Lean verification registry · Authored proofs · The Logos Architecture
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: 2026-10-03T01:37:03.225Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:37:50.475Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 6ab10bb1148cb3c6112530df710e5aecca69dce8a9dee67e1644db83222ce561
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.inference_1' does not depend on any axioms 'HunterAuthored.source_identity_rule' does not depend on any axioms
{P, Q, R, S, T, T -> U, P <-> T, P -> U} |= ((P & Q) & (R & S) & T) & U
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.
Law of Identity
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
Coherent Reality, Reason, Rationality, and Logic by Maclain Hunter:
Premises:
P: If Logic were not logical that would be a logical inconsistency and contradiction in the very basis of coherent Logic, Reasoning, Rationality, and Reality.
Q: If Reality were not real that would be a logical inconsistency and contradiction in the very basis of coherent Logic, Reasoning, Rationality, and Reality.
R: If Rationality were not rational that would be a logical inconsistency and contradiction in the very basis of coherent Logic, Reasoning, Rationality, and Reality.
S: If the Logical Origin of the Cosmos (which is “the True God” by definition since God refers to the Origin and Ruler of the Cosmos) were not the Original Logic of the Cosmos and like itself (internally consistent and universally consistent - God-like (Divine)) that would be a logical inconsistency and contradiction in the very basis of coherent Logic, Reasoning, Rationality, and Reality.
T: Assume any of the premises {P, Q, R, S} failed to hold true, that would lead to logical contradiction and cases where x was not x-like and intrinsically so, which is a logically untenable contradiction that defies logical rules including the Law of Identity and the Law of Non-Contradiction. Per the Law of the Excluded Middle this means that the set of premises {P, Q, R, S} is and must be logically and objectively true in the logical framework of Reality (the Logic of Reality), and not merely by some incoherent and subjective perspective that doesn’t hold as much weight logically.
U: Reality, Logic, Rationality, Reason, and Objective Coherence need to be coherent to be logically coherent and valid and for Logic to encompass what is real and rational (in order to be consistent with and integrated with Reality).
Formal Argument (Proof):
{P, Q, R, S, T, T -> U, P <-> T, P -> U} |= ((P & Q) & (R & S) & T) & U
Conclusion: ((P & Q) & (R & S) & T) & U:
It would defy Logic if Logic, Reality, Rationality, Reason, and Objective Coherence were not objectively coherent and different names for the same underlying Rationality that makes Reality and the Universe be Reality and the Universe. Logic must be coherent with the Reality that’s real, the Logic that’s logical, the sort of Objective Reason (Logos) that’s objectively reasonable (logiki), the sort of Rationality that’s actually rational, and the kind of Objective Coherence that is objectively coherent and actually one (singularly logical and totally integrated).
Logic is therefore synonymous with Reality and the logical consistency that allows for the Universe to be the Universe with logical consistency. It is the God-like nature of coherent Logic and Reality, the Divinity of Rationality and the rational, that allows for Reality (Rationality) to be real and rational - aligning with the godliness (logicality) of the True God (Logic).