Lean verification registry · Authored proofs · The Logos Architecture

Truth, Reality, and the Law of Identity

Written formal sequents verified
Axiom-free: true · 2 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: 2026-10-02T23:09:14.906Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:42:40.689Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.

Authored source SHA-256: d70fd4159d5ebd87872232c9c0642b3ea4b89885bb20becafea388514d8141c5

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.inference_1' does not depend on any axioms
'HunterAuthored.source_identity_rule' does not depend on any axioms

Source-bound formal statements

inference_1 · Kernel-verified · axiom-free

{P, ~~Q, P <-> Q} |= (P & Q)

Exact source sequent under finite two-valued propositional semantics. Source proposition meanings and Logic/Logos/God Ground are preserved separately; this checks the inference, not unencoded prose.

source_identity_rule · Kernel-verified · axiom-free

A is A

The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.

Exact authored source in the timestamped release

P: Truth as defined in the dictionary (OED) is defined by Reality and Coherence with Reality. 

Q: Truth is inherent in the validity of alignment with the First Principle of Validity (A is A) that makes Reality be Reality: the Law of Identity; Logic.

{P, ~~Q, P <-> Q} |= (P & Q)