Credits
BootLoops 1.0 was built by Matthew D. Schwartz, Harvard University. Contact information is on the Contribute & contact page.
Record of contributions
A contribution can be a newly closed integral, an independent check of a published number, a tool improvement, a new tool, or an application. Substantive ones are credited in this table, which documents results and improvements with BootLoops since its release.
| Date | Contributor | Contribution | Type | Contact | Links |
|---|---|---|---|---|---|
| Sep 30, 2026 | M. Schwartz | BootLoops 1.0: 49 toolkit packages | Toolkit | general@bootloops.ai | results · toolkit |
Third-party software
BootLoops builds on the third-party software and data sets below. Each entry names the authors, license and reference to cite; each tool page states its own provenance, and THIRD_PARTY.md and REFERENCES.md in the repository are the authoritative record. Please cite the original authors whenever a tool built on their work contributes to a result.
Engines and libraries
Obtained from their authors: none is bundled and no prebuilt binaries are shipped. BootLoops runs them as separate programs, imports them at run time, or links them from small bridge programs compiled from source.
Reduction, finite fields and numerical evaluation
| Software | Authors | Used in | License | Reference |
|---|---|---|---|---|
| Kira | P. Maierhöfer, J. Usovitsch, P. Uwer, F. Lange, Z. Wu, J. Klappert (Kira 2.0) and the Kira developers | Kira stack, Seedling, Numkin, Trust; embedded in the AMFlow.cpp fork; Winnow and FFCapital read its output | GPL-3.0-or-later | Comput. Phys. Commun. 230 (2018) 99, arXiv:1705.05610; Comput. Phys. Commun. 266 (2021) 108024, arXiv:2008.06494; Comput. Phys. Commun. 322 (2026) 109999, arXiv:2505.20197 |
| FireFly | J. Klappert, S. Y. Klein, F. Lange | Kira stack (as released inside Kira) | GPL-3.0-or-later | Comput. Phys. Commun. 247 (2020) 106951, arXiv:1904.00009; Comput. Phys. Commun. 264 (2021) 107968, arXiv:2004.01463 |
| Fermat | R. H. Lewis (Fordham University) | Kira stack (run by Kira for back-substitution) | Freeware; (author's site only) | – |
| FIRE | A. V. Smirnov, F. S. Chukharev; A. V. Smirnov, M. Zeng | Kira stack (independent cross-check, unmodified) | GPL-2.0 | Comput. Phys. Commun. 247 (2020) 106877, arXiv:1901.07808; Comput. Phys. Commun. 302 (2024) 109261, arXiv:2311.02370 |
| FiniteFlow | T. Peraro | Blade (linked unmodified by the fork build; the port runs its executables and uses its prime table and system grammar) | MIT | JHEP 07 (2019) 031, arXiv:1905.08019; JHEP 12 (2016) 030, arXiv:1608.01902 |
| AMFlow and AMFlow.cpp | X. Liu, Y.-Q. Ma (AMFlow); the AMFlow.cpp contributors | AMFlow; command-line driver run by Wayfinder, PMflow, Numkin, Landau Alphabet and amflow-kit | MIT | Comput. Phys. Commun. 283 (2023) 108565, arXiv:2201.11669; Phys. Rev. D 105 (2022) L051503, arXiv:2107.01864; method and AMFlow.cpp: see Forks |
