Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
Axiom-free: true · 1 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: 2026-10-03T01:34:09.158Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:39:46.281Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: f86cc0bb797a84091e1752913616ad3d2768dc1999336159ba9dd53a68149b27
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
{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.
Logical Proof is Empirical Data by Maclain Hunter:
Definition of Data:
Discrete facts or observations collected for reference, analysis, or processing. These may be quantitative measurements, qualitative descriptions, or recorded signals that represent information about reality.
Definition of Logical Proof:
A rigorous logical argument that demonstrates the truth of a conclusion by proceeding step-by-step from accepted premises or axioms using valid rules of inference, leaving no possibility of the conclusion being false if the premises are true.
Premises:
P: Data and logical proof can be coherent/one and are not mutually exclusive, including “empirical data”. A proof can be both proof and empirical data at once.
Q: Logical proof can be coherently considered data and can be observed when presented formally and in writing (or the like) - allowing for logical proof to serve (feasibly) as empirical data and evidence.
R: Assume for a moment that ~(P & Q) were true, and that a logical proof could not serve as empirically observable data and evidence (ie - in scientific processes aiming to verify the existence of the Source of Logic and Existence or “Logos”, where logical proof is direct evidence of the Logos in a local/finite context, scientifically admissible and valid also). That would lead to a logical contradiction where a logical proof, which amounts to a logically proven fact or set of facts, is somehow not data and fact or a set of data and facts.
S: To deny that a valid logical proof is data supporting the existence of the Logos (the Foundation of Logic in logically consistent identity and Logic) is a logically untenable position that amounts to denying the nature of both data and proof in the context of the Logic of Reality (Logos - the God of Reason or “Logical Origin”). Therefore, without logical flaw in this proof and premise this proof and premise are themselves empirically observed/observable data that supports the existence of the God of Reason (Logos - Logic - the Logical Origin of Logical Existence).
Formal Argument:
{P, P -> Q, Q -> R, R -> S} |= (P & Q) & (R & S)
Conclusion: {P, Q, R, S}:
Logical proof is data (empirically observable/observed) supporting the existence of the Logos/Logic, and to assume otherwise leads to logical contradiction affirming that proof is data and that logical proof can serve to help empirically confirm the Logos (Universal Logic - the God of Reason). As premise S affirms this proof and these premises are themselves empirically observed/observable data that supports the existence of the God of Reason (Logos - Logic - the Logical Origin of Logical Existence).
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 FTT TTT F FFT
TTFF⎪T TTT TFF FTF TTT F FFF
TFTT⎪T TFF FTT TTT TFF F TTT
TFTF⎪T TFF FTT TFF TFF F TFF
TFFT⎪T TFF FTF FTT TFF F FFT
TFFF⎪T TFF FTF FTF TFF F FFF
FTTT⎪F FTT TTT TTT FFT F TTT
FTTF⎪F FTT TTT TFF FFT F TFF
FTFT⎪F FTT TFF FTT FFT F FFT
FTFF⎪F FTT TFF FTF FFT F FFF
FFTT⎪F FTF FTT TTT FFF F TTT
FFTF⎪F FTF FTT TFF FFF F TFF
FFFT⎪F FTF FTF FTT FFF F FFT
FFFF⎪F FTF FTF FTF FFF F FFF
Q.E.D.