{
  "author": "Maclain Hunter",
  "title": "Validating the Pythagorean Theorem by Maclain Hunter",
  "identifier": "hunter-validating-pythagorean-theorem",
  "sourceKind": "authored-foundational-record",
  "content": "\n\nValidating the Pythagorean Theorem by Maclain Hunter: \n\nPremises:\n\nP: Let P represent side (leg) a of a right triangle squared. \n\nQ: Let Q equal the square of side (leg) b of a right triangle. \n\nR: Let R equal side c (the hypotenuse) of a right triangle. Let R also equal the conjunction of P and Q. \n\nS: Assume the relationship between P, Q, and R is not valid and doesn’t represent the Pythagorean Theorem. \n\nLogical Argument (Proof):\n\n{P, P <-> Q, Q <-> R, R <-> S} |= (P & Q) & (R & S)\n\nConclusion: (P & Q) & (R & S):\n\nThe logically valid relationship and structure, shown by the formal argument, between the premises {P, Q, R} representing the sides of a right triangle, validates the Pythagorean Theorem as a logically valid argument and structure. We prove the theorem here also through contradiction (ie - premise S). This assumption in premise S leads to paradox and contradiction since the relationship of these premises specifically represent the relationship between what these premise represent, which is, here, the sides of a right triangle, of an unfixed size. \n\nTherefore, the relationships are valid and display the same sort of objective logical relationship that the Pythagorean Theorem does, and that the sides of a given right angle do. When valid inputs are provided the theorem will produce the proper output, and like a logical proof the validity of the output (ie - c ^ 2) depends on the validity of the inputs (ie - a ^ 2 + b ^ 2). The theorem is valid, contingent upon the validity of a and b.\n\nTruth Table Analysis: \n\nvalid\n     ↓  ↓   ↓   ↓       ↓      \nPQRS⎪P P↔Q Q↔R R↔S╞(P&Q)&(R&S)\n―――――――――――――――――――――――――――――――\nTTTT⎪T TTT TTT TTT  TTT T TTT \nTTTF⎪T TTT TTT TFF  TTT F TFF \nTTFT⎪T TTT TFF FFT  TTT F FFT \nTTFF⎪T TTT TFF FTF  TTT F FFF \nTFTT⎪T TFF FFT TTT  TFF F TTT \nTFTF⎪T TFF FFT TFF  TFF F TFF \nTFFT⎪T TFF FTF FFT  TFF F FFT \nTFFF⎪T TFF FTF FTF  TFF F FFF \nFTTT⎪F FFT TTT TTT  FFT F TTT \nFTTF⎪F FFT TTT TFF  FFT F TFF \nFTFT⎪F FFT TFF FFT  FFT F FFT \nFTFF⎪F FFT TFF FTF  FFT F FFF \nFFTT⎪F FTF FFT TTT  FFF F TTT \nFFTF⎪F FTF FFT TFF  FFF F TFF \nFFFT⎪F FTF FTF FFT  FFF F FFT \nFFFF⎪F FTF FTF FTF  FFF F FFF \n\nQ.E.D. ",
  "formal": null,
  "structuredAuthoredProof": null,
  "authoredSteps": null,
  "recordedAt": "2026-10-02T16:41:39.389Z",
  "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."
}