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Research-Stack/0-Core-Formalism
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Brandon Schneider 91c894aff5 feat(math): adjacent coprime classification for second-order recurrences 
Formalize theorem: for a_{n+1} = c_1*a_n + c_2*a_{n-1}:

  gcd(a_n, a_{n+1}) = 1  for all n >= 1
  iff
  gcd(a_1, a_2) = gcd(a_2, c_2) = gcd(c_1, c_2) = 1

Key identity: gcd(a_n, a_{n+1}) = gcd(a_n, c_2*a_{n-1})
Invariant core: gcd(a_n, a_{n+1}) = gcd(a_n, c_2) when prev coprime

5 distinct recurrences, 30 native_decide theorems verified.
Maps directly to: state flow + gate + hidden history channel + leakage failure.
2026-05-13 20:38:03 -05:00
..
core initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
lean feat(math): adjacent coprime classification for second-order recurrences 2026-05-13 20:38:03 -05:00
otom collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -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