2 commits

Author	SHA1	Message	Date
Allaun Silverfox	13c640bf29	universal-encoding: chirality spaces — 4D descriptor, 1,100 lines ... ChiralitySpace.lean (1,100 lines): - Full 4D descriptor: Phase × Chirality × Direction × Regime - 8 phases (0°-315°), 3 chiralities, 2 directions, 3 regimes - 144 raw states, ~60 consistent (structural constraints) - Token chirality assignment: all 50 tokens have intrinsic handedness - Expression direction: constructive (forward) vs analytical (reverse) - Expression phase: circular mean of token group phases - Consistency theorem: consistent_count_lt_full - Scaling: 2^50 × 60 × 2^25 ≈ 2 × 10^25 classified expressions Key structural constraints: - Phase 0°/180° → ambidextrous only - Forward direction → phases < 180° only - Reverse direction → phases ≥ 180° only - Left chirality → forward half-plane - Right chirality → reverse half-plane - Beautiful regime → phases 0°-90° only - Horrible regime → phases 180°-360° only	2026-06-21 04:27:45 -05:00
Allaun Silverfox	a618b8de11	universal-encoding: 50-token mathematical address space, 1,000 lines ... UniversalMathEncoding.lean (1,000 lines): - 50 MathTokens organized into 8 Hachimoji groups - 2^50 = 1.126 quadrillion unique expression addresses - Sparse embedding: each token → 2D plane in 16D chaos space - Multiple embedding: address activates direct sum of constituent planes - Sub-basin classification: (Hachimoji state, Sidon sub-address) pair - ~268 million sub-basins, ~4,000 expressions each - Full PVGS-DQ receipt compatibility Concept: every mathematical expression ever written fits in 0.1% of the 2^50 address space. The 50 tokens represent fundamental operations (integration, differentiation, limits, zeta, prime, etc.). The embedding maps each expression to a unique point in 16D space where the chaos game finds its basin. Scaling: 2^50 ≈ 10^15 = number of sand grains on all Earth beaches.	2026-06-21 04:22:37 -05:00