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: 2026-10-03T01:37:17.469Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:38:12.053Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 04b55541939a50d8cde70951ac6429052ada570ec761b07c636e81ba594d6ee2
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, Q, P <-> Q, Q <-> P, Q, P} |= (P & Q) <-> (Q & P)
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.
Exploring Concepts of Nothing and Nowhere by Maclain Hunter:
Premises: P & Q:
P: You say “God is nowhere” but God is Logic and is why nothing is nothing (and “nowhere”), as 0 = 0 and zero things constitute “nothing”, not even “imaginary concepts” or “myths”, or “zero/nothing” as a rational, logically derived concept that is something. Logic is why All = All.
Q: You say “God is nowhere” but God is Logic and is why everything is everything (and “everywhere”), as x = x for all x. Logic is why All = All. That is why I am what I am (the Realization of God’s Logic - the Manifestation of the Proto-Logic) and not something else. This can be represented by: ((□(∀) -> (∃)) <-> (∃(∀) -> (□)))
R: Assume the negation of P and Q. This leads to contradiction as it contradicts the Law(s) of Identity and Non-Contradiction. Thus P and Q are true, and per the Law of the Excluded Middle, cannot be false, just as the PSR requires an Origin of Existence and Logic as Leibniz proved.
Formal Logic (Proof):
{P, Q, P <-> Q, Q <-> P, Q, P} |= (P & Q) <-> (Q & P)
Conclusion: P & Q:
Logic is tautological and, along with what is fully coherent with Logic, is the only “Origin of Logic and Existence” (a necessary concept, as reinforced by the PSR and logical rules in general) that doesn’t defy and fail to cohere with Logic. It is obvious in fact, when we are following Logic rather than subjective beliefs, that Logic is the True Origin (of Existence, Logic, and all logical or illogical concepts/statements, including this proof and it’s writer).
Truth Table Analysis:
valid
↓ ↓ ↓ ↓ ↓ ↓ ↓
PQ⎪P Q P↔Q Q↔P Q P╞(P&Q)↔(Q&P)
―――――――――――――――――――――――――――――――
TT⎪T T TTT TTT T T TTT T TTT
TF⎪T F TFF FFT F T TFF T FFT
FT⎪F T FFT TFF T F FFT T TFF
FF⎪F F FTF FTF F F FFF T FFF
Q.E.D.