Certificate data for the paper "Rigorous lower bounds for the truncated Weil form up to support length ln 71 via a lattice minorant"

Certificate data for the paper “Rigorous lower bounds for the truncated Weil form up to support length ln 71 via a lattice minorant”: Theorem 1.1 for c = 2, …, 31, 45 and 47 in both parity sectors and Proposition 1.3 for c = 71 in the even sector. For each of these c and sectors, the record contains two certificates, at ε = 0 and at the found constant εc (respectively εc−), 130 certificates in total: records of the runs: parameters, the outcome of the verification, the lower bound of the margin (seven digits, the rigorous bound is smaller by one unit in the seventh digit), the sizes of the sets and the SHA-256 checksums for 𝒢 and for the midpoints of the matrix I − Wup; the retained lattice nodes with the values of the symbol μ̂L and exact balls (midpoint and radius) without rounding; columns P and N with lower bounds of the weights and columns of the negative part N with rigorous bounds μ̂L; the choice of the constant ε of each certificate and rigorous upper bounds λc+ for c = 5, …, 8. The data are split into two archives, which are unpacked into a single folder truncated-weil-form-certificates-en/: truncated-weil-form-certificates-en-v1.1.zip (212 MB, 665 files): all files except the exact balls. SHA-256 f779dedd59f894e93e849f94dea26c864522122061a1edc323c1a4ffdfef1a99, MD5 5dba08db69804797817a500f9be729fd; truncated-weil-form-balls-en-v1.1.zip (936 MB, 65 files): exact balls of the symbol in the folder balls/. SHA-256 b2773e11c7f2a1a4b6b532bc73d51556710fee9ee87c2145c2bb4df84d4ec8cc, MD5 6a4240106d12c81b17712d85d1aff377. When unpacked, the contents of the archives occupy 546 and 936 MB. To verify the certificates following README.md, the first archive suffices, while comparing the recomputed values of the symbol with the exact balls requires the second one. The files README.md, SHA256SUMS and CITATION.cff are also posted separately, and they coincide with the copies in the first archive. The contents of the archives, the formats and rounding rules of all columns and the order of verifying a certificate are described in README.md. A machine-readable description of the tables is given in datapackage.json and schemas/, and the checksums of all files of both archives are listed in SHA256SUMS. The program that produced the certificates is not included in the record: it will be published after the paper is submitted to a journal. An earlier version of the manuscript (PDF under the title “Rigorous lower bounds for the truncated Weil form at c ≤ 31 via a lattice minorant”) has the SHA-256 checksum 10e7201cb04d5f1596db0c6185728c234574529cfa2f3ea29322eecc6439b521. Version 1.1 differs from version 1.0 in the data description, the reference fields of the run records, and the splitting of the package into two archives.