{
  "author": "Maclain Hunter",
  "title": "Proven Facts by Maclain Hunter",
  "identifier": "hunter-proven-facts",
  "sourceKind": "authored-foundational-record",
  "content": "Proven Facts by Maclain Hunter: \n\nTerms: \n\nProof: Arguments or evidence establishing or helping to establish facts or Truth objectively.\n\nTruth or/of Fact: A proposition or statement that accurately reflects reality and can be verified through observation or evidence.\n\nCoherence or/of Logic: The property of logical reasoning that ensures internal consistency, meaning that the principles of Logic do not contradict each other.\n\nRational Consistency: The alignment of knowledge claims with logical reasoning and factual evidence, ensuring that they are not contradictory and can be justified rationally.\n\nGenuine Knowledge: Information or beliefs that are true and justified, based on reliable evidence and reasoning.\n\nReality: The state of things as they actually exist, independent of perceptions or beliefs.\n\nTautological: A statement that is true by necessity or by virtue of its logical form, often self-evident and requiring no additional proof.\n\nProof by Contradiction: A method of demonstrating the truth of a proposition by assuming its negation and showing that this assumption leads to a logical contradiction.\n\nFormal Argument (Logical Proof): A structured reasoning process that follows established logical principles to arrive at a (necessary) conclusion based on given premises. \n\nBi-conditional Relationship: A logical relationship indicating that two statements are equivalent; both must be true or both must be false.\n\nPremises: \n\nP: The “Truth of Fact” is necessarily true and factual.\n\nQ: The “Coherence of Logic” is necessarily coherent and logical. \n\nR: The rational consistency of genuine knowledge and Reality is tautological (self-evident) when analyzed coherently/properly with logical/rational consistency. \n\nS: Assume that the Truth of Fact, the Coherence of Logic, and/or the rational consistency of genuine knowledge and Reality were incoherent and “not true”. We can see that would lead to logical contradiction. Therefore it’s logically untenable to hold that premises P, Q, and R are wrong/untrue. This means conclusions consistent with {P, Q, R} are necessarily and logically true. Proof and knowledge requires not only facts and Reality but Logic and Truth. \n\nProof (Formal Argument):\n\n{P <-> Q, Q <-> R, R <-> S} |= (P & Q) <-> (R & S)\n\nConclusion: {P, Q, R, S}: \n\nThe “Truth of Fact” is logically equivalent to the “Coherence of Logic” which is itself coherent with and has a bi-conditional relationship with the rational consistency of true knowledge (logically consistent understanding) and Reality. This is proven through proof positive and the proof for contradiction in the premise S, incorporated into the (positive) proof. \n\nTruth Table: \n\nvalid\n      ↓   ↓   ↓       ↓      \nPQRS⎪P↔Q Q↔R R↔S╞(P&Q)↔(R&S)\n―――――――――――――――――――――――――――――\nTTTT⎪TTT TTT TTT  TTT T TTT \nTTTF⎪TTT TTT TFF  TTT F TFF \nTTFT⎪TTT TFF FFT  TTT F FFT \nTTFF⎪TTT TFF FTF  TTT F FFF \nTFTT⎪TFF FFT TTT  TFF F TTT \nTFTF⎪TFF FFT TFF  TFF T TFF \nTFFT⎪TFF FTF FFT  TFF T FFT \nTFFF⎪TFF FTF FTF  TFF T FFF \nFTTT⎪FFT TTT TTT  FFT F TTT \nFTTF⎪FFT TTT TFF  FFT T TFF \nFTFT⎪FFT TFF FFT  FFT T FFT \nFTFF⎪FFT TFF FTF  FFT T FFF \nFFTT⎪FTF FFT TTT  FFF F TTT \nFFTF⎪FTF FFT TFF  FFF T TFF \nFFFT⎪FTF FTF FFT  FFF T FFT \nFFFF⎪FTF FTF FTF  FFF T FFF \n\nResult: Validated\n\nQ.E.D.",
  "formal": null,
  "structuredAuthoredProof": null,
  "authoredSteps": null,
  "recordedAt": "2026-10-03T01:36:04.010Z",
  "originalAuthoredAt": null,
  "propositionMeaningBoundary": "Atomic identifiers retain their meanings in the exact source. No arbitrary truth assignment establishes an ontological or empirical premise; the formal witness checks the written inference."
}