AdaWorldAPI · AdaWorldAPI · Sep 15, 2026 · Sep 15, 2026 · Sep 15, 2026 · Sep 15, 2026
diff --git a/.claude/board/EPIPHANIES.md b/.claude/board/EPIPHANIES.md
@@ -1,3 +1,144 @@
+## 2026-09-15 (5) — E-THE-99-90-PERCENT-IS-1023-OVER-1024-THE-CLUSTERED-SKIP-SATURATES-A-256x256-TILE-RATHER-THAN-APPROACHING-IT-1 — §8a's best measured order is the tile's arithmetic ceiling, so 256×256 is the skip's UNIT and not the fixture's accident
+
+**Status:** FINDING. Arithmetic over an already-recorded measurement — no new
+measurement was taken, and none is claimed.
+**Confidence:** HIGH on the identities (each is one line of arithmetic, restated
+below so a reader can check them without running anything); the pairings in
+§"8 B to 128 KiB" and §"why not bigger" are structural readings of numbers
+measured elsewhere and cited to their source.
+
+### The identity
+
+`adaptive_order_probe.rs` measures the clustered regime's best ordering at
+**99.90 %** of words skipped (§8a, `crates/lance-graph-quack/src/lib.rs`; the run is
+65 536 rows × five conjuncts × all 120 orderings). The skip's granularity is the
+**64-row word** — `MaskOp::Pred`'s own doc states it (`crates/lance-graph-mask-risc/src/ir.rs:88-94`:
+*"Its granularity is the facade's: 64-row WORDS"*), and `ndarray`'s `pack_under`
+is where it physically happens (`simd_masking_ops.rs:1541-1546`).
+
+65 536 rows ÷ 64 = **1024 words**, and
+
+```
+1023 / 1024 = 0.9990234…  →  99.90 %
+```
+
+The measured figure is not near the ceiling. It **is** the ceiling: one live word
+out of 1024, the least a non-empty mask can occupy. The probe's own `skipped_words`
+ramp says the same thing a second way — `[4092, 3069, 2046, 1023, 0]`, where
+`4092 = 4 × 1023` exactly and every adjacent delta is `−1023`. One unit, counted
+four times down to zero.
+
+So there is **no tuning headroom above 99.90 % on a 256×256 tile**, and a future
+session trying to push past it is chasing an arithmetic impossibility rather than
+an unoptimised path.
+
+### What that reframes
+
+256×256 stops being the fixture's geometry and becomes the skip's **unit**: a tile
+is exactly 1024 skip-units, and an address prefix collapses it to one. The tile and
+the word ladder are one object counted twice (65 536 bits ÷ 64).
+
+The complement is equally exact and is already in the quack doc: at 21.8 % survival
+with survivors SCATTERED a word is all-dead with probability `0.78163⁶⁴ ≈ 1.42e-7`,
+so no ordering skips anything. Contiguity, not density — and the two ends of that
+statement are both closed-form.
+
+### The carriers hand off at 10 bits of 16
+
+A 16-bit tile coordinate against 64-row words splits **10 / 6**: the top 10 bits
+select the word, the bottom 6 select a bit inside it. So descending a prefix buys
+skip for exactly 10 bits and then stops — the last 6 bits are structurally
+invisible to a mask carrier however precisely they are named, because they never
+cross a word boundary.
+
+That is a ceiling, not a defect, and it says where the mask form stops being the
+right carrier. Above 10 bits the skip does the work; below it the mask cannot
+discriminate at all.
+
+### Both questions have an 8-byte form; what differs is the CONDITION
+
+| reading | size | answers |
+|---|---|---|
+| literal mask | **8 KiB** | *which* cells — ANY subset |
+| prefix range (`Cmp::MatchU32`'s pattern+care) | **8 B** | *which* cells — a STRUCTURED subset |
+| `FisherZTable` materialized (i8, k=256) | **64 KiB + 8 B** | *how far* — one load |
+| `FamilyGamma` alone | **8 B** | *how far* — PARAMETERS, plus `atanh`/`tanh` + affine |
+
+`le-contract.md` §"The canonical cosine/centroid replacement is ANALYTIC" is
+explicit that **"a materialized k×k table is a CACHE of the formula, never the
+canon"**, the canon being `bgz-tensor::fisher_z` (cosine → `atanh` → per-family
+affine → normalized i8; certified ρ≥0.999, `E-PALETTE-NNUE-COSINE-GREEN-1`).
