2 commits

Author	SHA1	Message	Date
openresearch	e2054af08c	docs(research): chiral CRT multiplexing — Qwen 3.7 Max formalization ... 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.	2026-07-04 19:42:07 +00:00
allaun	fb2718842d	docs: synthesize chiral CRT multiplexing theory ... Unifies: - Dual quaternion algebra (screw motions) - CRT Torus Embedding (chiral pairs) - Sidon orthogonality (non-interfering channels) - BraidStorm/TreeBraid/COUCH architecture - Hutter Prize filtering as Sidon selection Theoretical guarantees: - Non-interference theorem (Sidon orthogonality) - Multiplexing capacity theorem (n/2 channels for n strands) - Hierarchical encoding theorem (TreeBraid/MMR)	2026-07-04 14:37:12 -05:00