| pySecDec | S. Borowka, G. Heinrich, S. Jahn, S. P. Jones, M. Kerner, J. Schlenk, T. Zirke; disteval also V. Magerya, A. Olsson | pySecDec and FIESTA; imported by Longhand and one SubTropica fixture script | GPL-3.0 | Comput. Phys. Commun. 222 (2018) 313, arXiv:1703.09692; Comput. Phys. Commun. 240 (2019) 120, arXiv:1811.11720; Comput. Phys. Commun. 295 (2024) 108956, arXiv:2305.19768 |
| FIESTA | A. V. Smirnov, N. D. Shapurov, L. I. Vysotsky | pySecDec and FIESTA (second cross-check, unmodified) | GPL | Comput. Phys. Commun. 277 (2022) 108386, arXiv:2110.11660 |
| Pentagon | D. Chicherin, V. Sotnikov, S. Zoia | PentagonFunctions-cpp (built unchanged; reference values only) | GPL-3.0 | JHEP 12 (2020) 167, arXiv:2009.07803; JHEP 01 (2022) 096, arXiv:2110.10111 |
Symbolic algebra, symbolic integration and singularities
| Software | Authors | Used in | License | Reference |
|---|---|---|---|---|
| FORM 5 | J. A. M. Vermaseren, T. Ueda, J. Davies, T. Kaneko, C. Marinissen and the FORM developers | FORM, Formglue | GPL-3.0 | J. A. M. Vermaseren, math-ph/0010025; J. Kuipers, T. Ueda, J. A. M. Vermaseren, J. Vollinga, Comput. Phys. Commun. 184 (2013) 1453, arXiv:1203.6543; FORM version 5.0, arXiv:2601.19982; diagram generator: T. Kaneko, Comput. Phys. Commun. 92 (1995) 127 |
| HyperFORM | A. Kardos, S.-O. Moch, O. Schnetz; core algorithms from E. Panzer's HyperInt | FORM, Formglue (run by FORM) | GPL-3.0 | arXiv:2607.01163; Zenodo doi:10.5281/zenodo.17706909 |
| SubTropica and HyperFLINT | M. Giroux, S. Mizera, G. Salvatori | SubTropica (HyperFLINT is built from the authors' repository and run as a separate program or in-process library) | MIT | arXiv:2604.20954 |
| HyperInt | E. Panzer | SubTropica, Surd (not run directly; HyperFLINT and HyperFORM reimplement its algorithms; the included SubTropica front end can drive it) | GPL-3.0-or-later; (Maple) | Comput. Phys. Commun. 188 (2015) 148, arXiv:1403.3385; JHEP 03 (2014) 071, arXiv:1401.4361 |
| GiNaC with CLN | C. Bauer, A. Frink, R. Kreckel; polylogarithms by J. Vollinga, S. Weinzierl; elliptic functions by M. Walden, S. Weinzierl | GiNaC; linked by the GPLEval and Eichler bridge programs (compiled locally from source) and by the Kira fork | GPL-2.0-or-later | J. Symb. Comput. 33 (2002) 1, cs/0004015; Comput. Phys. Commun. 167 (2005) 177, hep-ph/0410259; Comput. Phys. Commun. 265 (2021) 108020, arXiv:2010.05271 |
| PLD.jl | C. Fevola, S. Mizera, S. Telen | PLD and SOFIA, Leviathan, Landau Alphabet (optional, called at run time) | MIT (code); CC BY 4.0 (page) | Comput. Phys. Commun. 303 (2024) 109278, arXiv:2311.16219; Phys. Rev. Lett. 132 (2024) 101601, arXiv:2311.14669 |
| Homotopy | P. Breiding, S. Timme | PLD and SOFIA, Landau Alphabet, Leviathan | MIT | ICMS 2018, LNCS 10931, 458, arXiv:1711.10911 |
| OSCAR, with Singular, polymake and GAP | The OSCAR team; Singular by W. Decker, G.-M. Greuel, G. Pfister, H. Schönemann and the Singular team | Leviathan, SubTropica, Terrier, the PLD bridge; Singular also run as a separate program | GPL-3.0-or-later; GPL (Singular) | W. Decker, C. Eder, C. Fieker, M. Horn, M. Joswig (eds.), The Computer Algebra System OSCAR, Springer (2025), doi:10.1007/978-3-031-62127-7 |
| msolve | J. Berthomieu, C. Eder, M. Safey El Din | Leviathan (run directly or through OSCAR) | GPL-2.0-or-later | ISSAC 2021, 51, arXiv:2104.03572, doi:10.1145/3452143.3465545 |
