Lean verification registry · Authored proofs · The Logos Architecture

MCB Decidability

Verified sequents with unresolved formal parts
Axiom-free: true · 1 checked theorem statements.

Lean establishes the listed formal statements and dependencies. The exact authored source, Ground, known premise meanings, application validation and empirical evidence remain separately typed. No unencoded section is certified by a neighboring theorem.

Original source author: Maclain Hunter. Machine formalization: Replit Agent. No original wording was rewritten.

Source registered: not established (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:40:08.032Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.

Authored source SHA-256: d62a2a92c96cc26d04abb582b6443e4c54ad6e39c15684689418646741813d8d

Lean source · Verification JSON · Exact archived source JSON · Compiler report · Current authored source page · Signed release and verification instructions

Kernel output

Lean (version 4.7.0, commit v4.7.0, Release)
exitCode=0
'HunterAuthored.integer_parity_range' does not depend on any axioms

Source-bound formal statements

integer_parity_range · Kernel-verified · axiom-free

{
  "name": "MCB Decidability",
  "formal": "∀n ∈ ℤ: (-1)^n ∈ {+1, -1}",
  "proof": "By case analysis on parity of n",
  "implementation": "paritySign(n: number): MCBState"
}

Unbounded integer parity-defined signed power has exactly the authored two-state range. The integer-exponent realization is explicitly defined in the Lean file.

Exact authored source in the timestamped release

{
  "name": "MCB Decidability",
  "formal": "∀n ∈ ℤ: (-1)^n ∈ {+1, -1}",
  "proof": "By case analysis on parity of n",
  "implementation": "paritySign(n: number): MCBState"
}