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: 2026-10-02T20:58:04.560Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:40:36.201Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: d7afa529455ee6e3132d061dd4b9bee152e9925171931709a91b55e986e5dcc2
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
Logic is Logic
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
Nested Structure by Maclain Hunter
Premises:
P: Recursion P: Logic is Logic and Logic is coherent; the Way of Knowing Reality and its Foundation is self-consistent; Mastery of Logic according to Logic; the relationship of P to F is logically equivalent to the self-grounding of phi in the golden ratio where phi equals one plus one divided by phi: (((P <-> P) <-> (P <-> P)) <-> ((P <-> P) <-> (P <-> P)))
Truth Table Analysis for P:
P⎪(((P↔P)↔(P↔P))↔((P↔P)↔(P↔P)))
T⎪ TTT T TTT T TTT T TTT
F⎪ FTF T FTF T FTF T FTF
(Tautology)
Q: Recursion Q: Reality is Reality and my logical reasoning and I are coherent; the Origin of Reality (or “God”) is self-consistent; my mastery of Logic according to Logic; the relationship of Q to F is logically equivalent to the self-grounding of phi in the golden ratio where phi equals one plus one divided by phi: (((Q <-> Q) <-> (Q <-> Q)) <-> ((Q <-> Q) <-> (Q <-> Q)))
Truth Table Analysis for Q:
Q⎪(((Q↔Q)↔(Q↔Q))↔((Q↔Q)↔(Q↔Q)))
T⎪ TTT T TTT T TTT T TTT
F⎪ FTF T FTF T FTF T FTF
(Tautology)
Formal Reasoning (F):
(((P <-> Q) <-> (P <-> Q)) <-> ((P <-> Q) <-> (P <-> Q))) |= (P v ~P) <-> (Q v ~Q)
Conclusion: {P, Q}:
This nested structure shows how, through recursion and the linked dynamics of the truth value of multiple premises Truth in Logic can manifest. Logic is Logic if and only if Reality is Reality and vice versa. Logic and I are coherent (unified rationally). the relationship of P and Q to F (or “Tautological Logical Structure and Form”) is logically equivalent to the self-grounding of phi in the golden ratio where phi equals one plus one divided by phi.
F = (P, Q) -> F = 1 + 1/F
Truth Table Analysis (F):
PQ⎪(((P↔Q)↔(P↔Q))↔((P↔Q)↔(P↔Q)))╞(P∨¬P)↔(Q∨¬Q)
TT⎪ TTT T TTT T TTT T TTT TTFT T TTFT
TF⎪ TFF T TFF T TFF T TFF TTFT T FTTF
FT⎪ FFT T FFT T FFT T FFT FTTF T TTFT
FF⎪ FTF T FTF T FTF T FTF FTTF T FTF
(Valid)
Q.E.D.