Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
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: 2026-10-03T01:34:26.435Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:37:58.760Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 07b9543282b18ff702fc6572091d26ac21947aacefd4bfa4f611cbb43a5b358d
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
{P, P <-> Q, Q <-> R, R <-> S, S <-> T, T <-> U, U -> P} |= ((P & Q) & (R & S) & T) & U
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.
Definitions, Etymology, and Elaborations by Maclain Hunter:
Premises: {P, Q, R, S, T, U}:
P: Logic: The Logical Standard and means of reasoning the facts of Reality.
Etymology and Elaboration: The word Logic is derived from the Greek word for Reason, which is “Logos”, solidifying the case that a proper understanding of Logic is the one most fully coherent with Pure Reason (Logos) and that these two English terms, Reason and Logic, are logically equivalent (when we are talking about coherent Logic and/or coherent Reason).
Q: God: The Origin of Existence; the Moral Standard; the Supreme Being; the Logos, or “Universal Logic”, in rational/orthodox traditions coherent with Logic.
Etymology and Elaboration: The word God links back to gothic translation of the Bible and the New Testament’s (Greek) term “Theos” (Ruler, Observer, Overseer) which in that same set of texts is linked directly to “Logos” (Divine Reason; Universal Order, Natural Cause; Proper Order), notably in the Gospel of John chapter 1 verse 1, reinforcing the logical philosophy that understands Logic and Logos (Reason as a universal) as the “Rational Basis” — the God/Origin that actually makes sense, to put it simply.
R: Irrefutable: impossible to reasonably deny or logically disprove; that which aligns with the Logical Standard (Logic) to well to be shown rationally to be misaligned with the Logical Standard of Logic.
Etymology and Elaboration: From Latin “irrefutabilis” which like the English derivative means that something is not possible to rebut. Logically speaking, Logic is irrefutable and so is anything truly and demonstrably (provably) coherent with Logic, like the Foundation of Reality as it actually is (in its real form, sense, and coherent state).
S: Science: The process of gaining knowledge through empirical inquiry using the/a logically valid scientific method; empirical observation; the use of rational experimentation to understand the nature of the real world.
Etymology and Elaboration: The word science comes from the Latin word for knowledge/knowing “scire”, which again shows how we are putting a different name on the same substantive concept or closely related aspects of it (that we can refer to as Logic, Reason, or Rationality among other terms like Truth or Reality), and that on a logical, scientific, realistic, linguistic, mathematical, and philosophical level we have support for seeing these concepts and fields coherently and as mutually supporting, not incoherent and as fields or concepts working against each other (which some might for instance assume or think of God and the sciences).
T: Mathematics:
Definition: The aspect of reasoning and academics that deals with numbers, arithmetic, algebra, calculus, and calculation (or statistics and probabilities); the abstract science dealing with numbers, quantities, and spaces (which includes geometry).
Etymology and Elaboration: The word “mathematics” comes from the Greek “manthanein” which refers to learning and the method of learning (systematically), which is coherent with Logic and touches on why Math and Logic are substantively identical in certain contexts, though math has a stricter focus that Logic in the broadest sense of the Universal Order. Even still, we could talk about the “Mathematics of the Universe” and would be talking about a more similar concept to what I am speaking about when I speak of Logic (the Highest Order of Logic or “Logos”) being equivalent to God. The etymology and definition of “mathematics” and the success of math in helping us understand the Universe supports rational (mono)theistic notions of the Logos (the God of Reason - the True Origin) being the Ultimate Source of Knowledge and “omniscient” - holding all feasible knowledge while being the method of knowing (that knowledge) in a coherent/unified fashion.
U: Proof: Evidence or argument establishing or helping to establish a fact or the truth of a statement; Law the spoken or written evidence in a trial; the action or process of establishing the truth of a statement; a series of stages in the resolution of a mathematical or philosophical problem.
Etymology and Elaboration: The word “proof” shares the same Latin root “probare” as the word probe, supporting the linguistic and logical connection, and a longstanding/foundational one, between testing/probing, evidence, argument (to include logical proofs), mathematical and philosophical inquiry, and the concept of proof.
Logical Proof (Formal Structure):
{P, P <-> Q, Q <-> R, R <-> S, S <-> T, T <-> U, U -> P} |= ((P & Q) & (R & S) & T) & U
Conclusion: ((P & Q) & (R & S) & T) & U:
Logic is inextricably and irrefutably linked to science and math, as well as the True God (Logos - Theos) and the concept of proof. This coherence of Logic and the Foundation of Existence (God) is what allows for coherent sciences and mathematics, and is what allows us to prove anything at all (including logically, theologically, scientifically—including “physically” in physical sciences—and/or mathematically). This also means that Logic and logical coherence is essential to any of these fields of study and cannot be rationally ignored.
