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openresearch bd33007440 docs(research): chiral invariance — CRT Sidon check is chiral-invariant 
20,000 random trials found no boundary case. The chiral flip
(S-a vs a-S mod L) is a ring automorphism (negation) that preserves
the Sidon property. All chiral configs give the same Sidon result.

Proof: (a-S) mod L = -(S-a) mod L. The negation x→-x preserves
collision structure (x≡-x iff 2x≡0, same condition for both).

Implication: the chiral filter is trivial for CRT sums. It matters
for dual quaternion products (which involve multiplication, not
just addition). Next step: implement dual quaternion Sidon filter.
2026-07-04 20:35:35 +00:00
..
AUTOPROOF_INFRASTRUCTURE.md docs: document autoproof infrastructure + update plan 2026-07-04 02:42:43 -05:00
braid_group_action.md feat(braid/dag): land untracked research WIP + register 4 formal libs; ignore build artifacts 2026-07-03 15:11:37 -05:00
BRAIDSTORM_TREEBRAID_COUCH.md docs(research): BraidStorm × TreeBraid × COUCH chiral batch pipeline 2026-07-04 19:38:41 +00:00
CAPABILITY_GRID_MAPPING.md chore: commit all pending work from prior sessions 2026-06-30 04:54:40 -05:00
CHIRAL_BATCH_ENCODING.md docs(research): BraidStorm × TreeBraid × COUCH chiral batch pipeline 2026-07-04 19:38:41 +00:00
CHIRAL_CRT_MULTIPLEXING.md docs(research): chiral CRT multiplexing — Qwen 3.7 Max formalization 2026-07-04 19:42:07 +00:00
CHIRAL_INVARIANCE_FINDING.md docs(research): chiral invariance — CRT Sidon check is chiral-invariant 2026-07-04 20:35:35 +00:00
COLLECTIVE_INTELLIGENCE_OPTIMIZATION.md chore: commit all pending work from prior sessions 2026-06-30 04:54:40 -05:00
COMPRESSION_HONEST_FINDINGS.md docs(compression): add pi-as-tape-LUT coda (offset = data size, base conversion) 2026-07-03 15:56:01 -05:00
CONSERVATION_LAW_CORRECTION.md feat: implement CMYK coloring generator, autoproof infrastructure, and conservation fix 2026-07-04 01:05:14 -05:00
FIXEDPOINT_BRIDGE_DESIGN.md chore: commit all pending work from prior sessions 2026-06-30 04:54:40 -05:00
GERVER_SIDON_DESIGN.md feat: q-profile sweep + Gerver Sidon design + report 2026-07-04 14:50:28 +00:00
HCMR_CRT_MULTIPLEXER.md docs(research): HCMR × chiral CRT multiplexer — performance model 2026-07-04 19:46:15 +00:00
INVARIANT_COMPUTATION_GEOMETRY.md docs: invariant computation geometry — the unifying vision 2026-07-03 22:08:56 +00:00
iteration_dag.md feat(braid/dag): land untracked research WIP + register 4 formal libs; ignore build artifacts 2026-07-03 15:11:37 -05:00
iteration_regime.md feat(braid/dag): land untracked research WIP + register 4 formal libs; ignore build artifacts 2026-07-03 15:11:37 -05:00
MERGED_O1_TRANSFORM.md docs: explore merged O(1) transform — DNA as unified search-reconstruct-verify 2026-07-03 21:58:32 +00:00
NEXT_STEPS_PLAN.md docs: document autoproof infrastructure + update plan 2026-07-04 02:42:43 -05:00
O1_TRANSFORMS.md docs: document three O(n)→O(1) transforms + unification analysis 2026-07-03 21:54:46 +00:00
OCTAGON_PRINCIPLE.md docs: formal literature — octagon question answered at O(n^2) 2026-07-03 21:49:45 +00:00
PRIME_SIDON_NEGATIVE_RESULT.md chore(prime-sidon): documented negative result — primes indistinguishable from random in Sidon sum-degeneracy 2026-07-03 18:16:42 -05:00
REACTION_PRIMES.md docs: reaction primes — algebraic irreducibility for DNA computation 2026-07-03 22:00:21 +00:00
RENDERING_EQUATION_OBSERVERLESS.md docs(research): rendering equation as observerless observer 2026-07-04 20:00:51 +00:00
sidon_preservation_creation.md feat(lean): modular Sidon preservation theorem + meta-review fixes 2026-07-04 01:05:15 -05:00
SIDON_SOFA_COLORING.md fix(research): remove Direction F (OISC CMYK) — references abandoned infrastructure 2026-07-04 01:05:14 -05:00
SIDON_SOFA_COLORING_REVIEW.md docs: add SLOS disclaimer + clarify review count 2026-07-04 02:39:57 -05:00
SIX_STAGE_SEARCH_ENGINE.md docs(research): six-stage resource-aware search engine 2026-07-04 20:18:21 +00:00
SLOS_SIDON_VERIFICATION_RECEIPT.md feat(lean): modular Sidon preservation theorem + meta-review fixes 2026-07-04 01:05:15 -05:00
TOROIDAL_POLOIDAL_REFINEMENT.md feat: import photonic Sidon search from special branch 2026-07-04 02:27:40 -05:00
unified_crt_torus_dag.md feat(braid/dag): land untracked research WIP + register 4 formal libs; ignore build artifacts 2026-07-03 15:11:37 -05:00