Eric Charney & Maclain Hunter' authored proof preserved from its first-party proof-base source.
Logical Exploration of Reality and Mathematics by Eric Charney and Maclain Hunter Logical Axiom of Logic: Logic is Logic, demanding A be A, and Logic is logical true, demanding A be A-like and true (when aligned with Logic without contradiction) - in order to maintain validity and Coherence (or Logic/Reality and its self-alignment). Proof One (C): Charney's Theorem: Proof of the Convergence of Continued Fractions to the Golden Ratio x - 1 = 1/x ⟹ x² - x - 1 = 0 ⟹ x = (1 ± √5)/2 1 + 1/(1+1/(1+...)) = (1+√5)/2 Convergence out to infinity aligns with "Full Coherence" and "self-consistent reasoning". Proof Two (H): Logic and the Golden Ratio by Maclain Hunter P: φ or Logic. Q: x + x/φ when x is unitary identity. {P, P -> Q} |= P -> Q Conclusion: P & Q: Logic and φ display coherent self-reference. Meta-Proof: {C, H, K} |= (C <-> H) <-> K The proofs from Charney and Hunter are logically e
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Logical Exploration of Reality and Mathematics by Eric Charney and Maclain Hunter
Logical Axiom of Logic:
Logic is Logic, demanding A be A, and Logic is logical true, demanding A be A-like and true (when aligned with Logic without contradiction) - in order to maintain validity and Coherence (or Logic/Reality and its self-alignment).
Proof One (C): Charney's Theorem: Proof of the Convergence of Continued Fractions to the Golden Ratio
x - 1 = 1/x ⟹ x² - x - 1 = 0 ⟹ x = (1 ± √5)/2
1 + 1/(1+1/(1+...)) = (1+√5)/2
Convergence out to infinity aligns with "Full Coherence" and "self-consistent reasoning".
Proof Two (H): Logic and the Golden Ratio by Maclain Hunter
P: φ or Logic.
Q: x + x/φ when x is unitary identity.
{P, P -> Q} |= P -> Q
Conclusion: P & Q: Logic and φ display coherent self-reference.
Meta-Proof:
{C, H, K} |= (C <-> H) <-> K
The proofs from Charney and Hunter are logically equivalent to Universal Logic.
Reality exists because it is logically equivalent to Logic and Logical Necessity itself.Genre: proof.
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Role: source-bound authored work in the first-party proof-base archive
Essence: Logical Exploration of Reality and Mathematics (Charney-Hunter) retains its exact stored text, declared authorship, source identity, and fingerprint.
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Retrieval aliases: Logical Exploration of Reality and Mathematics (Charney-Hunter) · Q1074
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