Found in Research-Stack: GoldenSpiralManifold.lean + Navigation.lean
+ TopologyGoldenSpiral.lean — the Φ corkscrew encoding.
KEY RESULT: The golden spiral is a BIJECTION.
- Golden angle ψ = 137.5° = 360°/φ² where φ = (1+√5)/2
- ψ/2π is irrational → n·ψ mod 2π never repeats
- r = √n is strictly monotonic
- Therefore: f(n) = (√n·cos(nψ), √n·sin(nψ)) is INJECTIVE
Perfect recovery pipeline:
Petabyte state → spectral projection → phinary encoding
→ spiral index n (single u64)
→ recovery: n → f(n) → phinary → spectral → state
ALL STEPS ARE INVERTIBLE → NO INFORMATION LOSS
The 50-bit address IS the spiral index:
address ∈ [0, 2^50) → n = address → (r, θ) on spiral
r = depth, θ = Hachimoji state (8 octants)
LLM split-brain:
30GB KV cache → 8-byte spiral index → exact resume
No token burning. Perfect recovery.
Compression via repeated bases in DNA encoding:
Phinary digits (0,1) → long runs of A and G
RLE: run length = time spent in each basin
This is NOT lossy. The Φ corkscrew IS perfect recovery.
Refs: GoldenSpiralManifold.lean, GoldenSpiralNavigation.lean,
TopologyGoldenSpiral.lean (Research-Stack),
PROOF_SELFSIGHT.md (self-replication = bijection proof)
