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: 2026-10-02T19:42:29.243Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:39:40.847Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 7d56dc7b3ac75ae16613fe529c56e611089b96c6e4296b2edd564d1f51ca578e
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, P -> Q, Q -> P, R, R -> P, R -> Q} |= (P & Q) & R
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.
A is A
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
Logical Glue by Maclain Hunter:
Premises:
P: Logic is coherent with the A is A form of Reality being Reality. Is A is A form in Logic and non-contradictory reasoning did not match Reality then it would be consistent that logically “Reality is not Reality” (or may not be Reality) in such a scenario.
Q: Logic glues Reason and the interpretation of Reality to Reality itself - otherwise it would not work and would itself be logically unsound and contradictory. That cannot be as such a Logic would defy Logic (and would be internally inconsistent and “not Logic”).
R: Assume the negation of the premises P and Q and that Logic is not the thing that an intelligible Cosmos (or “Ordered Universe”) requires and comes from, logically speaking. Logical contradiction then arises from that set of assumptions. It would mean that Logic and Reality are incoherent and not fully aligned and that Reality has an “illogical origin” and/or lacks “Foundational Logical Structure” (Logos - the First Cause of Reason required by the PSR and rational fields of study like theology and ontology). This can also be understood as the Universe existing without a God of Reason.
That means that Logic would not be fully real/rational and capable of explaining Reality. This is logically untenable and the assumption of the Truth of the premises and the sound logical argument this leads to the acknowledgement of solve that issue - providing a logically justified position that acknowledges Reality, and Logic as the coherent framework unifying Reason and Reality (as Pure Rationality and Complete Logic or “Logos” in Greek philosophy).
Formal Argument:
{P, Q, P -> Q, Q -> P, R, R -> P, R -> Q} |= (P & Q) & R
Conclusion:
Logic glues Reason to Reality and provides the method by which knowledge is gained and Existence (or Being) is rationally interpreted and known beyond delusion or assumption. Logically it cannot be any other way, as both common sense and yeh exploration of the contradictions in alternatives tell us - along with the validity of the conclusion here that Logic is in fact what keeps Reason and Being aligned and linked.
Logic, Reason, Being (and “Coherence” itself) form a unified system embodying Objective Validity by which Reality itself can be real, and within which each feasible thing can be each feasible thing in a way that is valid and not mere illusion or unrealized possibility. This Supreme Rationality locked to the Supreme Being by the Ultimate Logic is the very definition of God (see the OED) - as the Supreme Being that rules the Cosmos and which serves as the Moral Authority and Standard.
Logic is what defines logical refutation (or irrefutability) and Reality, manifest logically by Logic, is what determines Truth, by definition, as Truth is what aligns with Reality and Reality with what is “logically real”. Thus the premises and therefore this proof are logically irrefutable and true (with 100% deductive certainty). It’s logically valid in Reality (glued to Logic), not merely “its own framework” (which implies there is something real beyond it).
Truth Table Analysis:
PQR⎪P Q P→Q Q→P R R→P R→Q╞(P&Q)&R
TTT⎪T T TTT TTT T TTT TTT TTT TT
TTF⎪T T TTT TTT F FTT FTT TTT FF
TFT⎪T F TFF FTT T TTT TFF TFF FT
TFF⎪T F TFF FTT F FTT FTF TFF FF
FTT⎪F T FTT TFF T TFF TTT FFT FT
FTF⎪F T FTT TFF F FTF FTT FFT FF
FFT⎪F F FTF FTF T TFF TFF FFF FT
FFF⎪F F FTF FTF F FTF FTF FFF FF
(Valid)
Q.E.D.