+Verified in source rather than from that prose: `FamilyGamma { z_min: f32,
+z_range: f32 }` with `BYTE_SIZE = 8`, and `FisherZTable { entries: Vec<i8>, k,
+gamma }` whose `byte_size()` is `k*k + 8` — so at k=256 the materialized form is
+**64 KiB + 8 B**, entries at ONE BYTE each because the codec's output grade is
+the normalized i8. The palette index is 8 BITS; the family's affine is 8 BYTES;
+they are different objects and this table keeps them apart.
+
+**The 8 B is parameters, not answers.** A distance from `FamilyGamma` still costs
+an `atanh`/`tanh` and the affine — it is compute-versus-table, not a smaller
+answer. Quoting the two sizes without that is the elision this row exists to
+prevent.
+
+**And the mask's compact form exists too — for STRUCTURED sets.** A prefix range
+is `Cmp::MatchU32 { pattern, care }`, 8 bytes of the same order as the gamma, and
+matrix row R5 says the same of DuckDB's `SequenceVector` ("a contiguous range to
+3 scalars", which DuckDB then throws away at the first predicate and V3 keeps).
+So the asymmetry is NOT metric-compacts / set-does-not:
+
+- *how far* compacts UNCONDITIONALLY — a metric is a function of two coordinates,
+  so a formula always exists and the 8 bytes are its parameters.
+- *which* compacts CONDITIONALLY — only when the set is structured. An arbitrary
+  subset of 65 536 cells is one of 2^65536 and has no compact form at all.
+
+The clustered regime of §8a **is** the structured case (its conjunct is an address
+prefix), so in exactly the regime this entry is about, both carriers have their
+8-byte form and the 8 KiB / 64 KiB materializations are the caches.
+
+⊘ An earlier draft of this section, corrected before merge: it gave the
+materialized LUT as **128 KiB** and claimed the mask has no analytic form. The
+128 KiB u16 figure is `E-X265-PROBE-GPU-LUT-1`'s GPU table — a DIFFERENT object
+from `bgz-tensor`'s i8 `FisherZTable`, matched on "256² LUT" and carried across.
+The no-analytic-form half was true of arbitrary sets and false of the prefix
+ranges the entry is otherwise entirely about.
+
+### Why 256×256 and not bigger — the bound is measured, elsewhere
+
+D-GTM-0n measured chained ternlog paying (`T3/T1 → 0.50` by K=8) **only while the
+masks stay L2-resident**, with the ratio back to `1.03` at a **512 KiB** mask
+(`STATUS_BOARD.md` D-GTM-0n / P3; the bound rides with the number and may not be
+dropped when it is cited).
+
+`512 KiB / 8 KiB = 64`. A 512 KiB mask at one bit per cell is 4 194 304 rows —
+**2048×2048**. So the tile at which chaining stops paying is exactly 8× per side
+from the one that works, and 256×256 sits 64× inside the measured-good band.
+That is a coincidence worth naming precisely because it is *not* load-bearing yet:
+nothing measured a tile-size sweep, and D-GTM-0n's fixture is not §8a's.
+
+### What this does NOT say
+
+- **Not that the skip is good in general.** §8a's permissive (94.3 %) and moderate
+  (21.8 %) rows are `0.00 % → 0.00 %` and are unchanged by anything here. The
+  ceiling is reachable only under the three conditions
+  `E-FUSING-FORFEITS-THE-SKIP-AND-ADAPTIVEFILTER-FAILS-IN-TWO-PLACES-NOT-ONE-1`
+  names: gated lowering × plane-free conjunction × contiguous survivors.
+- **Not a claim about the facet carrier.** The 12-byte `6 × (u8:u8)` facet is not a
+  compressed mask — it expresses six points, never a set — and nothing measured
+  here ranged over it. `E-CAM96-DISTRIBUTION-MEASURED-1` is a ranking result and
+  stays one.
+- **Not an identification of a facet RAIL with a cascade TIER.** Both are two
+  bytes and both index a 256×256 tile; the path carries three, the facet six.
+  Shape identity, not object identity. The 10/6 split above is arithmetic on a
+  16-bit index against a 64-row word and needs neither of those namings.
+- **Not a measurement.** Every number above is either re-stated from §8a /
+  D-GTM-0n / E-X265-PROBE-GPU-LUT-1 with its source, or one line of arithmetic on
+  such a number. The contribution is the identity, not the data.
