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Research-Stack/0-Core-Formalism
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Brandon Schneider bcc40a8318 feat: golden ratio unit separation + dense Sidon sets from sum-product disproof 
GoldenRatioSeparation.lean (Lean):
- Lemma 3.4 from Bloom-Sawin-Schildkraut-Zhelezov (2026)
- goldenRatio = 106008 (φ × 65536)
- goldenRatioInv = 40503 (1/φ × 65536)
- golden_angle_is_inverse_golden_ratio: goldenAngleStep = goldenRatioInv
- golden_ratio_squared_eq_plus_one: φ² = φ + 1
- sidon_generator_coprime: gcd(40503, 65536) = 1
- golden_angle_decodable: 40503 < 106008
- 3301 jobs, 0 errors, 5 #eval witnesses

braid_search.py:
- Mian-Chowla dense Sidon sets (65% smaller for n=8, 99% for n=16)
- Three methods: powers_of_2, greedy_optimal, algebraic
2026-05-28 17:01:25 -05:00
..
core Remove legacy Python prototypes superseded by Lean formalization 2026-05-19 15:34:17 +00:00
lean feat: golden ratio unit separation + dense Sidon sets from sum-product disproof 2026-05-28 17:01:25 -05:00
otom Add Phys.org May 2026 source intake for bees, biocoatings, THz, and diamond membranes 2026-05-23 19:27:37 -05:00
receipts docs: add bio optical witness living light equations 2026-05-09 20:53:51 -05:00
rust/ftdi_gimbal initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
README.md initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00

README.md

0-Core-Formalism

Purpose: Formal foundations for the entire Research Stack — Lean modules, bind primitive, Triumvirate consensus, core source.

No external dependencies. All other layers depend on this.

Contents (Target)

Source Destination
0-Core-Formalism/lean/Semantics/ 0-Core-Formalism/lean/Semantics/
core/ 0-Core-Formalism/core/

Concepts

  • bind — State → (State → Action) → State
  • TriumvirateClock — ternary consensus (ADD/PAUSE/SUBTRACT)
  • Builder/Judge/Warden — roles mapped to hardware registers
  • OTOM — Ordered Transformation & Orchestration Model

Build

cd "0-Core-Formalism"
lake build