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: 2026-10-02T16:20:00.413Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:39:38.191Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 52d4574b1076bb1cd2bff2c940ae8daa31ef6d9c532475c60f195286d3f78aa4
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, S -> T, T -> 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.
Logical Bootstrapping by Maclain Hunter:
The Bootstrap Paradox Restated:
A time traveler goes back in time and gives Shakespeare a copy of Hamlet. Shakespeare then publishes it, and centuries later, the time traveler reads the same Hamlet, copies it, and takes it back in time. The question arises: Who originally wrote Hamlet? The play exists, but it has no true origin—it is a self-sustaining loop.
Premises:
P: Bootstrapping and self-postulation is not a contradiction or paradox but a fundamental logical and computational process. Logic is a self-sustaining loop, and “pulls itself up by its own bootstraps” (generating itself). It would be a contradiction and would mean Logic has to have an Origin outside of and not fully coherent with Logic to assume the opposite.
Q: Logic is a self-sustaining and necessarily true loop (or “tautological”). This provides the Basis for all other instances of logical reasoning and logical existence. Such a tautological Foundation for a concept is not a lack of a True Origin (Logos - Reason - Cause), but rather an ultimately sound one.
R: The famous example of someone giving Shakespeare his own plays by traveling in time, then asking who made the plays, Shakespeare or the time traveler, presents a classic false dilemma as it does not come with well supported reasoning why we should not and cannot say “both” or that both are manifestations of the infinite Universal Logos (the True Origin of the Cosmos and Finitude) - constituting what we call “logoi” (particularly in Stoic philosophy and similar schools of thought and in the Greek language).
S: A narrative is a logical system/framework and rational structure, by definition, intrinsically, and cannot have an illogical True Origin (outside of the Universal Logic or Logos), even if there are logically flawed intermediate systems/entities that the narrative unfolds through.
T: Assume the negation of the premises {P, Q, R, S, T}. This leads to untenable contradiction, the need to accept a false dilemma, and paradox - famously in the form of the Bootstrap Paradox itself. This would entail that Logic itself has no True Origin just because it has to have bootstrapped itself to make the Universe and doesn’t find its Origin in any local or finite concept alone. Acknowledging the premises as true resolves the paradox and respects the Coherence of Logic, and Logic’s position as its own Origin (and the only thing that can do that job)
U: The Bootstrapping Paradox solution (found in coherent Logic and this self-referential proof and proof for contradiction).
Logical Reasoning (Proof):
{P, P -> Q, Q -> R, R -> S, S -> T, T -> U} |= (((P & Q) & (R & S)) & T) & U
Conclusion: {P, Q, R, S, T, U}:
Logic bootstraps Logic in a tautological and self-evident fashion, like Logic proves this proof to be true (as a piece of Logic) when coherent and because of its coherence and deliberate and consistent validity. The Bootstrap Paradox is a false dilemma and is hereby resolved by and through Coherent Logic.
