+Per-tier seeding (one ruler per 2-bit group, folded with its level) preserves
+ancestry by construction. **EXHAUSTIVE over all 256·255/2 = 32,640 cell pairs —
+no sampling, no thinning.** Eligible population = **8,064** pairs sharing ≥1
+address level: **flat intake preserves ancestry in 360/8,064 = 4.4643 %** against a base rate
+of **1,800/32,640 = 5.5147 %** over ALL pairs — Δ = **−1.05 pp**, i.e. the flat
+seed gives **no ancestry lift at all** and is in fact mildly ancestry-AVERSE
+(cells sharing an address prefix are numerically close, so they are *less* likely
+to be congruent mod 17). **Per-tier: 8,064/8,064 = 100 % BY CONSTRUCTION**,
+asserted as a construction check rather than as evidence.
+
+The acceptance criterion is a **declared null model**, not a threshold: H0 = "the
+flat seed carries no ancestry information", so the eligible rate must not EXCEED
+the base rate. Falsifier: an eligible rate materially above base, which would
+mean the flat seed *does* carry ancestry.
+
+> **⊘ THRESHOLD REPLACED (CodeRabbit on #876).** The gate was `flat_rate < 0.25`
+> — hand-tuned, and 24.9 % would have passed it while the prose claimed ≈1/17.
+> Replaced with the null-model comparison above. Running it immediately FAILED
+> the first formulation ("the two rates coincide"), which was itself wrong: the
+> rates do not coincide, they diverge by −1.05 pp. The gate now states the true
+> and weaker claim — no lift — and the direction is reported rather than assumed. The unblock is to feed the ruler the
+address's HIERARCHY, not its integer value.
+
+> **⊘ SAMPLE SIZE CORRECTED TWICE (codex P2, then CodeRabbit, both on #876).**
+> (1) The counter incremented BEFORE the `k > 0` eligibility check, so the
+> published "4,662 pairs sharing ≥1 address level" was really every thinned pair.
+> The ≈23× ratio was arithmetic on a mislabelled denominator. (2) The *fix* then
+> repeated the error one level up: 1,152 was the eligible **thinned sample**, not
+> the eligible **population**. Root cause of both: a `(a+b) % 7` thinning that
+> bought nothing — 32,640 pairs is trivial to enumerate. **The thinning is
+> removed**, so there is no sample left to mislabel; the figures are now the full
+> population, 360/8,064 = 4.5 %, independently reproduced by the reviewer.
+
+## Verification
+- `cargo run --release --manifest-path crates/helix/Cargo.toml --example
+  probe_hhtl_intake_blindness` → ALL GATES GREEN.
+- `cargo clippy --manifest-path crates/helix/Cargo.toml --example
+  probe_hhtl_intake_blindness -- -D warnings` → clean.
+- `cargo fmt --manifest-path crates/helix/Cargo.toml` → applied.
+
+## A self-caught vacuous gate (kept in the record)
+H3's first run sampled **0 pairs** and correctly FAILED: `for a in 0..CELLS as u8`
+where `CELLS = 256`, and `256 as u8 == 0`, so the loop was empty. Had the gate
+been written to pass on an empty set it would have reported success on zero
+evidence. Iterating in `u16` fixed it. Fourth instance in this arc of a defect
+living in the falsifier rather than the measurement.
+
+## Honest boundaries
+- H1/H2/H3 are properties of the RULER (integer arithmetic over 17). No residue
+  was encoded, no CLAM comparison ran, no cost was measured.
+- Gates (1) AGREEMENT and (2) COST from the #66 brief remain NOT RUN — they are
+  blocked on H1 being addressed, not skipped.
+- H2 compares two strides on gap-spread only; it does not claim stride 4 is
+  optimal, only that it is better than φ at n=4..6 and therefore not the defect
+  the pre-registration suspected.
+
+## Follow-ons
+- Decide whether to extend the ruler with a per-tier intake (H3 shows it works).
+  That is a helix API change and needs its own review — NOT done here.
+- Once the intake sees hierarchy, the original residue-vs-granularity sweep
+  becomes meaningful and gates (1)+(2) can run.