[validation] Paper 5 § 4 — Baker's 1966 theorem on the Pythagorean comma

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Claim

Paper: Paper 5 (Pythagorean companion), v1.1, § 4; also Paper 3 v9.1 § 5
Authoritative claim file: validation/claims/music-kernel-06-baker.md

Verify that Baker's 1966 theorem on linear forms in logarithms applies to |12 log 3 − 19 log 2| and yields an effective positive lower bound — the quantitative Diophantine floor on the Pythagorean comma.

What this issue asks for

A ~30-minute to 1-hour review by a number theorist confirming:

1. The FTA argument for |12 log 3 − 19 log 2| ≠ 0 is correct.
2. Baker 1966 applies to this specific linear form (log 2 and log 3 are trivially algebraic at height/degree 1).
3. The paper's framing of FTA as shared qualitative floor + Baker as quantitative extension for rank ≥ 2 is accurate, not overstated.
4. (Bonus) A specific effective cents-level bound from standard Waldschmidt / Laurent–Mignotte–Nesterenko estimates, if easily available.

See CONTRIBUTING.md § 1 for what counts as a valid response.

Domain

• Number theory (transcendence)

Status

Open; awaiting a number theorist.

Why it matters

This claim does double duty: technical core of Paper 5 and underwrites Paper 3's arithmetical-ladder argument in § 5. If Baker does not apply as cited, the paper retains the qualitative FTA argument but loses the effective-bound framing.

Related to the umbrella music-kernel review (#1) but independently addressable.