Lean verification registry · Authored proofs · The Logos Architecture

OR Commutativity (magnitude distinct)

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: 2026-10-03T10:40:49.711Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.

Authored source SHA-256: c468914d86f2d9feb2a549efb6c7ed74b22146a0392c5ce5968ba4ab325c4c9f

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.distinct_magnitude_or_commutative' does not depend on any axioms

Source-bound formal statements

distinct_magnitude_or_commutative · Kernel-verified · axiom-free

{
  "name": "OR Commutativity (magnitude distinct)",
  "formal": "∀a,b ∈ MCBExponent, |a| ≠ |b|: OR(a,b) = OR(b,a)",
  "proof": "The dominant (larger magnitude) operand determines the result",
  "implementation": "mcbExponentOR(a: MCBExponent, b: MCBExponent): MCBExponent"
}

Exact value selection by dominant integer magnitude with the authored first-operand tie behavior. The theorem retains the distinct-magnitude premise.

Exact authored source in the timestamped release

{
  "name": "OR Commutativity (magnitude distinct)",
  "formal": "∀a,b ∈ MCBExponent, |a| ≠ |b|: OR(a,b) = OR(b,a)",
  "proof": "The dominant (larger magnitude) operand determines the result",
  "implementation": "mcbExponentOR(a: MCBExponent, b: MCBExponent): MCBExponent"
}