From 5ce86c7c4a96e26d86554c5225984edb3d11e570 Mon Sep 17 00:00:00 2001 From: Claude Date: Thu, 16 Jul 2026 08:38:42 +0000 Subject: [PATCH] =?UTF-8?q?docs:=20=C2=A710=20forward=20synthesis=20?= =?UTF-8?q?=E2=80=94=20one=20WH=20family=20for=20both=20pyramid=20sides=20?= =?UTF-8?q?+=20signature=20as=20trajectory=20checksum=20(probe-gated)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Follow-up to merged #244 (branch restarted from master). Two candidate adoptions for the Morton-tile stacked inverse pyramid, operator-proposed, recorded [H]/[S] with named probes: - [H] One Walsh-Hadamard family for BOTH pyramid sides: OGAR canon already frames the bipolar-phase pyramid's sign side as the WH transform of the address tree; bgz-tensor's proven hadamard_rotate is the same family on the stored-magnitude side (outlier-flattening preconditioner before cheap uniform quantization). Proposal: WHT16 on a 4x4 tile's magnitude vector before nibble quantization; two-algebra rule untouched (the rotation is a coding-side preconditioner, not a merge mode). PROBE-WH-MAG: WHT16+i4/i2 vs direct i4/i2 on real tile magnitudes — the row-level win does not automatically transfer. - [S] Hambly-Lyons signature as the replayable-trajectory checksum: tree-like equivalence = the digest's exact null space — the formal version of "which detours leave no comma" (the §7 X-Trans/comma framing). PROBE-SIG-CHECKSUM on the existing Pillar-11 harnesses (jc forward/converse + hpc/pillar/signature.rs B7). Neither adds a stored field to the tile. Both stay conditional on the §10 honesty ledger; no kill condition touched. Blackboard entry appended. Knowledge-doc suite green (117/117). Co-Authored-By: Claude Fable 5 Claude-Session: https://claude.ai/code/session_01K3RyLEbuNSHxxB3NTTrGki --- .claude/blackboard.md | 9 +++++ .../pr-x12-h268-morton-wgpu-synergies.md | 33 +++++++++++++++++++ 2 files changed, 42 insertions(+) diff --git a/.claude/blackboard.md b/.claude/blackboard.md index a59e666f..044eb289 100644 --- a/.claude/blackboard.md +++ b/.claude/blackboard.md @@ -775,3 +775,12 @@ default is x86-64-v3 (avx2) so ndarray_simd activates on avx512 builds only. certification) + lance-graph jc Pillar 11 (`hambly_lyons.rs`, feature `hambly-lyons` → sigker). Only the ladder→signature MAPPING stays [S]; probe builds on the Pillar-11 harnesses. §8 sentence amended. +- **§10 forward synthesis (operator):** two candidate adoptions for the + tile pyramid, probe-gated — [H] one WH family for both pyramid sides + (OGAR sign side is already WH-of-the-address-tree; bgz-tensor's + hadamard_rotate = same family as magnitude-side preconditioner; + PROBE-WH-MAG = WHT₁₆+i4/i2 vs direct on real tile magnitudes) and + [S] signature-as-trajectory-checksum (tree-like equivalence = the + digest's null space, the formal "which detours leave no comma"; + PROBE-SIG-CHECKSUM on the Pillar-11 harnesses). Neither adds stored + tile fields. diff --git a/.claude/knowledge/pr-x12-h268-morton-wgpu-synergies.md b/.claude/knowledge/pr-x12-h268-morton-wgpu-synergies.md index fee7c304..8131f690 100644 --- a/.claude/knowledge/pr-x12-h268-morton-wgpu-synergies.md +++ b/.claude/knowledge/pr-x12-h268-morton-wgpu-synergies.md @@ -385,6 +385,39 @@ reinterpreted by this section — it names a shared object and its consequences *if* the probe queue passes; nothing here promotes a probe-gated claim to shipped. +**Forward synthesis (operator, 2026-07-16 — [H/S], probe-gated, two new +probe names):** the tile pyramid might adopt two mechanisms from the +fourth-mode/anchor discussion (§8): +- **[H] One Walsh–Hadamard family for BOTH pyramid sides.** OGAR canon + already frames the bipolar-phase pyramid's sign side as the + Walsh–Hadamard transform of the address tree (sign composition = XOR); + bgz-tensor's proven `hadamard_rotate` is the same family applied to the + stored-magnitude side (rotate the residual before i8/i4/i2 so outlier + energy spreads and cheap uniform quantizers work — the standard + incoherence trick). Proposal: Hadamard-rotate a 4×4 tile's 16-cell + magnitude vector (WHT₁₆) before nibble quantization — phase side keeps + address-derived WH signs, magnitude side gains the WH preconditioner; + the two-algebra rule is untouched (sign = XOR, magnitude = bundle; the + rotation is a *coding-side* preconditioner, not a merge mode). + **PROBE-WH-MAG:** reconstruction error of WHT₁₆+i4/i2 vs direct i4/i2 + on real tile magnitudes (bgz-tensor's row-level win does not + automatically transfer to 16-cell tiles). +- **[S] Signature as the replayable-trajectory checksum.** The x264 + contrast in §7 asked for a replayable, checksummable stream; the + Hambly–Lyons signature is the canonical path digest with a uniqueness + theorem, and **tree-like equivalence is the checksum's exact null + space** — the formal version of "which detours leave no comma" + (backtracking excursions vanish; genuine deviations leave non-zero + level-2 area). Both harnesses already exist (jc Pillar 11 + forward/converse probes; this repo's `pillar/signature.rs` B7 + sig-kernel). **PROBE-SIG-CHECKSUM:** truncated signature (depth 2, on + the Pillar-11 harness) of a temporal-stream trajectory as its digest — + verify replay-identity, tree-like edits invisible (correctly), non-tree + perturbations caught. +Both stay conditional on the same ledger above; neither adds a stored +field to the tile (the WH rotation is derivable, the signature is a +derived digest). + ## 11. Cross-references - `pr-x12-h266-h267-standards-landscape.md` — the industry walls, sourced