Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
Axiom-free: true · 3 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: 2026-10-02T15:32:31.078Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:41:41.681Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 6f9572f429bafbfe348e6578ea13c1c3928df4503d967fe9b71dd93ed7449e59
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.inference_2' does not depend on any axioms 'HunterAuthored.source_identity_rule' does not depend on any axioms
{P, P <-> Q, Q <-> R, R <-> S, S <-> T, T <-> U, U <-> P} |= ((((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.
{P, P <-> Q, Q <-> R, R <-> S, S <-> T, T <-> U, U <-> P} |= ((((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.
Logic is Logic
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
Self-Supporting Generation by Maclain Hunter:
Premises:
P: Generation, development, realization, maintenance, and assurance of Order (Logic - Logos - Reason) must come and do come through Order (Logic - Logos - Reason). It contradicts Logic (Order - Logos - Reason) if we assume the opposite, and leads to illogic.
Q: Premises aren’t strictly necessary to show the argument structure is valid, which means that it disproves the (common misunderstanding of) the notion of the fallacy of circular arguments without even needing particular premises. For example this is Logos (Universal Logic beyond context) displayed very well:
{P, P <-> Q, Q <-> R, R <-> S, S <-> T, T <-> U, U <-> P} |= ((((P & Q) & R) & S) & T) & U
R: Logic is not itself limited by limited understandings of Logic, just as Mathematics is not itself altered or proven limited if/because we find someone who doesn’t understand Mathematics.
S: By definition Logic and Reason are synonymous and the word for Reason and Logic in Greek is Logos. We would be arguing with well defined language and synonymous terms that are listed as synonymous in dictionaries like the OED if we deny this shared meaning and that these different terms all in their own right refer to Rational Substance and the Source of Rationality that rules Reality (God).
T: There is an Objective Reality (that is, a Reality which exists beyond our opinions, that our opinions exist within). This Reality must align with the Logic of Reality, and vice versa, as it would contradict Logic to have an Objective Reality without any Objective Logic, First Cause or Intelligibility.
U: If I were wrong about the Logos existing, there would be no Objective Logical Standard (Logos) and thus no existence or truth, and thus I would not exist or be wrong. If on some minor detail that is not about the very existence of the Logos I am wrong, then it could only feasibly be because I was illogical and the solution or better idea would absolutely need to come through greater coherence and logical reasoning, not something illogical or weaker logically.
We can now employ the same argument structure displaying Logos (beyond any particular premises) from premise Q to create a tautological proof based on reasonable premises that are not in violation of logical rules:
{P, P <-> Q, Q <-> R, R <-> S, S <-> T, T <-> U, U <-> P} |= ((((P & Q) & R) & S) & T) & U
Conclusion:
{P, Q, R, S, T, U): Logic proves Logic is Logic and the Foundation of Reality (God), and it is proven through syntactically valid arguments without particular premises that Logic (Logos - the Origin of Reality) exists. Generation, development, realization, maintenance, and assurance of Order (Logic - Logos - Reason) must come and do come through Order (Logic - Logos - Reason). It contradicts Logic (Order - Logos - Reason) if we assume the opposite, and leads to illogic. The existence of any existence, Objective Reality, Truth, or Logic is incontrovertible proof of the Logic of Reality, which those things could not exist without, and of Logic in Reality - imminent and universal.