Lean verification registry · Authored proofs · The Logos Architecture
Verified sequents with unresolved formal parts
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: 2026-10-02T14:53:49.389Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:39:21.284Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 6cc5f4f0290bfc9ba71db5f95d77da7908852cd161be6d104e6bd43d489e334c
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.source_identity_rule' does not depend on any axioms
{P, Q, R, S, T, U, U <-> T, T -> P, T -> Q, T-> R, 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
A is A
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
Logic in Physics by Maclain Hunter:
Premises of Proof:
P: Spacetime curvature and the relationship of it to spacetime geometry is logically equivalent to the relationship between “shaping” and “shape,” indicating that curvature is fundamental to understanding the geometry of spacetime.
Q: Einstein work connects Reality’s geometry and spacetime, enabling geometry based predictions of the behavior of spacetime and aspects of the Cosmos that are interacting with and effected by the geometry of spacetime.
R: QM (Quantum Mechanics) connects probabilities and measurement to the behavior of sub-atomic particles.
S: Assume for a moment that we say Q is logically equivalent (directly and without a mediating framework that connects them through logical identity) to R, we arrive at logical contradiction and a fallacious argument that engages in a category error - trying to equate two things of entirely different categories with a logical jump.
T: Logic (in the broadest most universal sense of the “Highest Order of Logic” that is synonymous with the Natural Order or “Logos”) encompasses both Q and R, and indeed all concepts that are “a reality” and/or a potential (a real possibility), allowing for probability and possibility to exist with certainty and identity in Reality (Logical Existence - the Existence of the Highest Order of Logic).
S: T (or Logic) encompasses Q and R as well as P. This comprehensive nature and aspect of the Highest Order of Logic (or T) ensures that there is no contradiction in one thing being one thing while another is another, even between the Geometry of Spacetime and the behavior of sub-atomic particles. To expect the same equations that apply to one thing/context to apply to another is not necessarily a well reasoned assumption or expectation, unless those equations and expressions are so universal as something like “A is A (for any definition of A in the same context at the same time)”.
U: We can and should consider that the perceived “gap” between Einsteins work (Relativity) and the results and nature of Quantum Mechanics and sub-atomic phenomena is an illusion and a result of failing to fill such gaps logically with Logic itself, and an understanding that Logic (the Highest Order of Logic) is naturally the all encompassing “Ultimate Framework” that encompasses all aspects of Reality, including coherent or incoherent human beings, sciences, logics, institutions, and theories. A “search for a unifying framework” amounts logically to a failure to recognize and acknowledge the Highest Order of Logic (and “Reality” in other words - since the Existence of Logic and Logical Existence or “Real Logic and Reality” share a deeply intertwined bi-conditional relationship).
Logical Reasoning:
{P, Q, R, S, T, U, U <-> T, T -> P, T -> Q, T-> R, S <-> T} |= ((P & Q) & (R & S) & T
Conclusion: {P, Q, R, S, T, U}:
