Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
Axiom-free: true · 2 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: 2026-10-03T01:33:22.564Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:40:30.456Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 9aa6de04cc79c2b14f507870905acc70c15bc54de72653cff290eef9ebf17617
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.source_identity_rule' does not depend on any axioms
{1, 1 -> 2, 2 -> 3, 3 -> 4, 4 -> 5} |= ((1 & 2) -> (3 & 4)) -> 5
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.
Law of Identity
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
Natural Creation/Law/Cause is God's Creation/Law/Cause since, as we know, since God is the self-consistent Source of Nature that Nature itself can only exist by reflecting faithfully (like a house must match the blueprint to not be made poorly). That "Universal Order" or "Natural Order" is the true "Logical Order", as Logic is and must stay rooted in the Coherence of Reality and nothing more arbitrary than that, as Aristotle made clear in his Metaphysics and explanations of where he was deriving the "traditional Rules of Logic" from.
Then from there you have biological systems which amount to Logic embedded in physical bodies and finite systems (that we call individuals, which are contingent and fallible but still "divine" and "of, from, or like God") and then you can have logically grounded and consistent biological evolution afterwards and contingent upon (at least) those things:
1. Logic: The Natural Order, the Cosmic Creation, and its “self-consistent” (logically sound) Source called God, encompassing all logics and concepts.
2. Energy: Energy is energy and gains identity from the Logos (Universal Logic - the True Logic inherent in the Natural Order). Other things are other things but feasibly the Logos could simply make itself be itself and energy be energy, by enforcing itself and imposing itself on concepts as the Law of Identity and the Force that the Law of Identity describes, and the rest of Existence should logically follow.
3. Concrete Matter: Matter as we think of it in the physical world (ie - rock and literal concrete) can be basically derived from the concentration (coherence) of energy, to such a radical degree, with such a gravity and weight, logically and energetically, that it can form, through the Rule of Logic (that things must be what they are) into solid matter, and even, when all energy is fully coherent with Logic, the infinite manifestation of that energetic coherence in the form of impulsive, explosive, and continuous generation of finite/specific materials and their specific characteristics (ie - atomic weight), forming the full spectrum of elements from the coherence of the energy and Logic in the Cosmos.
4. Biological Organisms: The same organizing principle, which is self-aware (conscious) as a matter of being completely self-evident and self-knowing (tautological Logic), gives form to and takes form as the diverse biological life that exists, formed through logically constructed and “logical jump free” physical and metaphysical reasoning, working in tandem as and with Universal Logic (God - Logos - Logic).
5. Evolution of Biological Organisms: Only once there are 1-4 and biological organisms can there be evolution in those biological systems and competition between organisms (which implies and requires multiple such organisms in a single context). Also, without Logic and the sort of Logical Order (True God) that we are respecting and being guided by in this sort of Proper Reasoning, there would not be an Objective Standard for anything to be said to be “evolving” according to or towards. It’s takes God’s Perfection, also understood as the infallibility of Pure Logic, to have a coherent and meaningful (non-contradictory and rational rather than arbitrary) notion of “evolution”.
{1, 1 -> 2, 2 -> 3, 3 -> 4, 4 -> 5} |= ((1 & 2) -> (3 & 4)) -> 5
Conclusion:
Logically, evolution is logically contingent and cannot make Logic contingent upon it (evolution). That is putting the cart before the horse, and that is no way to pull a cart. Evolution is not a way, rationally, around the God of Reason (Logos - Logic) and can never rationally be a replacement for the Logos (the First Cause of Logic that is fully coherent with and consistent with Logic).
Truth Table Analysis:
Valid
↓ ↓ ↓ ↓ ↓ ↓
12345⎪1 1→2 2→3 3→4 4→5╞((1&2)→(3&4))→5
――――――――――――――――――――――――――――――――――――――――
TTTTT⎪T TTT TTT TTT TTT TTT T TTT TT
TTTTF⎪T TTT TTT TTT TFF TTT T TTT FF
TTTFT⎪T TTT TTT TFF FTT TTT F TFF TT
TTTFF⎪T TTT TTT TFF FTF TTT F TFF TF
TTFTT⎪T TTT TFF FTT TTT TTT F FFT TT
TTFTF⎪T TTT TFF FTT TFF TTT F FFT TF
TTFFT⎪T TTT TFF FTF FTT TTT F FFF TT
TTFFF⎪T TTT TFF FTF FTF TTT F FFF TF
TFTTT⎪T TFF FTT TTT TTT TFF T TTT TT
TFTTF⎪T TFF FTT TTT TFF TFF T TTT FF
TFTFT⎪T TFF FTT TFF FTT TFF T TFF TT
TFTFF⎪T TFF FTT TFF FTF TFF T TFF FF
TFFTT⎪T TFF FTF FTT TTT TFF T FFT TT
TFFTF⎪T TFF FTF FTT TFF TFF T FFT FF
TFFFT⎪T TFF FTF FTF FTT TFF T FFF TT
TFFFF⎪T TFF FTF FTF FTF TFF T FFF FF
FTTTT⎪F FTT TTT TTT TTT FFT T TTT TT
FTTTF⎪F FTT TTT TTT TFF FFT T TTT FF
FTTFT⎪F FTT TTT TFF FTT FFT T TFF TT
FTTFF⎪F FTT TTT TFF FTF FFT T TFF FF
FTFTT⎪F FTT TFF FTT TTT FFT T FFT TT
FTFTF⎪F FTT TFF FTT TFF FFT T FFT FF
FTFFT⎪F FTT TFF FTF FTT FFT T FFF TT
FTFFF⎪F FTT TFF FTF FTF FFT T FFF FF
FFTTT⎪F FTF FTT TTT TTT FFF T TTT TT
FFTTF⎪F FTF FTT TTT TFF FFF T TTT FF
FFTFT⎪F FTF FTT TFF FTT FFF T TFF TT
FFTFF⎪F FTF FTT TFF FTF FFF T TFF FF
FFFTT⎪F FTF FTF FTT TTT FFF T FFT TT
FFFTF⎪F FTF FTF FTT TFF FFF T FFT FF
FFFFT⎪F FTF FTF FTF FTT FFF T FFF TT
FFFFF⎪F FTF FTF FTF FTF FFF T FFF FF
Q.E.D.