docs: §10 forward synthesis — one WH family for both pyramid sides + signature as trajectory checksum (probe-gated)#245
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…signature as trajectory checksum (probe-gated) 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 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01K3RyLEbuNSHxxB3NTTrGki
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Summary
Follow-up to merged #244 (branch restarted from master). Records the operator-proposed forward synthesis in the §10 honesty-ledger area of the matrix doc, graded and probe-gated:
hadamard_rotateis the same transform family on the stored-magnitude side (the standard outlier-flattening/incoherence preconditioner before cheap uniform quantization). Proposal: WHT₁₆ on a 4×4 tile's 16-cell magnitude vector before nibble quantization — the two-algebra rule is untouched (the rotation is a coding-side preconditioner, not a merge mode). PROBE-WH-MAG named: 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.pillar/signature.rsB7). PROBE-SIG-CHECKSUM named on those harnesses.Neither proposal adds a stored field to the tile. Both stay conditional on the standing §10 ledger; no kill condition touched. Blackboard entry appended. Twin board entry: lance-graph
E-WH-TWO-SIDES-SIG-CHECKSUM-1.Verification
bgz-tensor/src/adaptive_codec.rs::hadamard_rotate,jc/src/hambly_lyons.rs,src/hpc/pillar/signature.rs.🤖 Generated with Claude Code
https://claude.ai/code/session_01K3RyLEbuNSHxxB3NTTrGki
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