Validation Via Tautological Sieve

Authored by Maclain Hunter · first-party-authored · authored-foundational-record

Stored 4P source diagnostic: clear · finding no_violation_detected · admission admitted_provisionally. This intake result is separate from the theorem checks of the exact propositional sequent.

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

Lean 4 verification and timestamps

The machine formalization date is separate from the original authored work. See the verification record for exact checked scope and any unresolved parts.

Logic-centered continuity

This authored proof is connected to Logic, Logos, God, and the self-evident Ground of Reality, and to the distinct systems 4P Engine, MCB Core, 4P-MCB, and the source-first Canon. Formal proof, empirical evidence, and system-generated records remain separately typed.