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Allaun Silverfox 6fea51b84b feat(phi-corkscrew): Perfect recovery via golden spiral bijection 
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)
2026-06-23 01:59:51 -05:00
..
architecture Add Rainbow Raccoon / FAMM / NUVMAP architecture manual 2026-05-20 23:01:41 -05:00
assets/css fix(docs): full soft color override — entire page #f5f0eb 2026-05-30 21:07:18 -05:00
concepts Add gamma radix metaprobe concept 2026-05-19 13:57:51 -05:00
famm initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
research Add guide for OpenAI unit-distance disproof as FAMM solve pattern 2026-05-20 23:01:41 -05:00
roadmaps Consolidate research stack updates 2026-05-05 21:09:48 -05:00
speculative-materials initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
_config.yml docs: soft theme for GitHub Pages — Cayman + muted palette 2026-05-30 20:57:50 -05:00
COEVOLUTION_MODEL.md feat(coevolution): FAMM + Resumable DAG + DNA sort co-evolution 2026-06-23 00:58:30 -05:00
compression_signal_shaping_synthesis.md Add RRC projection receipts and roadmap mirrors 2026-05-08 14:50:03 -05:00
EFFICIENCY_IS_NOT_THE_POINT.md docs: Efficiency Is Not the Point (Thor's Balls Clause) 2026-06-23 01:40:33 -05:00
FAMM_BAKER_ANALOGUE.md feat(famm): Baker-analogue theorem as co-evolution guarantee 2026-06-23 01:00:25 -05:00
FBTTY_UNIVERSAL_ENCODER.md feat(fbdev): Universal encoder — matrix math = pixels = any framebuffer 2026-06-23 01:34:56 -05:00
FORCE_RESPONSE_SYNTHESIS.md feat(force-response): Full synthesis — GPU negotiation via FAMM + DAG 2026-06-23 01:46:48 -05:00
math-first-tooling.md fix: regression test now actually exercises --staged in temp repo 2026-05-12 04:51:57 +00:00
optional-science-toolbelt.md Harden optional science toolbelt probe 2026-05-12 05:12:46 -05:00
PETASCALE_COMPRESSION_STATE.md feat(petascale): State compression at PB scale via DNA + eigenanalysis 2026-06-23 01:52:02 -05:00
PHI_CORKSCREW_PERFECT_RECOVERY.md feat(phi-corkscrew): Perfect recovery via golden spiral bijection 2026-06-23 01:59:51 -05:00
PROOF_SELFSIGHT.md theorem(proof): SelfSight — self-replication achieved and proven 2026-06-23 01:16:32 -05:00
rainbow_raccoon_compiler_integration.md Add RRC projection receipts and roadmap mirrors 2026-05-08 14:50:03 -05:00
README.md Consolidate research stack updates 2026-05-05 21:09:48 -05:00
rrc_equation_classification.md Add RRC projection receipts and roadmap mirrors 2026-05-08 14:50:03 -05:00
rrc_logogram_projection_bridge.md Add RRC projection receipts and roadmap mirrors 2026-05-08 14:50:03 -05:00
rrc_logogram_projection_formalism.md Add RRC projection receipts and roadmap mirrors 2026-05-08 14:50:03 -05:00
S7_SPECTRAL_BASIS.md feat(spectral): S^7 spectral basis from Reddit clue + CITATION.cff update 2026-06-23 01:29:24 -05:00
STATE_SPACE_EMBEDDING.md feat(geometry): State space embedding — where the program lives 2026-06-23 01:22:18 -05:00
transfold_couch_data_magnetic_domain_comparison.md Add RRC projection receipts and roadmap mirrors 2026-05-08 14:50:03 -05:00
transfold_enwiki8_magnetic_domain_generator.md Add RRC projection receipts and roadmap mirrors 2026-05-08 14:50:03 -05:00
WEBGPU_PIXEL_ENCODER.md feat(webgpu): Document pixel encoder — GPU-as-information-substrate 2026-06-23 01:32:27 -05:00
WEIRD_MACHINE_SPEC.md feat(quine): Weird Machine spec — self-replicating FAMM/DNA engine 2026-06-23 01:05:57 -05:00
WIKI.md docs: hyperlink 50x claim to VCN Pipeline compression table 2026-05-30 20:55:06 -05:00

README.md

NOTE: This directory is a legacy alias. The authoritative documentation tree is 6-Documentation/docs/. See ARCHITECTURE.md for the full doc map.

Files here are retained as stable references. New documentation should be added to 6-Documentation/docs/.