Lean verification registry · Authored proofs · The Logos Architecture
Verified sequents with unresolved formal parts
Axiom-free: true · 4 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: 2026-10-03T01:33:02.748Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:38:30.694Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 81c9017e1f76d7211ebd691bf5fddf67038d86d994d408a64b382cf885b26449
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_2' does not depend on any axioms 'HunterAuthored.inference_4' does not depend on any axioms 'HunterAuthored.inference_5' does not depend on any axioms 'HunterAuthored.source_identity_rule' does not depend on any axioms
{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.
The written sequent alone has a countermodel. No authored wording or unstated premise was changed.
Countermodel to the isolated written sequent: {"P":false,"Q":false}{P, P -> Q, Q -> R} |= (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.
{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.
The written sequent alone has a countermodel. No authored wording or unstated premise was changed.
Countermodel to the isolated written sequent: {"P":false,"Q":false}{A, B, C, D} |= (A & B) <-> (C & D)
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.
{P1, P1 -> P2, P2 -> P3, P3 -> P4} |= (P1 & P2) & (P3 & P4)
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 = A
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
Four Proofs (4P):
Proof One (P1):
P: All proof proves the Logos (Logic) exists as no proof exists absent it. Logic is the “Source and Standard of Proof” and is evident in the existence of proof.
Necessity: It would contradict Logic if Logic weren’t the “Origin and Standard of Proof” that proof must satisfy and align with, so P must be true.
Q: Assume P were false then logically valid proof could exist minus Logic (Logos) and that would be a logical contradiction.
Necessity: If Q weren’t true then P could be false and Logic could be contradicted “without logical contradiction” which is a self-defeating proposition that is untenable.
{P <-> Q} |= P & Q
Conclusion: {P, Q}: All logically valid and coherent proof ultimately proves the “Source of Proof in Logic” and that the Logos (the Logical Foundation of Reality) exists as a self-evident (and particularly evident) logical necessity and framework.
Proof Two (P2):
P: It is valid to cite religious scripture or texts of any kind of those citations and references are then used in a logically coherent fashion.
Necessity: P must be true or citations would risk becoming logically unhinged and incoherent.
Q: Assume we allow citations of scripture or other texts to supersede or provide an alternative logical (or universal) Standard, besides Logic (Logos - the True Origin of Logical Frameworks and Existence), which contradicts Logic at its fundamental level (Logos - the Coherence of Reality being Reality).
Necessity: Q must be true or things, such as passages of texts, or arbitrary standards/goalposts, could supersede and undermine Logic (Logos - the Logical Standard of Logical Existence), which is untenable logically and objectively.
R: Even taking multiple passages from a single coherent text but using them to justify double standards in various contexts as some do with “proof-texting” can introduce deceptive (seemingly valid) “illogical standards” - meaning double standards and proposed standards besides Logic itself.
Necessity: R must be true as Logic must be the logical standard or it leads to logical contradiction in Reality and “Logical Systems” (which includes Reality and all logical systems within it). If R weren’t true then it could paradoxically be true by a newly valid “illogical standard” (or in other words if we can’t just say we’re right according to “whatever” then I declare I’m right according to such an illogical standard then too, as Logic says the logical is right/correct by the actual Logical Standard of Logic).
{P, P -> Q, Q -> R} |= (P & Q) & R
Conclusion: {P, Q, R}:
Logic is the Logical Standard universally and irrefutably (beyond feasible logical refutation as Logic is a self-reinforcing Standard and System not a self-defeating and self-undermining one as illogical systems are - by definition) and this is tautological - self evident in Logic and the very Nature of Logic. Letting other supposed “standards” (including laws and rules, but also personal and rational standards) supersede coherent Reason and Logic is inherently illogical.
Even things like the citation of holy scriptures or respected philosophical texts, or those texts themselves, cannot reasonably/logically (or actually) supersede logically consistent Logic (True Logic - the Logic rooted in Reality being Reality - the Logos also called God in classical theism and Greek philosophy).
Proof Three (P3):
P: Logic is synonymous with self-validating “Rational Law” (the “One Rule of coherent Logic and Reason”).
Q: The traditional “three rules” of Logic defy Logic and the necessity of coherent/singular Rational Law (logically integrated Logic).
{P <-> Q} |= P & Q
Conclusion: P & Q:
Logic must be one (coherent) and must integrate all rules and encompass all logical concepts, components, and laws/rules within the dynamic comprehension (infinite understanding) of Rational Law, which is synonymous with Logic itself. To fail to integrate the three traditional rules of Aristotle and classical Logic into one coherent law is incoherent and defies Logic.
Proof Four (P4):
A: All = All as A = A
B: Maclain (I) = All as All = All
C: God = All as All = All
D: Maclain (I) = God (Logos a.k.a. Jesus’s Essence) as All = All
{A, B, C, D} |= (A & B) <-> (C & D)
Conclusion: I (Maclain - the Logician) am God (Logic) and all things as A is A & All = All. This conclusion doesn’t rely on “metaphysical assumptions” or the like but rather it validly and appropriately relies on logical consistency as good arguments should and as Reality (being Reality consistently) does. Therefore it is knowledge based upon and coherent with the Foundation of Reality that I am “x” and “all” including concepts from Logic to Jesus and from Aristotle to the Sun.
Formal Argument (Proof) for “Four Proofs (4P):
{P1, P1 -> P2, P2 -> P3, P3 -> P4} |= (P1 & P2) & (P3 & P4)
Conclusion of 4P: {P1, P2, P3, P4}:
Coherent concepts include: Logos, God (the necessarily coherent and logical “Origin of Existence”), Logic, Truth, facts (including the fact that I am what I am), Reality, the Universe, logical reasoning, Reason, the logician, and all other fully coherent concepts including “Full Coherence” (Coherence) itself, and the all-encompassing and logically complete Reality that is inherent in what the string “Everything == Everything” or the tautology “All is All” represents - the so called “Cosmos”.
Logic is the Universal Standard, meaning Logic and being coherent with Logic is the epitome of what is good as well as the measure of things like: being successful, being wealth, being correct/right, being better, being superior, being more moral, being more caring or less careless, being more productive, being more intelligent, being more worthy (of life, love, etc.).
To deny these things would contradict Logic and would be to introduce illogical standards and/or double standards.