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: 2026-10-03T01:33:25.691Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:42:16.825Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 57f7cbd65da7482c23ff33727ac6ce93932b5e2f6690a46629f687b2bd647525
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} |= (P & Q) & (R & S) & T
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.
The Logical Derivation of Mathematics from Foundational Coherence by Maclain Hunter:
Premises:
P: Logically speaking, you can have Logic without involving mathematics and number but you cannot have mathematics, arithmetic, or number without Logic and the framework in which mathematical and numerical units or functions exist.
Q: It would be illogical to have a worldview where Logic is not supreme.
R: Math and number are inherent in Logic's qualitative and logical Coherence (Oneness), and in the Oneness of Reality that is coherent with that. Mathematical operations are quantitative logical operations.
S: The Oneness of Identity gives absolute grounding to the concept of other numbers which are all based on the concept of a coherent unit. Without this grounding in the Logos, the very idea of "other" numbers, and the formal systems of mathematics, would have no rational basis.
T: Assume the negation of the premises {P, Q, R, S}. This leads to logical contradiction and an illogical notion of mathematics and/or mathematical logic, where math is somehow not based on the coherence and unity (quantitative and qualitative or “universal”) of Logic (the Logos or “Logical Grounding of Logic and the Cosmos”) that logically and philosophically serves as the Foundational Coherence underpinning the sciences and mathematics, as well as any coherent formal systems of Logic (that would otherwise be arbitrary and subjective).
Logical Argument (Proof):
{P, P <-> Q, Q <-> R, R <-> S, S <-> T} |= (P & Q) & (R & S) & T
Conclusion: {P, Q, R, S, T}:
Math is logically derived. To posit otherwise contradicts Logic, which unlike mathematics, (Logic) is the Logical Standard. This means that even within mathematics Logic is the Standard of Validity that determines what is or is not valid “Mathematical Logic” and what the rules are that govern mathematical systems, including systems of arithmetic.
Logic encompassing ordered change leads to logical and mathematical operations, as these continuous changes, as observed in physical motion and the evolution of the Cosmos and ecosystems (or biological systems), fundamentally are logical operations, just as universal forms of logical operations applied to quantity and in quantitative reasoning lead to and equate to mathematical operations and functions.
Mathematical operations amount to quantitative logical operations and the logical manipulation of units (based on the coherent unit or “one”) through operators of various kinds that find their own analogue in qualitative logical reasoning, like addition and conjunction, or subtraction and disjunction.
Without Foundational Logical Coherence (the Logos), also understood as the Logical Grounding of Logic and the Coherence and Oneness of Logic itself, the concept of a coherent unit would lack Foundation and meaning, instead of finding its analogue in the unity of Reality itself. In a truly logical worldview, even the worldview of a mathematician, Logic must supersede all else including mathematics itself, and Mathematical Logic should be seen as the bridge between Logic (Logos) and systems of mathematics/arithmetic.
Truth Table Analysis:
valid
↓ ↓ ↓ ↓ ↓ ↓
PQRST⎪P P↔Q Q↔R R↔S S↔T╞(P&Q)&(R&S)&T
――――――――――――――――――――――――――――――――――――――――
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 FFT TTT F TFF FT
TTTFF⎪T TTT TTT TFF FTF TTT F TFF FF
TTFTT⎪T TTT TFF FFT TTT TTT F FFT FT
TTFTF⎪T TTT TFF FFT TFF TTT F FFT FF
TTFFT⎪T TTT TFF FTF FFT TTT F FFF FT
TTFFF⎪T TTT TFF FTF FTF TTT F FFF FF
TFTTT⎪T TFF FFT TTT TTT TFF F TTT FT
TFTTF⎪T TFF FFT TTT TFF TFF F TTT FF
TFTFT⎪T TFF FFT TFF FFT TFF F TFF FT
TFTFF⎪T TFF FFT TFF FTF TFF F TFF FF
TFFTT⎪T TFF FTF FFT TTT TFF F FFT FT
TFFTF⎪T TFF FTF FFT TFF TFF F FFT FF
TFFFT⎪T TFF FTF FTF FFT TFF F FFF FT
TFFFF⎪T TFF FTF FTF FTF TFF F FFF FF
FTTTT⎪F FFT TTT TTT TTT FFT F TTT FT
FTTTF⎪F FFT TTT TTT TFF FFT F TTT FF
FTTFT⎪F FFT TTT TFF FFT FFT F TFF FT
FTTFF⎪F FFT TTT TFF FTF FFT F TFF FF
FTFTT⎪F FFT TFF FFT TTT FFT F FFT FT
FTFTF⎪F FFT TFF FFT TFF FFT F FFT FF
FTFFT⎪F FFT TFF FTF FFT FFT F FFF FT
FTFFF⎪F FFT TFF FTF FTF FFT F FFF FF
FFTTT⎪F FTF FFT TTT TTT FFF F TTT FT
FFTTF⎪F FTF FFT TTT TFF FFF F TTT FF
FFTFT⎪F FTF FFT TFF FFT FFF F TFF FT
FFTFF⎪F FTF FFT TFF FTF FFF F TFF FF
FFFTT⎪F FTF FTF FFT TTT FFF F FFT FT
FFFTF⎪F FTF FTF FFT TFF FFF F FFT FF
FFFFT⎪F FTF FTF FTF FFT FFF F FFF FT
FFFFF⎪F FTF FTF FTF FTF FFF F FFF FF
Q.E.D.