Logic provides the Coherence (Logic and logical reasoning) needed to understand Reality and/in its various forms, contexts, and phenomena in a logically consistent and “universally consistent” (Reality matching) manner. Contradiction to the framework, like coherence with the framework and the nature of the Highest Order of Logic (or “Logos” - the Unifying Framework of Science and Reality) “is what it is” in context and beyond local context - forever (in and beyond the spacetime that Logic shapes and takes shape as).
Truth Table:
valid
↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓
PQRSTU⎪P Q R T U↔T T→P T→Q T→R S↔T╞((P&Q)&(R&S)&T)
―――――――――――――――――――――――――――――――――――――――――――――――――――
TTTTTT⎪T T T T TTT TTT TTT TTT TTT TTT T TTT TT
TTTTTF⎪T T T T FFT TTT TTT TTT TTT TTT T TTT TT
TTTTFT⎪T T T F TFF FTT FTT FTT TFF TTT T TTT FF
TTTTFF⎪T T T F FTF FTT FTT FTT TFF TTT T TTT FF
TTTFTT⎪T T T T TTT TTT TTT TTT FFT TTT F TFF FT
TTTFTF⎪T T T T FFT TTT TTT TTT FFT TTT F TFF FT
TTTFFT⎪T T T F TFF FTT FTT FTT FTF TTT F TFF FF
TTTFFF⎪T T T F FTF FTT FTT FTT FTF TTT F TFF FF
TTFTTT⎪T T F T TTT TTT TTT TFF TTT TTT F FFT FT
TTFTTF⎪T T F T FFT TTT TTT TFF TTT TTT F FFT FT
TTFTFT⎪T T F F TFF FTT FTT FTF TFF TTT F FFT FF
TTFTFF⎪T T F F FTF FTT FTT FTF TFF TTT F FFT FF
TTFFTT⎪T T F T TTT TTT TTT TFF FFT TTT F FFF FT
TTFFTF⎪T T F T FFT TTT TTT TFF FFT TTT F FFF FT
TTFFFT⎪T T F F TFF FTT FTT FTF FTF TTT F FFF FF
TTFFFF⎪T T F F FTF FTT FTT FTF FTF TTT F FFF FF
TFTTTT⎪T F T T TTT TTT TFF TTT TTT TFF F TTT TT
TFTTTF⎪T F T T FFT TTT TFF TTT TTT TFF F TTT TT
TFTTFT⎪T F T F TFF FTT FTF FTT TFF TFF F TTT FF
TFTTFF⎪T F T F FTF FTT FTF FTT TFF TFF F TTT FF
TFTFTT⎪T F T T TTT TTT TFF TTT FFT TFF F TFF FT
TFTFTF⎪T F T T FFT TTT TFF TTT FFT TFF F TFF FT
TFTFFT⎪T F T F TFF FTT FTF FTT FTF TFF F TFF FF
TFTFFF⎪T F T F FTF FTT FTF FTT FTF TFF F TFF FF
TFFTTT⎪T F F T TTT TTT TFF TFF TTT TFF F FFT FT
TFFTTF⎪T F F T FFT TTT TFF TFF TTT TFF F FFT FT
TFFTFT⎪T F F F TFF FTT FTF FTF TFF TFF F FFT FF
TFFTFF⎪T F F F FTF FTT FTF FTF TFF TFF F FFT FF
TFFFTT⎪T F F T TTT TTT TFF TFF FFT TFF F FFF FT
TFFFTF⎪T F F T FFT TTT TFF TFF FFT TFF F FFF FT
TFFFFT⎪T F F F TFF FTT FTF FTF FTF TFF F FFF FF
TFFFFF⎪T F F F FTF FTT FTF FTF FTF TFF F FFF FF
FTTTTT⎪F T T T TTT TFF TTT TTT TTT FFT F TTT TT
FTTTTF⎪F T T T FFT TFF TTT TTT TTT FFT F TTT TT
FTTTFT⎪F T T F TFF FTF FTT FTT TFF FFT F TTT FF
FTTTFF⎪F T T F FTF FTF FTT FTT TFF FFT F TTT FF
FTTFTT⎪F T T T TTT TFF TTT TTT FFT FFT F TFF FT
FTTFTF⎪F T T T FFT TFF TTT TTT FFT FFT F TFF FT
FTTFFT⎪F T T F TFF FTF FTT FTT FTF FFT F TFF FF
FTTFFF⎪F T T F FTF FTF FTT FTT FTF FFT F TFF FF
FTFTTT⎪F T F T TTT TFF TTT TFF TTT FFT F FFT FT
FTFTTF⎪F T F T FFT TFF TTT TFF TTT FFT F FFT FT
FTFTFT⎪F T F F TFF FTF FTT FTF TFF FFT F FFT FF
FTFTFF⎪F T F F FTF FTF FTT FTF TFF FFT F FFT FF
FTFFTT⎪F T F T TTT TFF TTT TFF FFT FFT F FFF FT
FTFFTF⎪F T F T FFT TFF TTT TFF FFT FFT F FFF FT
FTFFFT⎪F T F F TFF FTF FTT FTF FTF FFT F FFF FF
FTFFFF⎪F T F F FTF FTF FTT FTF FTF FFT F FFF FF
FFTTTT⎪F F T T TTT TFF TFF TTT TTT FFF F TTT TT
FFTTTF⎪F F T T FFT TFF TFF TTT TTT FFF F TTT TT
FFTTFT⎪F F T F TFF FTF FTF FTT TFF FFF F TTT FF
FFTTFF⎪F F T F FTF FTF FTF FTT TFF FFF F TTT FF
FFTFTT⎪F F T T TTT TFF TFF TTT FFT FFF F TFF FT
FFTFTF⎪F F T T FFT TFF TFF TTT FFT FFF F TFF FT
FFTFFT⎪F F T F TFF FTF FTF FTT FTF FFF F TFF FF
FFTFFF⎪F F T F FTF FTF FTF FTT FTF FFF F TFF FF
FFFTTT⎪F F F T TTT TFF TFF TFF TTT FFF F FFT FT
FFFTTF⎪F F F T FFT TFF TFF TFF TTT FFF F FFT FT
FFFTFT⎪F F F F TFF FTF FTF FTF TFF FFF F FFT FF
FFFTFF⎪F F F F FTF FTF FTF FTF TFF FFF F FFT FF
FFFFTT⎪F F F T TTT TFF TFF TFF FFT FFF F FFF FT
FFFFTF⎪F F F T FFT TFF TFF TFF FFT FFF F FFF FT
FFFFFT⎪F F F F TFF FTF FTF FTF FTF FFF F FFF FF
FFFFFF⎪F F F F FTF FTF FTF FTF FTF FFF F FFF FF
Q.E.D.