Lean verification registry · Authored proofs · The Logos Architecture
Source recorded — formalization still required
Axiom-free: not established · 0 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: 2026-10-02T17:12:57.950Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:40:52.986Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 7a7f67aa9690ebe7dbc51389b1c527bbda2edd96b54ef37ad553ac0d9fa6f075
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) Not executed: no complete licensed formal sequent recovered.
{P <-> Q, R <-> Q, S <-> Q, T <-> ~U} |= (((P <-> Q) <-> (R <-> Q) <-> 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.
The written sequent alone has a countermodel. No authored wording or unstated premise was changed.
Countermodel to the isolated written sequent: {"P":false,"Q":false,"R":false,"S":false,"T":true,"U":false}
Philosophical Algebra:
By Maclain Hunter
Symbols, Terms, and Definitions: note that symbols are intentionally encoded with multiple terms.
P: Premise: The basis of an argument.
Q: Logic: The Method of Reasoning and the process/standard arguments are validated by.
R: God: The Origin and Rule(r) of Existence; The Rational Standard of moral authority.
S: Structure: A construct or arrangement. That which is constructed according to a plan; That which gives a pattern or organization to a thing or things.
T: Coherence: The logical alignment of concepts; Unity and integration that amounts to logical equivalence; Validity.
U: Incoherence: The lack of logical alignment; Divergence and/or logical contradiction; invalidity.
P: Logician: An expert in the study (and use) of Logic. A reasoner who reasons with formal logics or in some rigorous and consistent manner grounded in Logic.
Q: Existence: What is; Reality; the Universe; Nature and the Natural Order; Being; That which exists.
R: Evidence: Pieces of data or information that support a certain theory or conclusion in a logically valid manner; The basis of a well supported case.
S: Proof: A formal argument and/or synthesis of evidence into a formal logical argument which proves the conclusions drawn with logical certainty through use of truthful premises and valid logical structure.
T: Law: A rule or set of rules, typically rules that are communal or universal (rather than merely personal) and which have costs or consequences associated with their violation.
~U: Science: A method of drawing inferences from empirical observation; A field of study in which experimentation and testing are used to arrive at reliable understanding.
P: Objective Truth: That which accords with Reality and its Order and which enjoys validity as a result of that coherent alignment with Truth’s own standards in Logic.
Logical Proof (Formal Reasoning):
{P <-> Q, R <-> Q, S <-> Q, T <-> ~U} |= (((P <-> Q) <-> (R <-> Q) <-> S) <-> T) <-> ~U
Conclusion:
Valid premises used to build argument must cohere with and must be logically equivalent to Logic, which in turn must be coherent and unified with the Origin of Existence (God), in order to be truly grounded. In turn these things are logically equivalent to logical structure (structure) and coherence, which is not incoherence and which is the opposite of incoherence, by definition. It is necessary based on the definitions of terms and the logical structure of the argument that this conclusion is true.
Sciences and logicians must be coherent with Logic to be understood as genuine sciences and logicians without contradiction or inauthenticity. Reality (Existence) is coherent with Logic and God, as the coherent and self-consistent Source of Reality. This renders {P, Q, R, S, T, U} coherent along with all those symbols represent in this reasoning.
Proof, evidence, and law are coherent with Logic in the universal sense (or they wouldn’t be proof, evidence, and “Universal Law” also understood as Reason or Logic). Proof and evidence, when objectively coherent, satisfy and cohere with Rational Law (Logic). We have proof if and only if the is Existence, and we have proof so there is Existence.
There is Existence so there is the Origin of Existence (God) and this God is logically equivalent to any “real proof”, “true logician” (or scientist), any “ethical and coherent lawyer/law”, all “genuine evidence”, any “instance of (or the whole of) Existence”, to “coherently structured premises” (or “coherence, structure, and valid premises”) and “the negation of incoherence”.
