Lean verification registry · Authored proofs · The Logos Architecture
Source recorded — formalization still required
Axiom-free: not established · 0 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: 2026-10-03T01:34:04.306Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:41:26.377Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 1823c904fdcb69e178c2200dd9b014d328cb7bbdf26a8f2a77cf36599972ad6d
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) Not executed: no complete licensed formal sequent recovered.
{P, P <-> Q, Q <-> R, R <-> S, S <-> T} |= ((P & Q) & (R & S) & T
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.
Unmatched formal parentheses
Redundancy in Proof for Logic, God, and Objective Principles by Maclain Hunter:
Premises (Logical Inputs):
P: Proof is logical, even when also empirical, legal, or otherwise, as if proof is not logical it is not logically valid and is logically and rationally “not proof”.
Q: Logic is the only logically consistent Source of Logic (Logos - God - First Cause of Logic and Existence). Another alleged “Source” that is “not Logic” would be (by definition) not completely “logically consistent”. It would not align fully with Logic as the Logical Source (or “True God”) absolutely and logically must.
R: Asking for proof of God is redundant, as God is and must be both the Foundation of the Cosmos (as that is the essence of the commonly accepted definition(s) of God) and must also be the Ground of Logic that is both fully logically coherent and that Logic itself coheres with (the Foundational and Real/Existential Coherence and Reality of), as alternatives to this coherence of God/Cosmos and Logic/Reason lead to incoherence and contradictions.
S: Assume that it were not the case, that the Logos (God - Cosmic Order - Logic - Coherence) were not inherently proven by even the concept of proof. That leads to logical contradiction. It is therefore inherently redundant to have proof when it comes to the Logos as God and Logic as the Standard of Proof. You’re asking for a concept that by definition must align with Logos to show that Logos exists. If that can’t be done, there is no such thing as proof.
T: If proof is not possible then theists need proof no more than anyone else, and if there is no Objective Reason (Logos - God - Coherence) then there is no Standard of Objective Truth or Moral Authority (another dictionary definition of “God”) to be wrong and immoral or in error and sinful according to, and thus a belief in the Logos is ethical and “not wrong” any way we turn things, including if the Logos (God of Reason) did not exist as atheism illogically (against the very existence of the Logical Standard of Existence and the Rational Structure intrinsic to the Cosmos) must posit to remain atheism and consistent in the denial of all conceptions, notions, and realities of God - including the coherent ones which atheism naturally denies (and must to remain atheism).
Logical Structure (Formal Proof - Logos):
{P, P <-> Q, Q <-> R, R <-> S, S <-> T} |= ((P & Q) & (R & S) & T
Conclusion (Logical Output):
Proof is proven to exist, which inherently proves (as a matter of the necessary logical alignment of proof, including this proof, with Objective Coherence and Logic itself) that the Universal Principle of Logic and Coherent Reason—the One True God or “Logos”—exists. To deny this or disbelieve it is irrational and contradicts Logic as it is using rational faculties that come from Pure Reason (Logos) to deny and undermine that Logos (True God) and thus the rational faculties and the doubters identity and existence itself. Therefore it is a redundancy to have proof for God (or Logic), as speaking of proof as a credible concept is to speak of God (Logos - Universal Reason) as a credible Standard, even when dealing with any sort of logically coherent (and thus “valid”) empiricism. This proof, even if incoherent would still (even through a misaligned position with Logos) prove the Standard (First Cause of Logic - the True God of Pure Reason - the Universal Logic that is genuine Logic according to Logic itself or “Logos” as it’s known in Greek Philosophy) exists.
Truth Table Analysis:
valid
↓ ↓ ↓ ↓ ↓ ↓
PQRST⎪P P↔Q Q↔R R↔S S↔T╞((P&Q)&(R&S))&T
――――――――――――――――――――――――――――――――――――――――
TTTTT⎪T TTT TTT TTT TTT TTT T TTT TT
TTTTF⎪T TTT TTT TTT TFF TTT T TTT FF
TTTFT⎪T TTT TTT TFF FFT TTT F TFF FT
TTTFF⎪T TTT TTT TFF FTF TTT F TFF FF
TTFTT⎪T TTT TFF FFT TTT TTT F FFT FT
TTFTF⎪T TTT TFF FFT TFF TTT F FFT FF
TTFFT⎪T TTT TFF FTF FFT TTT F FFF FT
TTFFF⎪T TTT TFF FTF FTF TTT F FFF FF
TFTTT⎪T TFF FFT TTT TTT TFF F TTT FT
TFTTF⎪T TFF FFT TTT TFF TFF F TTT FF
TFTFT⎪T TFF FFT TFF FFT TFF F TFF FT
TFTFF⎪T TFF FFT TFF FTF TFF F TFF FF
TFFTT⎪T TFF FTF FFT TTT TFF F FFT FT
TFFTF⎪T TFF FTF FFT TFF TFF F FFT FF
TFFFT⎪T TFF FTF FTF FFT TFF F FFF FT
TFFFF⎪T TFF FTF FTF FTF TFF F FFF FF
FTTTT⎪F FFT TTT TTT TTT FFT F TTT FT
FTTTF⎪F FFT TTT TTT TFF FFT F TTT FF
FTTFT⎪F FFT TTT TFF FFT FFT F TFF FT
FTTFF⎪F FFT TTT TFF FTF FFT F TFF FF
FTFTT⎪F FFT TFF FFT TTT FFT F FFT FT
FTFTF⎪F FFT TFF FFT TFF FFT F FFT FF
FTFFT⎪F FFT TFF FTF FFT FFT F FFF FT
FTFFF⎪F FFT TFF FTF FTF FFT F FFF FF
FFTTT⎪F FTF FFT TTT TTT FFF F TTT FT
FFTTF⎪F FTF FFT TTT TFF FFF F TTT FF
FFTFT⎪F FTF FFT TFF FFT FFF F TFF FT
FFTFF⎪F FTF FFT TFF FTF FFF F TFF FF
FFFTT⎪F FTF FTF FFT TTT FFF F FFT FT
FFFTF⎪F FTF FTF FFT TFF FFF F FFT FF
FFFFT⎪F FTF FTF FTF FFT FFF F FFF FT
FFFFF⎪F FTF FTF FTF FTF FFF F FFF FF
Q.E.D.