Claim
Paper: Paper 5 (Pythagorean), v1.1, § 7.5
Authoritative claim file: validation/claims/pythagorean-explanatory-debts.md
Paper 5 § 7.5 names three explanatory debts the paper does not close. This issue tracks all three; responses addressing any single one are welcome.
The three debts
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Uniform framework unifying rank-1 and rank-≥2 Diophantine cases. FTA settles rank 1 (irrationality of √2); Baker settles rank ≥ 2 (Pythagorean comma). Is there a uniform statement or categorical pattern that subsumes both — e.g., Schmidt's Subspace Theorem, a p-adic framework, etc.?
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Typology-mapping for foundations-of-mathematics schools. Kronecker ↔ Refusal; Dedekind ↔ Infrastructure; Cantor ↔ Exploitation; Brouwer ↔ Refusal (second kind); Lakatos ↔ Commitment. Is this mapping defensible to a philosopher of mathematics or mathematical historian, or does it misrepresent?
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Specific cents-level effective bound from Baker's theorem. Baker gives an effective positive lower bound on |12 log 3 − 19 log 2|; what's the best-known numerical value from standard Waldschmidt / Laurent–Mignotte–Nesterenko machinery?
See CONTRIBUTING.md § 1 and § 4 for acceptance criteria.
Domain(s)
- Number theory (debts 1, 3)
- Philosophy of mathematics / history of mathematics (debt 2)
Status
Open; each debt is independently tractable.
Why it matters
Each debt, if closed, either sharpens a specific claim in Paper 5 or redirects the paper to a more careful framing. Debt 2 in particular could upgrade § 6 from loose structural resonance to a real contribution to the philosophy of the Grundlagenstreit.
Claim
Paper: Paper 5 (Pythagorean), v1.1, § 7.5
Authoritative claim file:
validation/claims/pythagorean-explanatory-debts.mdPaper 5 § 7.5 names three explanatory debts the paper does not close. This issue tracks all three; responses addressing any single one are welcome.
The three debts
Uniform framework unifying rank-1 and rank-≥2 Diophantine cases. FTA settles rank 1 (irrationality of
√2); Baker settles rank ≥ 2 (Pythagorean comma). Is there a uniform statement or categorical pattern that subsumes both — e.g., Schmidt's Subspace Theorem, ap-adic framework, etc.?Typology-mapping for foundations-of-mathematics schools. Kronecker ↔ Refusal; Dedekind ↔ Infrastructure; Cantor ↔ Exploitation; Brouwer ↔ Refusal (second kind); Lakatos ↔ Commitment. Is this mapping defensible to a philosopher of mathematics or mathematical historian, or does it misrepresent?
Specific cents-level effective bound from Baker's theorem. Baker gives an effective positive lower bound on
|12 log 3 − 19 log 2|; what's the best-known numerical value from standard Waldschmidt / Laurent–Mignotte–Nesterenko machinery?See
CONTRIBUTING.md§ 1 and § 4 for acceptance criteria.Domain(s)
Status
Open; each debt is independently tractable.
Why it matters
Each debt, if closed, either sharpens a specific claim in Paper 5 or redirects the paper to a more careful framing. Debt 2 in particular could upgrade § 6 from loose structural resonance to a real contribution to the philosophy of the Grundlagenstreit.