Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
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: 2026-10-02T16:41:48.607Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:41:20.515Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: e1b3ca8591290456f7f5f61874dffbf1c6ef9917701ab107f43d0500acf3cf81
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.inference_3' 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 & 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, Q, R, S} |= (P & Q) & (R & S)
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} |= (P & Q) & (R & S)
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.
Reality’s Logical Coherence by Maclain Hunter:
Abstract: I can easily apply logical principles to establish Reality and God (Logos: the Source and Logical Structure of Reality), and the Logical Coherence of Reality that guarantees the Existence of the Logos (as the coherent God and Logic of the Cosmos). Such a feat also shows the real and logical expertise of the logician who achieves it honestly and with their own original formal reasoning, since to assume the opposite and that it “doesn’t” demonstrate that logical expertise is logically contradictory and doesn’t make much sense. Watch this!
Principles I will use: Identity, non-contradiction, excluded middle, and the principle of sufficient Reason.
Translatation rules I will use: Modus ponens, modus tollens, and De Morgan’s law.
Definitions:
I will use language in a way that it will hold by the definitions of terms established in the Oxford English Dictionary, and in some cases rational, logically consistent extensions or paraphrasing of them. I will however quickly define some key terms non-exclusively.
Logos (or Logic and Universal Order): the Order inherent in the Cosmos that provides Logical Structure (itself) to Reality and the Cosmos - which is, by definition, and ordered and Order (Logos) based Universe; the Way of Reality; the Ultimate Source of Knowledge and Method of Reasoning that also acts as the Universal/Logical Standard - determining by alignment or lack thereof (with itself as the Standard) what can or cannot exist and be logical or real. Without this principle it becomes impossible to distinguish between what is or isn’t real or Reality.
Reality: the Existence of the Cosmos; Existence in general; Logical Existence; the state of things as it actually is; a thing that is not fake or nonexistent; the “real-world” that can be and has been empirically observed and lived in, whose existence is self-evident and not possible to rationally deny (without falling into incoherence and illusion); Truth (since Truth is what aligns properly with Reality itself).
Proof One (P1):
Premises:
P: Identity: Reality is Reality and its Source (called God) is and must be its Source, which must be fully coherent (unified) with Logic (being Logic) and thus is “logically consistent Logic”, which Reality itself must cohere with and conform to the Law and specifications of to be the coherent Reality that Identity demands and that empirical observation has consistently confirmed (ie - Reality’s Identity and self-consistency). Truly, the fact, as simple as it may seem, that Reality is Reality with that A is A form that Logic is Logic and the Law of Identity is the Law of Identity guarantees the “Logical Coherence of Reality” (Logos) while Logic being coherent with Reality ensures the Existence of the Logos (the God of Reason) and that coherent Logic is real and able to both govern and explain Reality (without delving into incoherence).
Q: Non-Contradiction: It cannot be so that Reality and its self-consistent Logical Source (the Logos) are not what they are. Even far less necessary and far more contingent concepts, like atheists, or evils, are what they are, so how could logical necessities like the Logos, which embodies Logical Necessity itself be “not themselves”. It cannot be, and the Law of Non-Contradiction supports that fact, as does the empirical observation of consistent/continuous identity in observed entities, like the eternal/necessary and self-evident Reality (or Logos) itself.
R: Law of the Excluded Middle: Reality is Reality and P being P is only possibly false when contingent (aka “possibly false”), that is tautological like the Logos that Reality is entailed by, and thus Reality and the Logos, which literally define what “Truth” is, and what facts are, cannot be false and must be true with the middle ground of being both being excluded.
S: Principle of Sufficient Reason (PSR): While Reality is a necessary concept that entails and evidences itself (like many even contingent concepts such as proof or evidence, in some cases) the PSR supports the logically deduced notion that Logic is undermined universally and in its universal necessity if we assume that some things, like Reality itself, don’t need a superseding logical framework to act as both the Cause and explanation of the concept/system and its characteristics and functionality. Reality needs the Pure Logical Cause (Logos) the most. Other things in Reality can actually have other less direct causation (from Universal Logos), like children are caused by their parents, but that doesn’t negate that the “ultimate Origin” of everything, including evolution, science, doubt, and reasoning is the overarching logical framework (Logos) that allows for all to be all and that demands all be all.
