Eta quotients of level 4 at q = exp(-π): proofs of 369 evaluations of S. Plouffe in the OEIS, and one refutation

In 2025 S. Plouffe found numerically hundreds of evaluations of the form Sum_{n>=0} a(n) e^(-n*Pi) = C, where a is an OEIS sequence and C is built from Pi, e^Pi and values of the Gamma function. In the OEIS data of October 2, 2026, 766 of them are recorded in the form "Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = ...". Some have been proved individually in the entries, by S. Fried, P. Bala and V. Kotesovec, using the classical values of the Dedekind eta function. Here we prove 369 more at once. In each case the generating function of the sequence, as defined in its entry or given by a formula of the entry, is an eta quotient of level 4 (up to a constant term or a constant factor), and one classical formula gives the value of any such quotient at q = e^(-Pi) from the values of eta at i/2, i and 2i. The formula is not new (it follows from the Chowla-Selberg values); the contribution is its systematic application and verification. The two core entries among the cases (A000594 and A035099) were already treated in the author's report on core entries. We also show that one of the evaluations is false (A132970: the true value is e^(-Pi/24) 2^(-1/8) Pi^(1/4)/Gamma(3/4) = 0.87402913..., not 0.90486154...), and we point out three formulas in the OEIS that do not match the terms of their entries (A216711, A005883, A128713), with corrected versions. The identifications were found by the author's engine SyntheticMind. Every case was checked by programs separate from the engine: the defining line of the entry was parsed symbolically, the value was compared with Plouffe's constant by exact symbolic computation and to 50 digits, and with the partial sums of the listed terms. The verification program (verify_plouffe.py, Python with SymPy and mpmath) and the table of all cases (plouffe_cases.csv) are included. Contributions and use of AI: the author directs the project and designed its method (examining OEIS statements systematically and translating them into problems that his engine can process). An AI assistant (Claude, by Anthropic), working under the author's direction, implemented the method in the engine, ran it, wrote the verification programs and drafted the text. Details are given in the paper. The paper is provided in English and in Spanish.