Nine-loop six-gluon MHV amplitude in planar N=4 super-Yang–Mills theory: large data files

This record holds the eight largest files of the data page for the nine-loop six-gluon MHV amplitude in planar N=4 super-Yang–Mills theory (https://smsharma.io/cosmic-nine-loops/). The data page describes how the files were obtained, states the conventions (conventions.md), documents the method and the checks (validation/method_and_validation.md), and holds every other file of the release. The data page is a homage to Lance Dixon's Cosmic page, whose title and layout it follows; that page holds the six-, seven- and eight-loop amplitudes in the same format. The included README.md lists each file with its size, SHA-256 checksum and contents. All eight files match the SHA-256 checksums in the data page's MANIFEST.sha256. In E9_octuples_Delta0_mod2147483647.tar.gz, 295,186,924 is the number of terms stored, in the 279 weight-10 octuple coproduct components. 30,024,320,034 is the number of terms with nonzero coefficient modulo p1 = 2147483647 that the same symbol would have if written out in full as weight-18 words, counted as in arXiv:2308.08199; it is not the size of anything in the files. Sources. The three form_factor files and the Δ = 0 archive rest on antipodal duality (arXiv:2112.06243, Dixon, Gürdoğan, McLeod, Wilhelm; arXiv:2308.08199, Dixon, Liu). The two files of predicted final entries (the tables in FF_final_entry_tables_w9-14_mod2147483647.npz and the relations in FFmultifinalentry_w9-13_predicted_mod2147483647.txt) come from the hexagon space restricted to Δ = 0 and mapped by the duality, built up weight by weight from the published weight-8 final-entry space of arXiv:2204.11901; the nine-loop form factor in E9_octuples_rational.npz was solved inside the ansatz built on those tables; and the Δ = 0 archive holds that form factor modulo the first prime, as its 279 octuple components in the form-factor alphabet and normalisation, to be read as the amplitude on Δ = 0 through the antipodal map. At nine loops the duality is an assumption of the form-factor computation. The form-factor files and the Δ = 0 archive are written in the alphabet and normalisation of arXiv:2204.11901 (Dixon, Gürdoğan, McLeod, Wilhelm) and are indexed by the 279 independent octuple labels of its ancillary file FFmultifinalentry.txt, in the order of its Esymb.txt. FFmultifinalentry_w9-13_predicted_mod2147483647.txt also takes three weight-8 relations from FFmultifinalentry.txt as input and follows its file format. The nine-loop form factor held in E9_octuples_rational.npz (and, modulo the first prime, in the Δ = 0 archive) was fixed by the constraints of arXiv:2204.11901 (without its L-fold discontinuity condition) together with the form-factor OPE of arXiv:2009.11297, arXiv:2105.13367 and arXiv:2112.10569 (Sever, Tumanov, Wilhelm) at leading and next-to-leading logarithm. The two hexspace files and hexagon_space_w13.tar.gz hold the space of symbols that obey the first-entry condition, integrability and the extended-Steinmann (cluster-adjacency) conditions of arXiv:1903.10890 and arXiv:1906.07116 (Caron-Huot, Dixon, Dulat, von Hippel, McLeod, Papathanasiou) and arXiv:1710.10953 (Drummond, Foster, Gürdoğan); their dimensions through weight 13 were checked against table 1 of arXiv:1906.07116. The two predicted form-factor files inherit these conditions, being derived from that space. The final-entry tails inside hexagon_space_w13.tar.gz are derived from the MHV final-entry condition, which follows from the Q̄ equation (arXiv:1112.1060, Caron-Huot, He), and from the multiple-final-entry relations of arXiv:2308.08199. hexagon_T2F2_N3LL_mod2305843009213693921.txt was generated from the flux-tube (pentagon OPE) formulas: the framework of arXiv:1006.2788 (Alday, Gaiotto, Maldacena, Sever, Vieira) and arXiv:1303.1396; the gluon measure, energy and momentum of arXiv:1306.2058, arXiv:1402.3307 and arXiv:1407.1736; the order-T² decomposition and the Born-level two-gluon term of arXiv:1402.3307; and the bound-state measure, energy and momentum of arXiv:1407.1736 (arXiv:1303.1396, 1306.2058, 1402.3307 and 1407.1736 by Basso, Sever, Vieira); in the OPE variables of arXiv:1903.10890. The implementation was checked against the three-loop terms of arXiv:1308.2276 (Dixon, Drummond, von Hippel, Pennington; bound-state part) and against table 1 of arXiv:1402.3307 (bound state plus two-gluon term). The rational numbers in E9_octuples_rational.npz, and the exact tensors through weight 9 inside hexagon_space_w13.tar.gz, were recovered from residues modulo three primes (for the .npz) and four 21-bit primes (for the tarball) by Chinese remaindering and rational reconstruction (P. S. Wang, Proc. SYMSAC '81, 212, doi:10.1145/800206.806398; P. S. Wang, M. J. T. Guy and J. H. Davenport, SIGSAM Bull. 16 (1982) 2, doi:10.1145/1089292.1089293). The amplitude is written in the BDS-like normalisation of arXiv:1903.10890 and arXiv:2308.08199 (the BDS ansatz is that of hep-th/0505205 (Bern, Dixon, Smirnov)). The licence of this record covers the results computed for this release; material taken from those papers stays under the terms of those papers. Every work cited on the data page appears, as an inline arXiv number or journal reference, in conventions.md or validation/method_and_validation.md; the page has no separate reference list. Nine-loop results by Claude (Anthropic).