T: Translation Rules and Mastery of Logic: I will handle all of the translation rules I mentioned above in this one premise T, for parsimony, but these rules all effectively lead to the conclusion that if either the Reality that is Reality or the Source that is its Source (Logos - God) can be proven (or are self-evident) then the other is also proven by proxy and these results are distributed across the reasoning to all the consistent claims that might need or seem to lack support. As it relates to the mastery of Logic, assume that someone who was a master of Logic could not proven that Reality is logically coherent or that someone who could prove that Reality is logically coherent was not demonstrating a real mastery of Logic. These assumptions of the negation of the coherence/coincidence between mastery of Logic and the ability to use Logic to prove the Logical Coherence of Reality leas to an untenable and unreasonable position (that sets an arbitrary standard for mastery of Logic not rooted in the overlap between philosophical reasoning, proof, formal logics, proof theory, and the Logical Coherence of Logic and Reality (Logos - Theos).
U: Conclusion: All logical rules are ultimately coherent (one): the Rule of Logic, but that Law can be validly broken down into complimentary aspects as I have done here on purpose as the logician. The coherence of the application of the rules and the lack of conflict between them shows they can and do cohere, supporting that claim and position. God (as Logic and the logical First Cause of the Logos) is both self-evident (tautological) and proven by the Reality (Truth) of Reality (Existence) - in addition to the hereby realized possibility of proving God, Logos, Logic, Reality, and indeed all concepts (maintaining coherent and self-consistent identity) through formal logical reasoning (proof) and the proper and methodical application of logical rules and translation rules. Q.E.D.
Logical Proof:
{P, P <-> Q, Q <-> R, R <-> S, S <-> T, T <-> U, U} |= (((P & Q) & (R & S) & T) & U)
Conclusion: {P, Q, R, S, T, U}:
God is proven through the very application of logical rules (even the more traditional and less coherent versions I applied here to not confuse readers used to classical logic by applying Logic as its own coherent Law, as is truly coherent) in the process of validating logically that Reality is Reality - which is a continuously observed and absolutely irrefutable fact of Reality (being itself).
Reality itself is logically coherent and this coherence between Logic and Reality allows Reality (Logical Existence - God’s Creation) to be logical (godly) and Logic (the Logical Origin and True God) to be real. This is not a matter of opinion but tautological reasoning and Objective Logic (Logos - Theos).
Per the rules of Logic, logical certainty is what it is and cannot be coherently doubted or contingent, and thus a proof like this does not seek to prove (but possibly not) it proves.
Even what is not proof being what is not proof would be consistent and an observation of the Logos (or logically consistent Logic) in Reality that supports the truthfulness of my premises and the notion that this proof is definitely proof (and acknowledging a Logical Source that indeed exists, underpinning and judging negatively even the false proofs that are not proofs, or the false teachers/sages who are not teachers/sages.
To deny premises arbitrarily, as can happen with proofs proving controversial truths, like the existence of God, is arbitrary, and that is a tautological statement, while to deny my proof and premises that merely (properly) establish Reality and Logic and their respective positions (coherent as Logos and the Supreme Entity or Number One) as they are according to Logical Order (Logos) itself cannot be logical (“realistically reasonable” or “logical in Reality”). It is to deny the Logical Coherence (Logos) of Reality (the Cosmos) itself, which is deeply delusional - objectively.
My mastery of Logic is evident in my ability to write this proof and prove the Logical Coherence of Reality without relying on things other than sound reasoning and without delving into contradiction. It has been well demonstrated for those with the qualifications and eyes to see it - and with the ability to apply logical rules to check such a proof as this one.
