gustafGitHub/born-rule-lean: v1.0 — Machine-checked Born-rule core and two-cell reduction

First tagged release. A Lean 4 + Mathlib formalization of the mathematical core of the note A Note on the Born Rule (G. Ullman): Theorem 2 and the Appendix A reduction, with complex states.

Verified

• BornCore.born_core — Theorem 2: a nonnegative F with F(r) = F(ru) + F(rv) (for r,u,v ≥ 0, u² + v² = 1) equals c·r². The squeeze step is done by hand.
• exists_angle, reduction_core, density_quadratic — Appendix A, the trigonometric and algebraic reduction onto born_core.
• cell_weight, born_density, born_rule_weight — Appendix A, the measure-theoretic layer with complex states ψ : Ω → ℂ, ending at W_E(ψ) = c·∫_E ‖ψ‖².

Trust base

• No sorry. All seven theorems depend only on propext, Classical.choice, and Quot.sound (checked with #print axioms).
• Pinned to toolchain leanprover/lean4:v4.31.0-rc1 and the Mathlib revision in lake-manifest.json.

Build

Run lake exe cache get (prebuilt Mathlib), then lake build.

See the README and Appendix B of the note for the full theorem-to-paper correspondence and the modeling choices.