Arithmetic, scientific libraries and runtime
| Software | Authors | Used in | License | Reference |
|---|---|---|---|---|
| FLINT and Arb, with MPFR and GMP | W. Hart, F. Johansson, A. Ahlbäck and the FLINT team; Arb by F. Johansson; Riemann theta functions by J. Kieffer, with N. D. Elkies | Arb and mpmath, Baller, POSQ (through the bindings below; linked by the POSQ kernel compiled from source) | LGPL-3.0-or-later; GMP also GPL-2.0-or-later | IEEE Trans. Comput. 66 (2017) 1281, arXiv:1611.02831; arXiv:2203.02000; arXiv:2505.22382 |
| python-flint and Arblib.jl | F. Johansson, O. Benjamin and contributors (python-flint); M. Kaluba, J. Dahne and contributors (Arblib.jl) | Arb and mpmath, Eichler, GPLEval (the FLINT and Arb bindings for Python and Julia) | MIT | – |
| Nemo, Hecke, AbstractAlgebra | C. Fieker, W. Hart, T. Hofmann, F. Johansson and contributors | Arb and mpmath, Eichler, Terrier; also SOFIA.jl, LandauAlphabet.jl, Counterweight, GPLEval, SubTropica | BSD-2-Clause | ISSAC 2017, 157, doi:10.1145/3087604.3087611, arXiv:1705.06134 |
| mpmath | F. Johansson and the mpmath contributors | Arb and mpmath, PSLQ and LLL (core dependency, including its PSLQ) | BSD-3-Clause | – |
| fplll | The FPLLL development team | PSLQ and LLL, Lockpick (optional LLL and BKZ through fpylll) | LGPL-2.1-or-later | – |
| PARI/GP | The PARI Group, Univ. Bordeaux | Abacus (run directly and through cypari2), Terrier | GPL-2.0-or-later | – |
| SageMath with ore_algebra | The Sage Developers; ore_algebra by M. Kauers, M. Jaroschek, F. Johansson, M. Mezzarobba | Holonomic (imported; Holonomic runs under Sage's Python) | GPL-2.0-or-later; (each) | arXiv:1306.4263; ICMS 2016, arXiv:1607.01967 |
| SymPy, NumPy, SciPy, networkx | Their development teams; networkx by A. Hagberg, D. Schult, P. Swart | General Python dependencies; Dogtag's graph isomorphism is networkx's VF2 (Cordella, Foggia, Sansone, Vento) | BSD | networkx: SciPy 2008 proceedings |
| msprime, tskit, moments | J. Kelleher et al. and the tskit developers; moments by J. Jouganous, W. Long, A. P. Ragsdale, S. Gravel | Popcorn (optional imports, skipped when absent) | GPL-3.0-or-later (msprime); MIT (tskit, moments) | J. Kelleher, A. M. Etheridge, G. McVean, PLoS Comput. Biol. 12 (2016) e1004842; F. Baumdicker et al., Genetics 220 (2022) iyab229; P. Ralph, K. Thornton, J. Kelleher, Genetics 215 (2020) 779; moments: Genetics 206 (2017) 1549 |
| etas | L. Mizrahi, S. Nandan, S. Wiemer | Clinch (imported for reference values) | MIT | Seismol. Res. Lett. 92 (2021) 2333, doi:10.1785/0220200231 |
| Julia | J. Bezanson, A. Edelman, S. Karpinski, V. B. Shah | All Julia packages | MIT | SIAM Rev. 59 (2017) 65 |
Forks
Three engines run as patched forks. Each fork is a repository of its own under github.com/BootLoops-ai that keeps the original history, license and notices unchanged, carries the BootLoops changes on a branch of its own, and records every change and how it was verified in a PATCHES.md. No fork is relicensed; the built engines run as separate programs.
