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Research-Stack/0-Core-Formalism
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allaun a8eacc143f fix(lean): complete picard-lindelof existence proof in legacy HamiltonianMechanics 
The existence half of Picard-Lindelöf for finite-dimensional systems (Fin n → ℝ)
is now fully proven. The proof factors into:

1. exists_forward_solution — generic lemma building a forward solution on [0,∞)
   for any Lipschitz vector field via Nat.rec over τ-intervals with
   HasDerivWithinAt.union at boundaries and Nat.find indexing.

2. Time reversal via f_neg (x ↦ -f x) applied to exists_forward_solution gives
   the backward solution.

3. γ_full splices both halves with case split at t=0.

4. The splice point t=0 is resolved via
   hasDerivAt_iff_tendsto_slope_left_right, with the left slope obtained by
   composing the negative-forward slope with y ↦ -y and an algebraic identity
   γ_full(y) = γ_neg_fwd(-y) on y ≤ 0.

Previously 1 sorry (the existence existence) remained; it is now closed.
The uniqueness half was already proven via ODE_solution_unique_univ.

Build: 3583 jobs, 0 errors (lake build)
2026-06-16 00:09:31 -05:00
..
core fix(adversarial-review): resolve 35 critical coding bugs across 8 subsystems 2026-05-31 23:38:03 -05:00
lean fix(lean): complete picard-lindelof existence proof in legacy HamiltonianMechanics 2026-06-16 00:09:31 -05:00
otom chore(repo): push local 768-commit branch state onto clean remote baseline 2026-06-15 22:46:50 -05:00
receipts
rust/ftdi_gimbal
scripts chore: commit accumulated working tree changes 2026-05-30 00:10:02 -05:00
README.md

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