Lean verification registry · Authored proofs · The Logos Architecture
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: 2026-10-03T10:42:52.751Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 28472d6dc9c60fbdbba33f9b0355e6ac0a4b3bbf26b0fca5bad11409894eb6a3
Lean source · Verification JSON · Exact archived source JSON · Compiler report · Current authored source page · Signed release and verification instructions
Lean (version 4.7.0, commit v4.7.0, Release) exitCode=0 'HunterAuthored.exponent_xor_self_positive' does not depend on any axioms
Formal statement: ∀a ∈ MCBExponent: state(XOR(a,a)) = +1
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.
Formal statement: ∀a ∈ MCBExponent: state(XOR(a,a)) = +1 Proof: (|a| + |a|) mod 2 = 0, and (-1)^0 = +1