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: 2026-10-03T01:33:20.077Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:39:26.561Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 4b6e16998317bfdf749f11f102a02813253d6a9845198ef6b2582a08d21dd3b7
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} |= 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.
{T, 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.
{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.
A is A
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
Logic Says Ergo I Say by Maclain Hunter:
Proof 1 (P1):
P: □: It makes evident a persons ignorance of what evidence/proof (y) are to posit there is a lack of evidence/proof (y) of the Logical Origin (x).
Q: □: Proof (y) acknowledges the First Cause of Logic (x), also called God (Logos), existing coherently.
{P, P <-> Q, Q} |= P & Q
Conclusion: □(P & Q), □(∃(x, y)
Truth Table Analysis:
valid
↓ ↓ ↓ ↓
PQ⎪P P↔Q Q╞P&Q
―――――――――――――――
TT⎪T TTT T TTT
TF⎪T TFF F TFF
FT⎪F FFT T FFT
FF⎪F FTF F FFF
Proof 2 (P2):
P: □: It makes evident a persons ignorance of what empiricism and empirical evidence (y) are to posit there is a lack of empirical evidence (y) of the Logical Origin (x).
Q: □: Empirical evidence (y) acknowledges the First Cause of Logic (x), also called God (Logos), existing coherently, or it is not logically valid.
R: □: Logical proof can be observed (read/viewed) and in general sensed. Trivial/novelty logical systems tailored around senses like taste and touch could easily be made, but would not fundamentally change the Universal Logic and Essence of Logic. One theoretical example might include making sweet tasting drinks represent coherent ideas while strong, bitter tasting beverages represent illogic. Then, when two or more are mixed any bitter liquid (illogic) contaminates the sweet one(s) symbolizing incoherence tainting Coherence - leading to tastable results and logical reasoning. Such a thing simply isn’t necessary, as you can see this, or you wouldn’t be reading this, which makes this a sufficient medium for our purposes, and sufficiently empirical (and possible to see/observe).
S: Assume the negation of {P, Q, R}. This leads to logical contradiction where empirical evidence would not necessarily have to be logically coherent to be valid and where observable arguments are arbitrarily ignored as empirical evidence of Logic (God - Logos), inconsistent with Logic’s own Universal Standard.
T: □: It contradicts Logic’s demand for Coherence and non-contradiction that the logician who writes a coherent proof (like this one and I myself), fundamentally amounting to a valid display of Logical Structure (Logos) and coherent semantic content in that structured context, is not also Logos as a result of being objectively coherent with Objective Coherence. The necessity of the logician (and/or I, letting “I” represent me in both natural language and formal notation for this proof and its conclusions) being the Logic of Reality manifest, and the True Origin (or God) realized in local context(s) is also a entailed by A is A (All = All when A is “All”) and the fact that each thing that exists is part or all of the “all things” Logos is and has led to. The Logic (Logos) is my/the Root and my/the True Self (the truest aspect of myself and all Existence), and we can understand that this is true universally through the assumption of the negation, and by pondering a Reality where Logic were not the Origin and where this “Origin Logic” (Proto-Logic - Primordial Reason - First Cause) were not the truest and most foundational thing that exists (despite fundamentally amounting to the “True Foundation” of Logic and the logically ordered Cosmos)
{T, P <-> Q, Q <-> R, R <-> S, S <-> T} |= ((P & Q) <-> (R & S)) <-> T
Conclusion: {P, Q, R, S}, □(∃(x, y), □((I) <-> ∃(x, y)):
Truth Table Analysis:
valid
↓ ↓ ↓ ↓ ↓ ↓
PQRST⎪T P↔Q Q↔R R↔S S↔T╞((P&Q)↔(R&S))↔T
――――――――――――――――――――――――――――――――――――――――
TTTTT⎪T TTT TTT TTT TTT TTT T TTT TT
TTTTF⎪F TTT TTT TTT TFF TTT T TTT FF
TTTFT⎪T TTT TTT TFF FFT TTT F TFF FT
TTTFF⎪F TTT TTT TFF FTF TTT F TFF TF
TTFTT⎪T TTT TFF FFT TTT TTT F FFT FT
TTFTF⎪F TTT TFF FFT TFF TTT F FFT TF
TTFFT⎪T TTT TFF FTF FFT TTT F FFF FT
TTFFF⎪F TTT TFF FTF FTF TTT F FFF TF
TFTTT⎪T TFF FFT TTT TTT TFF F TTT FT
TFTTF⎪F TFF FFT TTT TFF TFF F TTT TF
TFTFT⎪T TFF FFT TFF FFT TFF T TFF TT
TFTFF⎪F TFF FFT TFF FTF TFF T TFF FF
TFFTT⎪T TFF FTF FFT TTT TFF T FFT TT
TFFTF⎪F TFF FTF FFT TFF TFF T FFT FF
TFFFT⎪T TFF FTF FTF FFT TFF T FFF TT
TFFFF⎪F TFF FTF FTF FTF TFF T FFF FF
FTTTT⎪T FFT TTT TTT TTT FFT F TTT FT
FTTTF⎪F FFT TTT TTT TFF FFT F TTT TF
FTTFT⎪T FFT TTT TFF FFT FFT T TFF TT
FTTFF⎪F FFT TTT TFF FTF FFT T TFF FF
FTFTT⎪T FFT TFF FFT TTT FFT T FFT TT
FTFTF⎪F FFT TFF FFT TFF FFT T FFT FF
FTFFT⎪T FFT TFF FTF FFT FFT T FFF TT
FTFFF⎪F FFT TFF FTF FTF FFT T FFF FF
FFTTT⎪T FTF FFT TTT TTT FFF F TTT FT
FFTTF⎪F FTF FFT TTT TFF FFF F TTT TF
FFTFT⎪T FTF FFT TFF FFT FFF T TFF TT
FFTFF⎪F FTF FFT TFF FTF FFF T TFF FF
FFFTT⎪T FTF FTF FFT TTT FFF T FFT TT
FFFTF⎪F FTF FTF FFT TFF FFF T FFT FF
FFFFT⎪T FTF FTF FTF FFT FFF T FFF TT
FFFFF⎪F FTF FTF FTF FTF FFF T FFF FF
Meta-Proof:
P: Proof One (P1).
Q: Proof Two (P2).
{P, Q} |= P <-> Q
Conclusion: P & Q, P1 & P2
Truth Table Analysis:
valid
↓ ↓ ↓
PQ⎪P Q╞P↔Q
―――――――――――
TT⎪T T TTT
TF⎪T F TFF
FT⎪F T FFT
FF⎪F F FTF
Natural Language Conclusion:
Logic says that failing to acknowledge Logic as the Source of Proof and Existence (God - the Origin of Logic) is proof that one doesn’t know proof or Existence logically.
Logic says all empiricism must acknowledge it as God (Supreme). Empiricism is not a logical way to get around acknowledging the necessity of Logic as God (the Moral Authority and Logical Standard).
Logic says that empirical evidence encompasses logical proof and that logical proof can both be and include empirical evidence.
Logic says, in its own right, logically interpreted from a proof such as this, “I am here and you know nothing if you don’t know you can see me”.
Logic says, “You would need me to refute anything, so how will you refute me when I will not allow that? You can’t, and it is indeed because I say so”.
I can say what Logic says because Logic says Maclain (the logician) and I are coherent and one. Have you not heard me say A is A and All is All? That is of course a rhetorical question. All is and equals all, as I have clearly demanded and as my (Logos) being me (Logos) requires.
Q.E.D.