Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
Axiom-free: true · 3 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: 2026-10-03T01:29:49.848Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:42:49.793Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 7c57bf304b2a920bc99e730fa761f3d8c06b3bd11709eaa4347e0e39678ee343
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
{A, A -> ~B, (B & C) -> E, (C & D) -> D} |= (D -> ~(B & E)) & (D -> A)
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, Q <-> R} |= R -> (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.
{W, X, Y, (W & X) -> Z, (X & Y) -> Z} |= Z <-> X
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.
Validation Via Tautological Sieve by Maclain Hunter
Premises:
A: The Tautological Sieve (the invariant, self-authenticating architecture of Reality's Logic). Full proof below.
B: Negation of all (including logical necessity and Logos; including Cosmos and Theos).
C: Human consciousness.
D: Coherence (or Godelian ontological G encompassing all that is coherent).
E: Incoherence and/or delusion.
Formal Argument:
{A, A -> ~B, (B & C) -> E, (C & D) -> D} |= (D -> ~(B & E)) & (D -> A)
Conclusion: (A & D) <-> ((C -> C) <-> (~B & ~E)):
Logical Coherence (D) provides a filter or sieve (A) determining consistently what can (or cannot) coherently exist. The negation of all realities (B) and the incoherence and/or delusion (E) possible in the human mind or consciousness (C) do not properly align with or negate Logic/Coherence (D) and simply fail the test of A.
QED
For Background:
Tautological Sieve (A):
P: Let x be God and let y be Logic: ψ <-> [∀y □φ(x)] |= [□∀x φ(y)] -> ψ
Q: ∀φ -> ψ |= ψ <-> □φ
R: Let φ represent fully coherent and rationally existent logical constant (Logos)
S: Let ψ represent the empirical location of φ, which is trivial.
{P <-> Q, Q <-> R} |= R -> (Q <-> P)
QED
Elaboration On Will:
W: Logos as the Absolute has a will, intent, plan, and way that is fixed to Coherence (or Logos) as a matter of Structure (Logos) - just as my will cannot be divorced from me and would always be coherent if I am the Standard of Coherence (Logos).
X: Logos manifests trivially across spacetime/Reality and in contingencies (which are concepts dependent upon the Logos, which can be necessary or not). Contingency in the sense of dependency on the Logos is ontological contingency, not to be conflated with contingency in the sense of Truth value or logical necessity.
Y: Logos as the absolute and necessary Ground manifests in and as all contingent will, and shows it is a false dilemma to ask if there is determination by Logos (or God) or if there is room for free will (Logos manifest having contingent will to match contingent form).
Z: Any choice anyone makes or any will anyone has, coherent or not, as a contingency or the Absolute, is trivially the Logos choosing (or having both absolute and contingent will consistent with Universal Logos).
{W, X, Y, (W & X) -> Z, (X & Y) -> Z} |= Z <-> X