Computational data for the paper "The logarithmic Laplacian, the Hadamard formula and the boundary balance for the infimum of the truncated Weil form"

Computational data for the paper “The logarithmic Laplacian, the Hadamard formula and the boundary balance for the infimum of the truncated Weil form”. The numbering of sections, statements, figures and tables follows the current text of the paper. The archive contains the following data: Galerkin values of the infimum λN of the truncated Weil form in the even sector, its derivative with respect to dilation βN2 = −½ dλN/da, its parts (the Archimedean, the pole, and the prime number theorem remainder) and the boundary balance rc at c = 6, 10, 12, 14.5 together with verification computations: reconciliation with the eigenvalue difference, a test perturbation, recomputation, elementary bounds and double-precision computations; rc on the grid c ∈ [6, 14] with step 0.1, a comparison of the two bases at c = 7, one-sided values at prime powers and convergence of the Galerkin values at c = 7, 8, 9 and at c = 6, 6.5 for N up to 1024, and up to 768 in the cosine basis (Section A.2, Tables A.1–A.3); the terms of the boundary balance expansion at c = 6, 6.5, …, 20 (Section A.3, Figure 5, Table A.6); Rayleigh-Ritz values at N = 512 for c = 40, 41, 50, 51, 60, 61 (Tables A.4 and A.5); the scale Θc and κΘ at integer points c = 5…1000; rigorous bounds on the infimum at c = 5…31, 45, 47 and 71 and upper bounds at c = 5…8 from the record doi:10.5281/zenodo.23091912, the inputs of Corollary 5.7 (mean of the boundary balance), from which, in particular, ⟨r⟩[5, 71] ≤ 1.0022; coefficients of the Galerkin minimizers; data for Figures 1–6. All values except the rigorous bounds were obtained numerically. The Galerkin and Rayleigh-Ritz numbers are upper estimates of the infimum, not rigorous bounds. The only rigorous numbers in the archive are the bounds from the record doi:10.5281/zenodo.23091912, repeated in scale/strict_inputs.csv. For verification, the table “Correspondence with the text of the paper” in README.md indicates, for each section, statement, figure and table of the paper, the files from which its numbers were obtained. The contents of the archive and the formats of all files are described in README.md, a machine-readable description of the tables is given in datapackage.json, and the SHA-256 checksums of all files are listed in SHA256SUMS. The program code used to compute these results is not included in the record and will be published after the paper is submitted to a journal. The archive contains 40 files, 0.4 MB when unpacked. The size of the archive itself is 0.2 MB. SHA-256 of the archive truncated-weil-form-boundary-balance-data-en-v1.1.zip: 4ebcf32a98fcb2b349b580c0fbec879fd9ce46a066bc994f38e31c557d75ff15. Version 1.0 is the archive of 6 October 2026. Version 1.1 corresponds to the current text of the paper. It does not contain the values of the Epstein zeta function and the Osgood constant: these are not used in the current text of the paper. Rigorous bounds for c = 45, 47 and 71 and the data for Tables A.1–A.3 have been added, and the section, figure and table numbers in the comments have been brought into agreement with the current paper.