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e2054af08c
Formalizes the unification of CRT, dual quaternions, Sidon sets, and compression filtering. Three theorems: 1. Sidon Orthogonality: if A is Sidon and moduli coprime, dual quaternion sums are orthogonal (non-interfering). Proof follows from CRTSidon.lean sidon_preserved_mod. 2. Multiplexing Capacity: n strands → n/2 orthogonal channels. Each channel encodes an independent data stream without interference. 3. Hierarchical Encoding: TreeBraid/MMR merge tree allows decode at any scale. CRT reconstruction is a ring isomorphism mod M. KEY PRACTICAL RESULT: CRT replaces the CMIX mixer algebraically. The mixer's O(n² × models) cost becomes O(n²) with exact separation. The mixer was a computational approximation of what CRT does exactly. The only operation that matters is the FILTER (COUCH gate): which Sidon pairs to retain at each scale. Compression is dead (conservation law, 8× measured), but multiplexing/filtering is alive. Source: Qwen 3.7 Max theoretical framework, integrated with SilverSight's measured results and formal proofs. |
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| .. | ||
| AUTOPROOF_INFRASTRUCTURE.md | ||
| braid_group_action.md | ||
| BRAIDSTORM_TREEBRAID_COUCH.md | ||
| CAPABILITY_GRID_MAPPING.md | ||
| CHIRAL_BATCH_ENCODING.md | ||
| CHIRAL_CRT_MULTIPLEXING.md | ||
| COLLECTIVE_INTELLIGENCE_OPTIMIZATION.md | ||
| COMPRESSION_HONEST_FINDINGS.md | ||
| CONSERVATION_LAW_CORRECTION.md | ||
| FIXEDPOINT_BRIDGE_DESIGN.md | ||
| GERVER_SIDON_DESIGN.md | ||
| INVARIANT_COMPUTATION_GEOMETRY.md | ||
| iteration_dag.md | ||
| iteration_regime.md | ||
| MERGED_O1_TRANSFORM.md | ||
| NEXT_STEPS_PLAN.md | ||
| O1_TRANSFORMS.md | ||
| OCTAGON_PRINCIPLE.md | ||
| PRIME_SIDON_NEGATIVE_RESULT.md | ||
| REACTION_PRIMES.md | ||
| sidon_preservation_creation.md | ||
| SIDON_SOFA_COLORING.md | ||
| SIDON_SOFA_COLORING_REVIEW.md | ||
| SLOS_SIDON_VERIFICATION_RECEIPT.md | ||
| TOROIDAL_POLOIDAL_REFINEMENT.md | ||
| unified_crt_torus_dag.md | ||