docs(v3): Fisher-z analytic codec ruled THE canonical cosine/centroid replacement; helix : Fisher-2z :: cosine-replacement : Fisher-z

.claude/board/EPIPHANIES.md

@@ -1,3 +1,11 @@
+## 2026-07-16 — E-FISHERZ-CANONICAL-COSINE-REPLACEMENT-1 — THE canonical cosine/centroid replacement = the analytic Fisher-z codec (FamilyGamma, no materialization); helix : Fisher-2z :: cosine-replacement : Fisher-z
+
+**Status:** OPERATOR RULING (2026-07-16) + FINDING for the grounding identity. No layout changed; the L4 semantics are sharpened, not altered.
+**Ruling 1 — the canon:** the workspace's canonical cosine/centroid replacement is the **analytic Fisher-z codec** — `bgz-tensor::fisher_z::{FamilyGamma, FisherZTable}`: cosine → `atanh` → per-family affine (`FamilyGamma` = 8 bytes) → normalized i8; hydrate via `tanh`. Certified ρ≥0.999 (21 roles) + E-PALETTE-NNUE-COSINE-GREEN-1 (ρ_all 0.99971) with the standing rule "for RANKING you never materialize — read the Fisher-z distance directly." Consequences: (a) L4 "cosine-replacement palette256" reads through THIS canon — a materialized k×k table (bgz17's explicit 256², the FisherZTable buffer) is a **CACHE of the formula, an adapter — never the canon**; ranking = raw-i8 monotone compares, distance = |Δi8|·(z_range/254), i8 SIMD (VNNI/`matmul_i8_to_i32`/wasm i8x16) applies at 4× f32 density with F16/F32-equivalent RANK fidelity (measured; reconstruction-grade beyond the certified corpora stays [H]). (b) The "no residue" scoping is intrinsic: cosine-valued quantities are bounded and single-scale — the i4+i2 ladder and Passthrough exist for unbounded heavy-tailed rows, not for this lane. (c) HONEST BOUNDARY: Fisher-z replaces the distance/rank READ, not the semiring COMPOSE (tanh(z_a)·tanh(z_b) ≠ tanh(z_a+z_b)); multi-hop keeps the compose table.
+**Ruling 2 — the ladder:** **helix is to Fisher-2z what the cosine-replacement is to Fisher-z.** Grounded in shipped, tested code, not analogy: helix pins `hyperbolic_depth = 2·fisher_z` as an identity at 1e-15 (`crates/helix/src/fisher_z.rs:110-121` — 2·arctanh(s) = ln((1+s)/(1−s)), the hyperbolic/Poincaré depth), and the residue pipeline names the Fisher-Z arctanh as its ONE transcendental (`crates/helix/src/simd.rs:3-4`, `batch_fisher_z`). So: **1z = the similarity scale** (FamilyGamma-normalized i8, the cosine/centroid replacement); **2z = the hyperbolic location/depth scale** (the helix residue register; `Signed360` doubles the hemisphere — bidirectional full-sphere over the same analytic pipeline). Same pattern at both rungs: variance-stabilized transform → normalized small-int register → formula hydration → zero materialization.
+**Queued follow-up:** extract the `FamilyGamma` contract (2×f32 + encode/decode formulas, BBB-safe zero-dep) from bgz-tensor into `lance-graph-contract` so consumers (L4 ClassViews, ndarray SpoDistanceMatrices analytic planes, thinking-engine lenses, stockfish-rs) speak the canon without the bgz-tensor dep; i8 SIMD kernels stay ndarray-side per the hardware/thinking split. [H] until shipped.
+**Cross-ref:** E-PALETTE-NNUE-COSINE-GREEN-1 (the certification), E-PALETTE-RESIDUAL-LADDER-1 (the ladder this lane does NOT need), E-H268-PROBE-WAVE-1-RESULTS (survivors context), le-contract §3 L4 row + the new canonical-note subsection, `encoding-ecosystem.md` (codec map), TD-BGZ-TENSOR-PRE-LANE-REVIEW (the extraction follow-up feeds its outcome). ndarray §8 mirror folds into the next ndarray doc pass.
+
 ## 2026-07-16 — E-H268-PROBE-WAVE-1-RESULTS — three H.268 conjectures measured: WH-tile NEUTRAL/not-transferring, signature-checksum PASS (depth-2 blind spot), walk-spectrum KILL of §10(g)'s "decorrelated" half
 
 **Status:** FINDING (three probes run against shipped code, deterministic seeds, Opus-adjudicated; grades E-WH-TWO-SIDES-SIG-CHECKSUM-1 legs 1+2 and §10(g); plan `h268-probe-wave-v1.md`). No canon changed; one claim-leg CLOSED NOT-TRANSFERRING, one KILLED, one PASSes with a bounded caveat.

.claude/v3/soa_layout/le-contract.md

@@ -154,6 +154,25 @@ facet payloads, lens-selected per class. Consequences:
   `edges[16B]` block in the CANON node is untouched by this (it is
   one-byte SLOT refs, not packed mantissas).
 
+### The canonical cosine/centroid replacement is ANALYTIC (operator, 2026-07-16)
+
+L4's "cosine-replacement palette256" reads through the **analytic Fisher-z
+codec** (`bgz-tensor::fisher_z::{FamilyGamma, FisherZTable}` — cosine →
+`atanh` → 8-byte per-family affine → normalized i8; hydrate via `tanh`;
+certified ρ≥0.999, E-PALETTE-NNUE-COSINE-GREEN-1). **A materialized k×k
+table is a CACHE of the formula, never the canon**: ranking compares raw
+i8 (monotone), distance is `|Δi8|·(z_range/254)`, and hydration is one
+affine + `tanh` — so an L4 ClassView may declare an analytic codebook
+(the 8-byte gamma) with zero table materialization. Boundary: this
+replaces the distance/rank READ; the semiring COMPOSE keeps its table
+(z-addition does not compose cosines). The location-side sibling, one
+rung up: **helix is to Fisher-2z what the cosine-replacement is to
+Fisher-z** — helix pins `hyperbolic_depth = 2·fisher_z` as a tested
+identity (`crates/helix/src/fisher_z.rs:110-121`) and runs its residue
+pipeline on that doubled scale (`Signed360` = the hemisphere-doubled
+register). Canonical ruling text: EPIPHANIES
+`E-FISHERZ-CANONICAL-COSINE-REPLACEMENT-1`.
+
 ### CAM_PQ grounding (digital vs analog)
 
 CAM_PQ's codebook is the **DeepNSM 4096-word English-native-speaker