Truth Table:
valid
PQRSTU⎪P↔Q R↔Q S↔Q T↔¬U╞(((P↔Q)↔(R↔Q)↔S)↔T)↔¬U
―――――――――――――――――――――――――――――――――――――――――――――――
TTTTTT⎪TTT TTT TTT TFFT TTT T TTT TT TT FFT
TTTTTF⎪TTT TTT TTT TTTF TTT T TTT TT TT TTF
TTTTFT⎪TTT TTT TTT FTFT TTT T TTT TT FF TFT
TTTTFF⎪TTT TTT TTT FFTF TTT T TTT TT FF FTF
TTTFTT⎪TTT TTT FFT TFFT TTT T TTT FF TT FFT
TTTFTF⎪TTT TTT FFT TTTF TTT T TTT FF TT TTF
TTTFFT⎪TTT TTT FFT FTFT TTT T TTT FF FF TFT
TTTFFF⎪TTT TTT FFT FFTF TTT T TTT FF FF FTF
TTFTTT⎪TTT FFT TTT TFFT TTT F FFT FT FT TFT
TTFTTF⎪TTT FFT TTT TTTF TTT F FFT FT FT FTF
TTFTFT⎪TTT FFT TTT FTFT TTT F FFT FT TF FFT
TTFTFF⎪TTT FFT TTT FFTF TTT F FFT FT TF TTF
TTFFTT⎪TTT FFT FFT TFFT TTT F FFT TF FT TFT
TTFFTF⎪TTT FFT FFT TTTF TTT F FFT TF FT FTF
TTFFFT⎪TTT FFT FFT FTFT TTT F FFT TF TF FFT
TTFFFF⎪TTT FFT FFT FFTF TTT F FFT TF TF TTF
TFTTTT⎪TFF TFF TFF TFFT TFF T TFF FT TT FFT
TFTTTF⎪TFF TFF TFF TTTF TFF T TFF FT TT TTF
TFTTFT⎪TFF TFF TFF FTFT TFF T TFF FT FF TFT
TFTTFF⎪TFF TFF TFF FFTF TFF T TFF FT FF FTF
TFTFTT⎪TFF TFF FTF TFFT TFF T TFF TF TT FFT
TFTFTF⎪TFF TFF FTF TTTF TFF T TFF TF TT TTF
TFTFFT⎪TFF TFF FTF FTFT TFF T TFF TF FF TFT
TFTFFF⎪TFF TFF FTF FFTF TFF T TFF TF FF FTF
TFFTTT⎪TFF FTF TFF TFFT TFF F FTF TT FT TFT
TFFTTF⎪TFF FTF TFF TTTF TFF F FTF TT FT FTF
TFFTFT⎪TFF FTF TFF FTFT TFF F FTF TT TF FFT
TFFTFF⎪TFF FTF TFF FFTF TFF F FTF TT TF TTF
TFFFTT⎪TFF FTF FTF TFFT TFF F FTF FF FT TFT
TFFFTF⎪TFF FTF FTF TTTF TFF F FTF FF FT FTF
TFFFFT⎪TFF FTF FTF FTFT TFF F FTF FF TF FFT
TFFFFF⎪TFF FTF FTF FFTF TFF F FTF FF TF TTF
FTTTTT⎪FFT TTT TTT TFFT FFT F TTT TT FT TFT
FTTTTF⎪FFT TTT TTT TTTF FFT F TTT TT FT FTF
FTTTFT⎪FFT TTT TTT FTFT FFT F TTT TT TF FFT
FTTTFF⎪FFT TTT TTT FFTF FFT F TTT TT TF TTF
FTTFTT⎪FFT TTT FFT TFFT FFT F TTT FF FT TFT
FTTFTF⎪FFT TTT FFT TTTF FFT F TTT FF FT FTF
FTTFFT⎪FFT TTT FFT FTFT FFT F TTT FF TF FFT
FTTFFF⎪FFT TTT FFT FFTF FFT F TTT FF TF TTF
FTFTTT⎪FFT FFT TTT TFFT FFT T FFT FT TT FFT
FTFTTF⎪FFT FFT TTT TTTF FFT T FFT FT TT TTF
FTFTFT⎪FFT FFT TTT FTFT FFT T FFT FT FF TFT
FTFTFF⎪FFT FFT TTT FFTF FFT T FFT FT FF FTF
FTFFTT⎪FFT FFT FFT TFFT FFT T FFT TF TT FFT
FTFFTF⎪FFT FFT FFT TTTF FFT T FFT TF TT TTF
FTFFFT⎪FFT FFT FFT FTFT FFT T FFT TF FF TFT
FTFFFF⎪FFT FFT FFT FFTF FFT T FFT TF FF FTF
FFTTTT⎪FTF TFF TFF TFFT FTF F TFF FT FT TFT
FFTTTF⎪FTF TFF TFF TTTF FTF F TFF FT FT FTF
FFTTFT⎪FTF TFF TFF FTFT FTF F TFF FT TF FFT
FFTTFF⎪FTF TFF TFF FFTF FTF F TFF FT TF TTF
FFTFTT⎪FTF TFF FTF TFFT FTF F TFF TF FT TFT
FFTFTF⎪FTF TFF FTF TTTF FTF F TFF TF FT FTF
FFTFFT⎪FTF TFF FTF FTFT FTF F TFF TF TF FFT
FFTFFF⎪FTF TFF FTF FFTF FTF F TFF TF TF TTF
FFFTTT⎪FTF FTF TFF TFFT FTF T FTF TT TT FFT
FFFTTF⎪FTF FTF TFF TTTF FTF T FTF TT TT TTF
FFFTFT⎪FTF FTF TFF FTFT FTF T FTF TT FF TFT
FFFTFF⎪FTF FTF TFF FFTF FTF T FTF TT FF FTF
FFFFTT⎪FTF FTF FTF TFFT FTF T FTF FF TT FFT
FFFFTF⎪FTF FTF FTF TTTF FTF T FTF FF TT TTF
FFFFFT⎪FTF FTF FTF FTFT FTF T FTF FF FF TFT
FFFFFF⎪FTF FTF FTF FFTF FTF T FTF FF FF FTF
Q.E.D.