+
+**Cross-ref:** `E-FUSING-FORFEITS-THE-SKIP-AND-ADAPTIVEFILTER-FAILS-IN-TWO-PLACES-NOT-ONE-1`
+(2026-09-15 (4)) — the conditions under which the lever exists at all, and the A1
+seed/loop split; `ISS-QUACK-AND-BY-SKIP-IS-INERT-UNDER-A-PLANE`; `ISS-NO-MASK-HOP-OP`
+(the hop that would consume a saturated gate still does not exist).
+
 ## 2026-09-15 (4) — E-FUSING-FORFEITS-THE-SKIP-AND-ADAPTIVEFILTER-FAILS-IN-TWO-PLACES-NOT-ONE-1 — the fused lowering is order-independent BY CONSTRUCTION, two readers derived it from source because the crate doc does not say so, and DuckDB's A1 turns out to have a dead seed as well as an unrunnable loop
 
 **Status:** FINDING. Convergent — derived independently in two sessions from the same

diff --git a/CLAUDE.md b/CLAUDE.md
@@ -412,6 +412,49 @@ anti-pattern. The 2026-04-20 session surfaced this gap between
 PR #223/#224/#225 merges and the LATEST_STATE / PR_ARC update;
 this rule exists so it does not recur.
 
+### The matching rule (P0, operator-ruled 2026-09-15 — 5 instances in one session)
+
+**Matching without reading is strictly prohibited.** A shared surface feature —
+a width, a count, a phrase, a file path, a name — is never evidence that two
+things are the same thing. **Before claiming A tells you about B, read B.**
+
+Measured instances, all in one session
+(`E-I-GRAFTED-HELIX-ONTO-HEXAGON-AND-THEN-DEPRECATED-THE-OPERATORS-TENANTS-ON-MY-OWN-AUTHORITY-1`
+carries 1–3 with their censuses):
+
+| # | matched on | transferred | what B actually was |
+|---|---|---|---|
+| 1 | `6 B == 6 rails` | helix residue → a Hexagon synapse surface | 6 B is ONE 48-bit `Signed360` sphere angle (`canonical_node.rs:868-871`) |
+| 2 | `48 bit == 48 bit` | cam_pq's ranking result → `HelixResidue` | the measurement never ranged over `HelixResidue` |
+| 3 | the words "multi-hop" | jc's synthetic-SPD EWA bound → graph recall | that pillar never traverses a graph |
+| 4 | a citation in a neighbouring entry | `le-contract.md:160-170` cited for the LUT | `:160-170` is CausalEdge64 residual carriers; the LUT section starts at `:169` |
+| 5 | the phrase "256² LUT" | 128 KiB u16 → `bgz-tensor`'s Fisher-z canon | that table is `Vec<i8>`, `byte_size() = k*k + 8` → 64 KiB + 8 B |
+
+**Instances 2, 4 and 5 occurred INSIDE the correction of 1, 3 and 4.** The rule
+therefore binds the correction as hard as the claim; a retraction written by
+matching is another instance, not a fix.
+
+Consequences, non-negotiable for new work:
+
+- **A cardinality is not a mapping.** Two things being six wide, or 48 bits, or
+  `256²` says nothing about whether they are the same object. Shape identity is
+  not object identity — state it that way when both are true.
+- **Name the read, not the match.** A claim of the form "A tells you about B"
+  must name the measurement, declaration, or line that ranged over **B**. If the
+  only thing that ranged over B is a resemblance to A, there is no claim yet.
+- **A citation you did not open is not a citation**, including one copied from a
+  neighbouring entry that looked authoritative. Copying a `path:line` forward
+  without reading the target is instance 4 exactly.
+- **Prefer the precise form, because precision is what makes a claim
+  falsifiable.** Instance 4 was invisible while the path was partial
+  (`UNVERIFIABLE`); widening it to repo-relative is what let
+  `citation_decay.py` check it and fail. A vaguer citation is not safer — it is
+  merely unfalsifiable.
+- **Grep is a heuristic for presence, never a proof of absence** — the prior
+  statement of one corner of this rule
+  (`E-ABBREVIATION-GREP-MANUFACTURED-AN-ABSENCE-1`), kept here because it is the
+  same move in the other direction: a non-match read as evidence.
+
 ### `SUPERSESSION-INDEX.md` is generated and CI-gated — never hand-edit it
 
 `.claude/board/SUPERSESSION-INDEX.md` is produced by