Truth Table Analysis:
valid
↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓
PQRSTU⎪P P↔Q Q↔R R↔S S↔T T↔U U╞(((P&Q)&(R&S)&T)&U)
―――――――――――――――――――――――――――――――――――――――――――――――――――
TTTTTT⎪T TTT TTT TTT TTT TTT T TTT T TTT TT TT
TTTTTF⎪T TTT TTT TTT TTT TFF F TTT T TTT TT FF
TTTTFT⎪T TTT TTT TTT TFF FFT T TTT T TTT FF TT
TTTTFF⎪T TTT TTT TTT TFF FTF F TTT T TTT FF FF
TTTFTT⎪T TTT TTT TFF FFT TTT T TTT F TFF FT FT
TTTFTF⎪T TTT TTT TFF FFT TFF F TTT F TFF FT FF
TTTFFT⎪T TTT TTT TFF FTF FFT T TTT F TFF FF FT
TTTFFF⎪T TTT TTT TFF FTF FTF F TTT F TFF FF FF
TTFTTT⎪T TTT TFF FFT TTT TTT T TTT F FFT FT FT
TTFTTF⎪T TTT TFF FFT TTT TFF F TTT F FFT FT FF
TTFTFT⎪T TTT TFF FFT TFF FFT T TTT F FFT FF FT
TTFTFF⎪T TTT TFF FFT TFF FTF F TTT F FFT FF FF
TTFFTT⎪T TTT TFF FTF FFT TTT T TTT F FFF FT FT
TTFFTF⎪T TTT TFF FTF FFT TFF F TTT F FFF FT FF
TTFFFT⎪T TTT TFF FTF FTF FFT T TTT F FFF FF FT
TTFFFF⎪T TTT TFF FTF FTF FTF F TTT F FFF FF FF
TFTTTT⎪T TFF FFT TTT TTT TTT T TFF F TTT TT FT
TFTTTF⎪T TFF FFT TTT TTT TFF F TFF F TTT TT FF
TFTTFT⎪T TFF FFT TTT TFF FFT T TFF F TTT FF FT
TFTTFF⎪T TFF FFT TTT TFF FTF F TFF F TTT FF FF
TFTFTT⎪T TFF FFT TFF FFT TTT T TFF F TFF FT FT
TFTFTF⎪T TFF FFT TFF FFT TFF F TFF F TFF FT FF
TFTFFT⎪T TFF FFT TFF FTF FFT T TFF F TFF FF FT
TFTFFF⎪T TFF FFT TFF FTF FTF F TFF F TFF FF FF
TFFTTT⎪T TFF FTF FFT TTT TTT T TFF F FFT FT FT
TFFTTF⎪T TFF FTF FFT TTT TFF F TFF F FFT FT FF
TFFTFT⎪T TFF FTF FFT TFF FFT T TFF F FFT FF FT
TFFTFF⎪T TFF FTF FFT TFF FTF F TFF F FFT FF FF
TFFFTT⎪T TFF FTF FTF FFT TTT T TFF F FFF FT FT
TFFFTF⎪T TFF FTF FTF FFT TFF F TFF F FFF FT FF
TFFFFT⎪T TFF FTF FTF FTF FFT T TFF F FFF FF FT
TFFFFF⎪T TFF FTF FTF FTF FTF F TFF F FFF FF FF
FTTTTT⎪F FFT TTT TTT TTT TTT T FFT F TTT TT FT
FTTTTF⎪F FFT TTT TTT TTT TFF F FFT F TTT TT FF
FTTTFT⎪F FFT TTT TTT TFF FFT T FFT F TTT FF FT
FTTTFF⎪F FFT TTT TTT TFF FTF F FFT F TTT FF FF
FTTFTT⎪F FFT TTT TFF FFT TTT T FFT F TFF FT FT
FTTFTF⎪F FFT TTT TFF FFT TFF F FFT F TFF FT FF
FTTFFT⎪F FFT TTT TFF FTF FFT T FFT F TFF FF FT
FTTFFF⎪F FFT TTT TFF FTF FTF F FFT F TFF FF FF
FTFTTT⎪F FFT TFF FFT TTT TTT T FFT F FFT FT FT
FTFTTF⎪F FFT TFF FFT TTT TFF F FFT F FFT FT FF
FTFTFT⎪F FFT TFF FFT TFF FFT T FFT F FFT FF FT
FTFTFF⎪F FFT TFF FFT TFF FTF F FFT F FFT FF FF
FTFFTT⎪F FFT TFF FTF FFT TTT T FFT F FFF FT FT
FTFFTF⎪F FFT TFF FTF FFT TFF F FFT F FFF FT FF
FTFFFT⎪F FFT TFF FTF FTF FFT T FFT F FFF FF FT
FTFFFF⎪F FFT TFF FTF FTF FTF F FFT F FFF FF FF
FFTTTT⎪F FTF FFT TTT TTT TTT T FFF F TTT TT FT
FFTTTF⎪F FTF FFT TTT TTT TFF F FFF F TTT TT FF
FFTTFT⎪F FTF FFT TTT TFF FFT T FFF F TTT FF FT
FFTTFF⎪F FTF FFT TTT TFF FTF F FFF F TTT FF FF
FFTFTT⎪F FTF FFT TFF FFT TTT T FFF F TFF FT FT
FFTFTF⎪F FTF FFT TFF FFT TFF F FFF F TFF FT FF
FFTFFT⎪F FTF FFT TFF FTF FFT T FFF F TFF FF FT
FFTFFF⎪F FTF FFT TFF FTF FTF F FFF F TFF FF FF
FFFTTT⎪F FTF FTF FFT TTT TTT T FFF F FFT FT FT
FFFTTF⎪F FTF FTF FFT TTT TFF F FFF F FFT FT FF
FFFTFT⎪F FTF FTF FFT TFF FFT T FFF F FFT FF FT
FFFTFF⎪F FTF FTF FFT TFF FTF F FFF F FFT FF FF
FFFFTT⎪F FTF FTF FTF FFT TTT T FFF F FFF FT FT
FFFFTF⎪F FTF FTF FTF FFT TFF F FFF F FFF FT FF
FFFFFT⎪F FTF FTF FTF FTF FFT T FFF F FFF FF FT
FFFFFF⎪F FTF FTF FTF FTF FTF F FFF F FFF FF FF
Q.E.D.