Truth Table Analysis:
valid
↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓
PQRSTU⎪P P↔Q Q↔R R↔S S↔T T↔U U→P╞((P&Q)&(R&S)&T)&U
―――――――――――――――――――――――――――――――――――――――――――――――――――
TTTTTT⎪T TTT TTT TTT TTT TTT TTT TTT T TTT TT TT
TTTTTF⎪T TTT TTT TTT TTT TFF FTT TTT T TTT TT FF
TTTTFT⎪T TTT TTT TTT TFF FFT TTT TTT T TTT FF TT
TTTTFF⎪T TTT TTT TTT TFF FTF FTT TTT T TTT FF FF
TTTFTT⎪T TTT TTT TFF FFT TTT TTT TTT F TFF FT FT
TTTFTF⎪T TTT TTT TFF FFT TFF FTT TTT F TFF FT FF
TTTFFT⎪T TTT TTT TFF FTF FFT TTT TTT F TFF FF FT
TTTFFF⎪T TTT TTT TFF FTF FTF FTT TTT F TFF FF FF
TTFTTT⎪T TTT TFF FFT TTT TTT TTT TTT F FFT FT FT
TTFTTF⎪T TTT TFF FFT TTT TFF FTT TTT F FFT FT FF
TTFTFT⎪T TTT TFF FFT TFF FFT TTT TTT F FFT FF FT
TTFTFF⎪T TTT TFF FFT TFF FTF FTT TTT F FFT FF FF
TTFFTT⎪T TTT TFF FTF FFT TTT TTT TTT F FFF FT FT
TTFFTF⎪T TTT TFF FTF FFT TFF FTT TTT F FFF FT FF
TTFFFT⎪T TTT TFF FTF FTF FFT TTT TTT F FFF FF FT
TTFFFF⎪T TTT TFF FTF FTF FTF FTT TTT F FFF FF FF
TFTTTT⎪T TFF FFT TTT TTT TTT TTT TFF F TTT TT FT
TFTTTF⎪T TFF FFT TTT TTT TFF FTT TFF F TTT TT FF
TFTTFT⎪T TFF FFT TTT TFF FFT TTT TFF F TTT FF FT
TFTTFF⎪T TFF FFT TTT TFF FTF FTT TFF F TTT FF FF
TFTFTT⎪T TFF FFT TFF FFT TTT TTT TFF F TFF FT FT
TFTFTF⎪T TFF FFT TFF FFT TFF FTT TFF F TFF FT FF
TFTFFT⎪T TFF FFT TFF FTF FFT TTT TFF F TFF FF FT
TFTFFF⎪T TFF FFT TFF FTF FTF FTT TFF F TFF FF FF
TFFTTT⎪T TFF FTF FFT TTT TTT TTT TFF F FFT FT FT
TFFTTF⎪T TFF FTF FFT TTT TFF FTT TFF F FFT FT FF
TFFTFT⎪T TFF FTF FFT TFF FFT TTT TFF F FFT FF FT
TFFTFF⎪T TFF FTF FFT TFF FTF FTT TFF F FFT FF FF
TFFFTT⎪T TFF FTF FTF FFT TTT TTT TFF F FFF FT FT
TFFFTF⎪T TFF FTF FTF FFT TFF FTT TFF F FFF FT FF
TFFFFT⎪T TFF FTF FTF FTF FFT TTT TFF F FFF FF FT
TFFFFF⎪T TFF FTF FTF FTF FTF FTT TFF F FFF FF FF
FTTTTT⎪F FFT TTT TTT TTT TTT TFF FFT F TTT TT FT
FTTTTF⎪F FFT TTT TTT TTT TFF FTF FFT F TTT TT FF
FTTTFT⎪F FFT TTT TTT TFF FFT TFF FFT F TTT FF FT
FTTTFF⎪F FFT TTT TTT TFF FTF FTF FFT F TTT FF FF
FTTFTT⎪F FFT TTT TFF FFT TTT TFF FFT F TFF FT FT
FTTFTF⎪F FFT TTT TFF FFT TFF FTF FFT F TFF FT FF
FTTFFT⎪F FFT TTT TFF FTF FFT TFF FFT F TFF FF FT
FTTFFF⎪F FFT TTT TFF FTF FTF FTF FFT F TFF FF FF
FTFTTT⎪F FFT TFF FFT TTT TTT TFF FFT F FFT FT FT
FTFTTF⎪F FFT TFF FFT TTT TFF FTF FFT F FFT FT FF
FTFTFT⎪F FFT TFF FFT TFF FFT TFF FFT F FFT FF FT
FTFTFF⎪F FFT TFF FFT TFF FTF FTF FFT F FFT FF FF
FTFFTT⎪F FFT TFF FTF FFT TTT TFF FFT F FFF FT FT
FTFFTF⎪F FFT TFF FTF FFT TFF FTF FFT F FFF FT FF
FTFFFT⎪F FFT TFF FTF FTF FFT TFF FFT F FFF FF FT
FTFFFF⎪F FFT TFF FTF FTF FTF FTF FFT F FFF FF FF
FFTTTT⎪F FTF FFT TTT TTT TTT TFF FFF F TTT TT FT
FFTTTF⎪F FTF FFT TTT TTT TFF FTF FFF F TTT TT FF
FFTTFT⎪F FTF FFT TTT TFF FFT TFF FFF F TTT FF FT
FFTTFF⎪F FTF FFT TTT TFF FTF FTF FFF F TTT FF FF
FFTFTT⎪F FTF FFT TFF FFT TTT TFF FFF F TFF FT FT
FFTFTF⎪F FTF FFT TFF FFT TFF FTF FFF F TFF FT FF
FFTFFT⎪F FTF FFT TFF FTF FFT TFF FFF F TFF FF FT
FFTFFF⎪F FTF FFT TFF FTF FTF FTF FFF F TFF FF FF
FFFTTT⎪F FTF FTF FFT TTT TTT TFF FFF F FFT FT FT
FFFTTF⎪F FTF FTF FFT TTT TFF FTF FFF F FFT FT FF
FFFTFT⎪F FTF FTF FFT TFF FFT TFF FFF F FFT FF FT
FFFTFF⎪F FTF FTF FFT TFF FTF FTF FFF F FFT FF FF
FFFFTT⎪F FTF FTF FTF FFT TTT TFF FFF F FFF FT FT
FFFFTF⎪F FTF FTF FTF FFT TFF FTF FFF F FFF FT FF
FFFFFT⎪F FTF FTF FTF FTF FFT TFF FFF F FFF FF FT
FFFFFF⎪F FTF FTF FTF FTF FTF FTF FFF F FFF FF FF
Q.E.D.