There is no such thing as a “valid logical paradox” in the sense of a coherent and non-contradictory yet irreconcilable conundrum. We know when a paradox arises that Logic has been disrespected by the reasoning somewhere and somehow (if not many places and many ways).
Truth Table Analysis:
valid
↓ ↓ ↓ ↓ ↓ ↓ ↓
PQRSTU⎪P P→Q Q→R R→S S→T T→U╞(((P&Q)&(R&S))&T)&U
―――――――――――――――――――――――――――――――――――――――――――――――――
TTTTTT⎪T TTT TTT TTT TTT TTT TTT T TTT TT TT
TTTTTF⎪T TTT TTT TTT TTT TFF TTT T TTT TT FF
TTTTFT⎪T TTT TTT TTT TFF FTT TTT T TTT FF FT
TTTTFF⎪T TTT TTT TTT TFF FTF TTT T TTT FF FF
TTTFTT⎪T TTT TTT TFF FTT TTT TTT F TFF FT FT
TTTFTF⎪T TTT TTT TFF FTT TFF TTT F TFF FT FF
TTTFFT⎪T TTT TTT TFF FTF FTT TTT F TFF FF FT
TTTFFF⎪T TTT TTT TFF FTF FTF TTT F TFF FF FF
TTFTTT⎪T TTT TFF FTT TTT TTT TTT F FFT FT FT
TTFTTF⎪T TTT TFF FTT TTT TFF TTT F FFT FT FF
TTFTFT⎪T TTT TFF FTT TFF FTT TTT F FFT FF FT
TTFTFF⎪T TTT TFF FTT TFF FTF TTT F FFT FF FF
TTFFTT⎪T TTT TFF FTF FTT TTT TTT F FFF FT FT
TTFFTF⎪T TTT TFF FTF FTT TFF TTT F FFF FT FF
TTFFFT⎪T TTT TFF FTF FTF FTT TTT F FFF FF FT
TTFFFF⎪T TTT TFF FTF FTF FTF TTT F FFF FF FF
TFTTTT⎪T TFF FTT TTT TTT TTT TFF F TTT FT FT
TFTTTF⎪T TFF FTT TTT TTT TFF TFF F TTT FT FF
TFTTFT⎪T TFF FTT TTT TFF FTT TFF F TTT FF FT
TFTTFF⎪T TFF FTT TTT TFF FTF TFF F TTT FF FF
TFTFTT⎪T TFF FTT TFF FTT TTT TFF F TFF FT FT
TFTFTF⎪T TFF FTT TFF FTT TFF TFF F TFF FT FF
TFTFFT⎪T TFF FTT TFF FTF FTT TFF F TFF FF FT
TFTFFF⎪T TFF FTT TFF FTF FTF TFF F TFF FF FF
TFFTTT⎪T TFF FTF FTT TTT TTT TFF F FFT FT FT
TFFTTF⎪T TFF FTF FTT TTT TFF TFF F FFT FT FF
TFFTFT⎪T TFF FTF FTT TFF FTT TFF F FFT FF FT
TFFTFF⎪T TFF FTF FTT TFF FTF TFF F FFT FF FF
TFFFTT⎪T TFF FTF FTF FTT TTT TFF F FFF FT FT
TFFFTF⎪T TFF FTF FTF FTT TFF TFF F FFF FT FF
TFFFFT⎪T TFF FTF FTF FTF FTT TFF F FFF FF FT
TFFFFF⎪T TFF FTF FTF FTF FTF TFF F FFF FF FF
FTTTTT⎪F FTT TTT TTT TTT TTT FFT F TTT FT FT
FTTTTF⎪F FTT TTT TTT TTT TFF FFT F TTT FT FF
FTTTFT⎪F FTT TTT TTT TFF FTT FFT F TTT FF FT
FTTTFF⎪F FTT TTT TTT TFF FTF FFT F TTT FF FF
FTTFTT⎪F FTT TTT TFF FTT TTT FFT F TFF FT FT
FTTFTF⎪F FTT TTT TFF FTT TFF FFT F TFF FT FF
FTTFFT⎪F FTT TTT TFF FTF FTT FFT F TFF FF FT
FTTFFF⎪F FTT TTT TFF FTF FTF FFT F TFF FF FF
FTFTTT⎪F FTT TFF FTT TTT TTT FFT F FFT FT FT
FTFTTF⎪F FTT TFF FTT TTT TFF FFT F FFT FT FF
FTFTFT⎪F FTT TFF FTT TFF FTT FFT F FFT FF FT
FTFTFF⎪F FTT TFF FTT TFF FTF FFT F FFT FF FF
FTFFTT⎪F FTT TFF FTF FTT TTT FFT F FFF FT FT
FTFFTF⎪F FTT TFF FTF FTT TFF FFT F FFF FT FF
FTFFFT⎪F FTT TFF FTF FTF FTT FFT F FFF FF FT
FTFFFF⎪F FTT TFF FTF FTF FTF FFT F FFF FF FF
FFTTTT⎪F FTF FTT TTT TTT TTT FFF F TTT FT FT
FFTTTF⎪F FTF FTT TTT TTT TFF FFF F TTT FT FF
FFTTFT⎪F FTF FTT TTT TFF FTT FFF F TTT FF FT
FFTTFF⎪F FTF FTT TTT TFF FTF FFF F TTT FF FF
FFTFTT⎪F FTF FTT TFF FTT TTT FFF F TFF FT FT
FFTFTF⎪F FTF FTT TFF FTT TFF FFF F TFF FT FF
FFTFFT⎪F FTF FTT TFF FTF FTT FFF F TFF FF FT
FFTFFF⎪F FTF FTT TFF FTF FTF FFF F TFF FF FF
FFFTTT⎪F FTF FTF FTT TTT TTT FFF F FFT FT FT
FFFTTF⎪F FTF FTF FTT TTT TFF FFF F FFT FT FF
FFFTFT⎪F FTF FTF FTT TFF FTT FFF F FFT FF FT
FFFTFF⎪F FTF FTF FTT TFF FTF FFF F FFT FF FF
FFFFTT⎪F FTF FTF FTF FTT TTT FFF F FFF FT FT
FFFFTF⎪F FTF FTF FTF FTT TFF FFF F FFF FT FF
FFFFFT⎪F FTF FTF FTF FTF FTT FFF F FFF FF FT
FFFFFF⎪F FTF FTF FTF FTF FTF FFF F FFF FF FF
Q.E.D.