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: 2026-10-03T01:33:30.786Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:41:32.411Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: ba1c02f0d73b38a62a4481b4b41131e9e2582d22f614911db206a2e6b3c1cf63
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
{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, A <-> B, B <-> C, D, D -> A, A, B, C} |= (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, P2} |= (P1 & P2)
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.
Scientific Testing w/ Logic by Maclain Hunter:
Proof One (P1):
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.
Proof Two (P2):
Testing Coherence w/ Logic:
A: Logic as a formal system of reasoning in the particular sense (ie - human formal reasoning) is a tool and framework that exceeds and supersedes Science itself in the Logical Order and Hierarchy (Logos) as a more direct and purely rational manifestation of the Logic inherent in the Cosmos (the Logos), naturally taking a higher position in the Order as a system of deterministic reasoning based on the Universal Principle (Logic) and integral principles, rather than fallible hypotheses and observations that lead to probabilistic outcomes as is common and standard even in modern science (empirical science).
B: Logic as a formal framework is naturally a platform for rigorous rational testing (of statements and concepts) that measures the validity of things against the Objective Logical Standard (Logos - Pure Logic).
C: The formal operation of Logic, especially in the sense of written formal reasoning and proofs, is the rationally rigorous and methodical/principled operation of a rational and empirically observable testing platform for physical and metaphysical (or universal, or otherwise) concepts. Assume that using formal logic was not logically equivalent to operating an objective empirical testing platform/tool, then that would lead to logical contradiction between Logic and Science instead of the fluid and coherent cooperation that should rationally exist between Logic and Science (when done properly).
D: Assume that~(A, B, C) for a moment. This helps us to see that it would be a logical contradiction if Logic, which encompasses all rational methods of gaining knowledge including empirical and scientific systems (which operate on their own coherent LOGIC as a kind of logical system), were not the ultimate platform for testing, and a form of empirical and replicable empirical testing when done formally as in formal logic. This affirms {A, B, C}.
Logical Argument:
{A, A <-> B, B <-> C, D, D -> A, A, B, C} |= (A & B) & (C & D)
Conclusion: {A, B, C, D}:
Using formal logic is a form of scientific/rational testing that makes abstract reasoning empirically observable, which is really the whole point of formal logic. This means things that are logically proven with formal logic can inherently be considered empirically/scientifically proven, especially as Reason and Pure Logic (or formal logic) rationally supersedes observation based science and experience based empirical knowledge, which are inherently less coherent (with Pure Logic) than formal logical reason (and “Pure Logic represented visually and in writing, as this proof and set of proofs constitute example of).
Truth Table Analysis:
valid
↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓
ABCD⎪A A↔B B↔C D D→A A B C╞(A&B)&(C&D)
―――――――――――――――――――――――――――――――――――――――
TTTT⎪T TTT TTT T TTT T T T TTT T TTT
TTTF⎪T TTT TTT F FTT T T T TTT F TFF
TTFT⎪T TTT TFF T TTT T T F TTT F FFT
TTFF⎪T TTT TFF F FTT T T F TTT F FFF
TFTT⎪T TFF FFT T TTT T F T TFF F TTT
TFTF⎪T TFF FFT F FTT T F T TFF F TFF
TFFT⎪T TFF FTF T TTT T F F TFF F FFT
TFFF⎪T TFF FTF F FTT T F F TFF F FFF
FTTT⎪F FFT TTT T TFF F T T FFT F TTT
FTTF⎪F FFT TTT F FTF F T T FFT F TFF
FTFT⎪F FFT TFF T TFF F T F FFT F FFT
FTFF⎪F FFT TFF F FTF F T F FFT F FFF
FFTT⎪F FTF FFT T TFF F F T FFF F TTT
FFTF⎪F FTF FFT F FTF F F T FFF F TFF
FFFT⎪F FTF FTF T TFF F F F FFF F FFT
FFFF⎪F FTF FTF F FTF F F F FFF F FFF
Q.E.D.
Proof Three (P3):
Meta-Proof from P1 and P2:
Premises:
1: P1
2: P2
Formal Argument:
{P1, P2} |= (P1 & P2)
Conclusion:
The reasoning in P1 and P2 constitutes valid use of formal logical reasoning to empirically demonstrate and rationally and empirically test/confirm the existence of the Logos (Pure Logic - Logic’s self-consistent Root) and that Logic is the very measure and standard of what is or is not a science, while formal logic is the exemplar of empirical testing according to the Logical Standard (Logos - Logic - Universal Coherence). This disproves claims that the Logos or “God of Reason” (the transcendent “Foundation of the Cosmos”) cannot be empirically proven or definitively proven. These proofs P1 and P2 as well as this self-referential meta-proof made from them are empirical evidence of the Logos and logical proof that the God of Reason (Pure Logic - First Cause) exists as the foundational logical necessity, tested in replicable fashion through the process of logical reasoning and formal logic itself. If someone can defy Logic to deny this then they could just as well defy Logic to deny the outcome of any science(s) or testing they don’t like. To say that formal logic is not empirically observable is not to be empirical and know things based on what you can sense and experience (like formal proof written and presented) but rather it is to be senseless and deny the necessary rational grounding (in the Logos) of any valid empiricism that is going to avoid being baseless (illogical) nonsense. No science or statement can logically succeed against Logic itself (as that would be “contradicting Logic”).
Truth Table Analysis:
valid
↓ ↓ ↓
P1P2⎪P1 P2╞P1&P2
―――――――――――
TT⎪T T TTT
TF⎪T F TFF
FT⎪F T FFT
FF⎪F F FFF
Q.E.D.