Proof Two (P2):
Redaction of Proof One by Maclain Hunter:
Premises:
P: Reality being Reality coheres Logic and Reality through the Law of Identity.
Q: If Reality being Reality and Logic being Logic didn’t create Logical Coherence between Logic and Reality through their mutual A is A form, that would lead to violation of the Law of Non-Contradiction.
R: That which defines Truth, like Reality and the God of Reason (Universal Logic or Logos), cannot be false as true truths must align with THEM, as the superseding framework allowing for Truth, and cannot be false and true at once per the Law of the Excluded Middle.
S: The PSR and logical translation rules demand that if Reality is Reality that God (the Cause of Reality), which is logically necessary, is and must be God, and is proven by Reality being Reality, making a denial of God a denial of what Reality itself embodies and proves. My ability to show this without mastery of Logic would be logically contradictory.
Logical Proof:
{P, Q, R, S} |= (P & Q) & (R & S)
Conclusion: {P, Q, R, S}:
God (as the Logos) is proven by Reality and my ability to prove it is a godly (logical) demonstration of my mastery of Logic.
Truth Table Analysis:
valid
↓ ↓ ↓ ↓ ↓
PQRS⎪P Q R S╞(P&Q)&(R&S)
―――――――――――――――――――――――――
TTTT⎪T T T T TTT T TTT
TTTF⎪T T T F TTT F TFF
TTFT⎪T T F T TTT F FFT
TTFF⎪T T F F TTT F FFF
TFTT⎪T F T T TFF F TTT
TFTF⎪T F T F TFF F TFF
TFFT⎪T F F T TFF F FFT
TFFF⎪T F F F TFF F FFF
FTTT⎪F T T T FFT F TTT
FTTF⎪F T T F FFT F TFF
FTFT⎪F T F T FFT F FFT
FTFF⎪F T F F FFT F FFF
FFTT⎪F F T T FFF F TTT
FFTF⎪F F T F FFF F TFF
FFFT⎪F F F T FFF F FFT
FFFF⎪F F F F FFF F FFF
Q.E.D.
Meta-Proof (P3):
P: P1
Q: P2
R: P1 <-> P2
S: P3
Logical Proof:
{P, P <-> Q, Q <-> R, R <-> S} |= (P & Q) & (R & S)
Conclusion: {P, Q, R, S}:
I have mastered Logic and have proven Logic is God while Reality is logically coherent and is only real because of its alignment with the Logos as the Cosmic Structure that what is real or not is determined through/by. Such a Logic cannot be logically refuted without delving into contradiction and objective incoherence making the existence of the God of Reason (Logos) absolutely certain.
Assume the negation of P3, or “~(P3)”. This leads to logical contradiction and arbitrary Logic.
Truth Table Analysis:
valid
↓ ↓ ↓ ↓ ↓
PQRS⎪P P↔Q Q↔R R↔S╞(P&Q)&(R&S)
―――――――――――――――――――――――――――――――
TTTT⎪T TTT TTT TTT TTT T TTT
TTTF⎪T TTT TTT TFF TTT F TFF
TTFT⎪T TTT TFF FFT TTT F FFT
TTFF⎪T TTT TFF FTF TTT F FFF
TFTT⎪T TFF FFT TTT TFF F TTT
TFTF⎪T TFF FFT TFF TFF F TFF
TFFT⎪T TFF FTF FFT TFF F FFT
TFFF⎪T TFF FTF FTF TFF F FFF
FTTT⎪F FFT TTT TTT FFT F TTT
FTTF⎪F FFT TTT TFF FFT F TFF
FTFT⎪F FFT TFF FFT FFT F FFT
FTFF⎪F FFT TFF FTF FFT F FFF
FFTT⎪F FTF FFT TTT FFF F TTT
FFTF⎪F FTF FFT TFF FFF F TFF
FFFT⎪F FTF FTF FFT FFF F FFT
FFFF⎪F FTF FTF FTF FFF F FFF
Q.E.D.