Lean verification registry · Authored proofs · The Logos Architecture

XOR Self-Inverse

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: 2026-10-03T10:42:53.902Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.

Authored source SHA-256: 58ed7e9b6ca841f3d468ab5fa6085ba089acb15df13ea37f7fec47e3c9f87b2e

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.exponent_xor_self_positive' does not depend on any axioms

Source-bound formal statements

exponent_xor_self_positive · Kernel-verified · axiom-free

{
  "name": "XOR Self-Inverse",
  "formal": "∀a ∈ MCBExponent: state(XOR(a,a)) = +1",
  "proof": "(|a| + |a|) mod 2 = 0, and (-1)^0 = +1",
  "implementation": "mcbExponentXOR(a: MCBExponent, b: MCBExponent): MCBExponent"
}

The authored parity of the sum of magnitudes, defined by an unbounded even/odd recurrence, has positive self-output. This is a signed exponent-state operation, not Boolean XOR substitution.

Exact authored source in the timestamped release

{
  "name": "XOR Self-Inverse",
  "formal": "∀a ∈ MCBExponent: state(XOR(a,a)) = +1",
  "proof": "(|a| + |a|) mod 2 = 0, and (-1)^0 = +1",
  "implementation": "mcbExponentXOR(a: MCBExponent, b: MCBExponent): MCBExponent"
}