| Software | Authors | Fork and changes | License | Reference |
|---|---|---|---|---|
| Kira 3.1 | The Kira developers (as above) | Fork BootLoops-ai/kira: Parallel coefficient processing and idempotent SQLite guards, reduction output byte-identical to stock; two GPL Python utilities written by reading Kira's and FireFly's sources, attributed to their authors | GPL-3.0-or-later | Comput. Phys. Commun. 322 (2026) 109999, arXiv:2505.20197, and the Kira references above |
| Blade | X. Guan, X. Liu, Y.-Q. Ma, W.-H. Wu | Fork BootLoops-ai/blade: Mathematica-free build against FiniteFlow; C wrappers transcribed from FiniteFlow's MathLink layer, with its notice; command-line executables in place of MathLink | MIT | Comput. Phys. Commun. 310 (2025) 109538, arXiv:2405.14621; T. Peraro, JHEP 07 (2019) 031, arXiv:1905.08019 |
| AMFlow.cpp v1.1.0 | The AMFlow.cpp contributors; a C++17 reimplementation of AMFlow by X. Liu, Y.-Q. Ma | Fork BootLoops-ai/amflow-cpp: Precision and reliability fixes, resumable embedded reduction, boundary and vacuum extensions, validation wrappers | MIT | Zenodo doi:10.5281/zenodo.20087172; Comput. Phys. Commun. 283 (2023) 108565, arXiv:2201.11669; method: X. Liu, Y.-Q. Ma, C.-Y. Wang, Phys. Lett. B 779 (2018) 353, arXiv:1711.09572; Phys. Rev. D 105 (2022) L051503, arXiv:2107.01864 |
Translated and included code
Source by other authors that a BootLoops package carries, in translation or verbatim, under the authors' license and with their notice.
| Original | Authors | In BootLoops | License | Reference |
|---|---|---|---|---|
| SubTropica | M. Giroux, S. Mizera, G. Salvatori | SubTropica: Unofficial Julia and Python translation of the Wolfram Language front end; original and license files included; not affiliated with or endorsed by the authors | MIT | arXiv:2604.20954 |
| HyperFLINT command-line sources | S. Mizera and SubTropica contributors | SubTropica: Two source files and the README included, modified in comments only; code unchanged | MIT | arXiv:2604.20954 |
| HyperInt | E. Panzer; mathematics by F. Brown (arXiv:0910.0114) | SubTropica, Surd: Julia transliteration of four Maple compatibility-graph reduction procedures, rational letters only | GPL-3.0-or-later | Comput. Phys. Commun. 188 (2015) 148, arXiv:1403.3385 |
| SOFIA | M. Correia, M. Giroux, S. Mizera | PLD and SOFIA (SOFIA.jl): Julia translation of the Wolfram Language package; originals included unmodified | MIT | Comput. Phys. Commun. 320 (2026) 109970, arXiv:2503.16601 |
| Effortless | A. Matijašić, J. Miczajka | PLD and SOFIA (SOFIA.jl): Julia translation of the odd-letter construction; original included unmodified | MIT | Algorithm: A. Matijašić, PhD thesis, LMU Munich (2024); J. Henn, A. Matijašić, J. Miczajka, T. Peraro, Y. Xu, Y. Zhang, Phys. Rev. Lett. 135 (2025) 031601, arXiv:2501.01847 |
| SageMath genus-2 modules | F. Bouyer, M. Streng (Mestre reconstruction); N. Alexander, with Kunzweiler, Ma and Pope (Igusa–Clebsch invariants); after Mestre (1991), Lauter and Yang (2011), Igusa (1960) | Eichler (genus 2): SymPy transliteration of the two modules; the rest of Eichler is MIT | GPL-2.0-or-later | – |
| Blade | X. Guan, X. Liu, Y.-Q. Ma, W.-H. Wu | Blade: Python port of the search and solve modules of the Wolfram Language code, with the authors' notice | MIT | Comput. Phys. Commun. 310 (2025) 109538, arXiv:2405.14621; method: Phys. Rev. D 99 (2019) 071501, arXiv:1801.10523; Chin. Phys. C 44 (2020) 093106, arXiv:1912.09294 |
| HyperFORM driver template | A. Kardos, S.-O. Moch, O. Schnetz | Formglue, FORM: The generated FORM job follows HyperFORM's shipped example drivers line for line; no HyperFORM library source included | GPL-3.0-only; (that module) | arXiv:2607.01163; Zenodo doi:10.5281/zenodo.17706909 |
| FORM reference manual | J. A. M. Vermaseren and the FORM developers | FORM, Formglue: Short QCD model example from the manual reproduced in one example and one test; no FORM source or manual prose included | GPL-3.0 | FORM version 5.0, arXiv:2601.19982 |
| etas | L. Mizrahi, S. Nandan, S. Wiemer | Clinch: Two small helper functions copied unchanged, with their notice | MIT | Seismol. Res. Lett. 92 (2021) 2333, doi:10.1785/0220200231 |
Re-implemented methods
BootLoops' own implementations of published methods. The methods, conventions and formulas are the cited authors'; no third-party code is copied beyond what the previous section states.
