Proof of Established Certainty by Maclain Hunter

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.

Proof of Established Certainty by Maclain Hunter Premises: P: Truth can be demonstrated with 100% certainty (rationally) though deductive logical proof. This can be represented by DT (standing for “Deductive Truth”) Q: In the context I am sharing this proof I have shown deductive logical proof to support my claims, thus I can be 100% certain. If the context changes then the level of certainty may change but where proof is present my certainty is complete. This can be encoded as PS (ie - proof shown). R: If A) I were uncertain then B) would contradict my certainty expressed confidently here in written (even “empirically observable”) form. This can be encoded as EOC (ie - empirically observable certainty). S: Since proof supports my rational certainty it is not blind acceptance, it is rationally justified. For my level of certainty to change it would take superior logical proof (SP) that refutes and/or logically supersedes the proof(s) at hand - not merely assertions or disbelief without superseding proof and Coherence. This can be encoded as PRN (ie - proper refutation necessary). T: The premises {P, Q, R, S} and the symbolic representations encoded within them have relationship that include the expression: {PS, PS -> DT, DT & EOC, PS -> PRN} |= ((DT & EOC) -> PRN) <-> PS Formal Reasoning: {P, P -> Q, Q & R, P -> S} |= ((P & Q) -> R) <-> S Truth Table Analysis: PQRS⎪P P→Q Q&R P→S╞((Q&R)→S)↔P TTTT⎪T TT TT TT TT T T TTTF⎪T TT TT TF TT F T TTFT⎪T TT TF TT TF T T TTFF⎪T TT TF TF TF F T TFTT⎪T TF FT TT FT T T TFTF⎪T TF FT TF FT F T TFFT⎪T TF FF TT FF T T TFFF⎪T TF FF TF FF F T FTTT⎪F FT TT FT TT T F FTTF⎪F FT TT FF TT F F FTFT⎪F FT TF FT TF T F FTFF⎪F FT TF FF TF F F FFTT⎪F FF FT FT FT T F FFTF⎪F FF FT FF FT F F FFFT⎪F FF FF FT FF T F FFFF⎪F FF FF FF FF F F (Valid) Q.E.D.

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.