| Method | Authors | In BootLoops | License | Reference |
|---|---|---|---|---|
| Euler-characteristic-drop method; SPQR | V. Chestnov, G. Crisanti, M. Giroux (Landau's Leviathans); V. Chestnov, G. Crisanti (SPQR) | Leviathan: Own Julia implementation; the authors' public Mathematica code (Landau's Leviathans; DiscKosky by G. Crisanti, L. Lippstreu, A. J. McLeod, M. Polackova) consulted for five details; nothing copied or translated | No license file; (authors' code) | arXiv:2606.29612; arXiv:2511.14875 |
| Hecke.jl short-vector search rule | C. Fieker, T. Hofmann and the Hecke contributors | Terrier: Search-window rule and output contract re-implemented; two conventions follow their code | BSD-2-Clause | C. Fieker, W. Hart, T. Hofmann, F. Johansson, ISSAC 2017, 157, arXiv:1705.06134 |
| matPTF tsunami forecasting (INGV) | Selva et al. | Baller: Hazard-curve percentiles and alert ladder re-implemented, with modifications, as ball-arithmetic enclosures | CC BY 4.0 | Nat. Commun. 12 (2021) 5677 |
| pyCSEP Poisson L-test | W. H. Savran, M. J. Werner, D. Schorlemmer, P. J. Maechling et al. | Baller: Monte Carlo sampling semantics re-implemented and vectorized | BSD-3-Clause | J. Open Source Softw. 7(69) (2022) 3658 |
| Poisson-random-field spectrum and DFE likelihoods | Sawyer and Hartl; Bustamante, Wakeley, Sawyer and Hartl; Williamson, Fledel-Alon and Bustamante | Popcorn: Implemented exactly, with certificates; conventions of dadi, fitdadi, polyDFE, fastDFE and moments followed | – | Genetics 132 (1992) 1161; 159 (2001) 1779; 168 (2004) 463; conventions: Gutenkunst et al. (2009); Kim, Huber and Lohmueller (2017); Tataru et al. (2017); Sendrowski and Bataillon (2024); Jouganous et al. (2017) |
| Exact mixture evidence and sampling formulas | Lin, Sturmfels and Xu; Etienne; Etienne and Haegeman; Peccoud and Ycart; Madsen, Kauchak and Elkan | Mixalot: Mixture-evidence integrals, Etienne sampling formula, telegraph model and Dirichlet compound multinomial implemented as exact evaluators | – | JMLR 10 (2009) 1611; Ecol. Lett. 8 (2005) 253; 10 (2007) 608; Theor. Ecol. 4 (2011) 87; Theor. Popul. Biol. 48 (1995) 222; ICML 2005 |
| ETAS likelihood and EM algorithm | Ogata; Veen and Schoenberg; etas package conventions of Mizrahi et al. | Clinch: Re-implemented for certification | – | JASA 83 (1988) 9; JASA 103 (2008) 614 |
| AMFlow ending-system boundary values | X. Liu, Y.-Q. Ma; as carried by AMFlow.cpp | Wayfinder: Five closed forms and the prefactor re-expressed in Python, arguments and powers carried over number for number; no AMFlow or AMFlow.cpp source text copied | MIT (AMFlow) | Comput. Phys. Commun. 283 (2023) 108565, arXiv:2201.11669 |
| FireFly saved-state file layout | J. Klappert, F. Lange; J. Klappert, S. Y. Klein, F. Lange | FFCapital: Layout read as a format specification; FireFly not bundled, linked or run | GPL-3.0-or-later; (FireFly) | Comput. Phys. Commun. 247 (2020) 106951; Comput. Phys. Commun. 264 (2021) 107968 |
| SAS and R quantile conventions | Hyndman and Fan | Qinvert: Conventions followed | – | Am. Stat. 50 (1996) 361 |
Data sets
| Data | Authors | In BootLoops | License | Reference |
|---|---|---|---|---|
| N=4 super-Yang–Mills energy-correlator collinear-limit symbol letters | D. Chicherin, I. Moult, E. Sokatchev, K. Yan, Y. Zhu | Surd: Adapted to a one-parameter slice; bundled | CC BY 4.0 | Ancillary files of arXiv:2401.06463 |
| Tree-level quark quadruple-collinear splitting function | V. Del Duca, C. Duhr, R. Haindl, A. Lazopoulos, M. Michel | Surd: Adapted as exact cell integrands | CC BY 4.0; (journal versions) | JHEP 02 (2020) 189, arXiv:1912.06425; JHEP 10 (2020) 093, arXiv:2007.05345 |
| KKLT flux vacuum 5-81-3213 | M. Demirtas, M. Kim, L. McAllister, J. Moritz, A. Rios-Tascon | Terrier: Derived card from the paper and its ancillary data; no ancillary file reproduced | CC BY 4.0 | JHEP 12 (2021) 136, arXiv:2107.09064 |
| K3×K3 flux matrix with D3 charge 25 | I. Bena, J. Blåbäck, M. Graña, S. Lüst | Terrier: Transcribed as a positive control; paper cited, no text reproduced | – | JHEP 11 (2021) 223, arXiv:2010.10519, Appendix B |
| Hulek–Verrill fourfold diagonal-slice operators | T. W. Grimm, D. van de Heisteeg; order-5 operator from Jockers, Kotlewski and Kuusela; K3 operator after Verrill | Terrier: Transcribed as match targets; periods, fits and certificates are BootLoops' own | – | arXiv:2404.12422; arXiv:2312.07611; J. Math. Kyoto Univ. 36 (1996) 423 |
| Two-modulus flux-vacuum example | M. Demirtas, M. Kim, L. McAllister, J. Moritz | Terrier: Defining data transcribed into a regression card | – | Phys. Rev. Lett. 124 (2020) 211603, arXiv:1912.10047 |
| Hecke eigenvalues of three newforms, and a few elliptic-curve equations | The LMFDB Collaboration | Terrier: Reference values for finite-field fingerprint checks | CC BY-SA 4.0 | The L-functions and Modular Forms Database, lmfdb.org (newforms 14.4.a.a, 34.2.b.a, 180.4.a.e) |
| DravLex v1.0 lexical cognate data | Kolipakam, Jordan, Dunn, Greenhill, Bouckaert, Gray and Verkerk | ERAS, Baller, POSQ: Derived quartet-collapse summary bundled | CC BY 4.0 | R. Soc. Open Sci. 5 (2018) 171504; lexibank/dravlex, doi:10.5281/zenodo.5121580 |
| Diphoton-amplitude ancillary data | M. Becchetti, F. Coro, C. Nega, L. Tancredi, F. J. Wagner | Eichler: Fetched on demand for validation; not included | CC BY 4.0 | JHEP 06 (2025) 033, arXiv:2502.00118; Zenodo doi:10.5281/zenodo.14733100 |
| PLD database | C. Fevola, S. Mizera, S. Telen; as redistributed by SOFIA | PLD and SOFIA: Bundled as a test reference | CC BY 4.0 (data); MIT (SOFIA copy) | Comput. Phys. Commun. 303 (2024) 109278, arXiv:2311.16219 |
Notes
- BootLoops' own code is released under the MIT license, copyright (c) 2026 Anthropic, PBC. Every component listed here keeps its own license and copyright; the full notices are in
THIRD_PARTY.md. - Where a BootLoops module imports or links a GPL-licensed library at run time (pySecDec, OSCAR, SageMath with ore_algebra, msprime, GiNaC), the running combination is under GPL terms. The GiNaC bridge programs ship as source only, and the compiled bridges are GPL-covered works.
- The SubTropica module includes the GPL HyperInt transliteration, so the module as loaded is a combined work under GPL terms; removing that file gives an MIT-only build. In Formglue, only the module that writes the HyperFORM job is GPL-3.0-only, because it follows HyperFORM's example drivers; the rest of Formglue is MIT and does not import it.
- Fork modifications are contributed under each fork's own license. The original Mathematica AMFlow is not bundled anywhere.
Corrections and omissions, including a missing or inaccurate credit, go through the page-correction form on the feedback repository (see Contribute & contact); questions about the tools go to tools@bootloops.ai.