# Ancillary files: code and data

Data and checkers accompanying "Exact methods for string flux vacua" (M. D. Schwartz), main text and Supplementary
Material (SM). This folder also contains `kklt-evaluate.py`, `kklt-expression.md` and `kklt-w0-ball.json`, the
stand-alone evaluator for the KKLT benchmark of Section 5 with its input description and the certification record it
identifies by SHA-256 (`MANIFEST.sha256` and `CHANGES.md` are their manifest and changelog); the four directories below add
the lattice data of Section 3, the arithmetic data of the charge-22 flux, the data of the Hulek-Verrill sector of
Section 4, and the full certificate set for Section 5.

`lattice/` (Section 3; SM Sections S1.2 and S5). The Gram matrices, invariants and gluings into Gamma_(3,19) of the
root-free rank-19 lattices W512, W512', W1024 of Theorem 3.5 (Eq. (34), Table 3; SM Eqs. (S5.1)-(S5.3), (S5.5)-(S5.7),
Table S5) and of Lambda_19 (SM Section S1.2, Eq. (S5.4), Table S5); the 54 admissible genera of Lemma 3.3 with the
complete class lists of their rank-5 complement genera, the exact masses, and the 1,764 rational Farkas certificates of
the Niemeier argument (Eq. (33); SM Section S5.2, Tables S6-S8, Eqs. (S5.8)-(S5.11)); the five exact certificates behind
Table 3 and Theorem 3.5 and the 38 released-column certificates, the two-released-columns coverage and the 156 local
witnesses (SM Section S5.3, Tables S9-S10, Eqs. (S5.14)-(S5.20)); and the seven root-free admissible lattices at
determinants 160-224, six of them with explicit isometries to the Leech coinvariant lattices Lambda_M20, Lambda_A6,
Lambda_L2(7) and to lattices in Martinet's and the Nebe-Sloane tables (the determinant-224 lattice was not found in the
literature), together with five isometries among those reference lattices (Section 3.3; SM Section S1.2).
`verify_lattice.py` recomputes determinants, evenness, minimum 4 and
root-freeness by exhaustive exact enumeration, kissing numbers, discriminant groups, the unimodularity and signature of
the glued lattices, the mass identities, every Farkas certificate in exact rationals, every charge-bound certificate
(positive definiteness of the residual matrix by exact LDL^T, the value as an exact fraction, the threshold), the local
witnesses, and every isometry U^T B U = A.

`charge22/` (Section 3.4, Eqs. (40)-(43), Table 4; SM Section S6). The complete specification of the charge-22 flux on
K3 x K3: delta and eps_S in the power basis of Z[zeta_66] with the one-positive-place condition, the Toeplitz Gram
matrix of L and the Gram matrix of Lambda = U + L, the U-block matrices, the integer matrices g, gtilde, S, Stilde and N,
tr S = 44, N_flux = 22, n_M2 = 2, the characteristic polynomial (x^2-6x+1) m(x)^2 with m and disc(m), the eigenplanes
with the sign of the form on each (three positive directions), Lambda cap Sigma^perp = 0, and the isometry P onto entry
0.66.0.1 of the K3Groups database (Kondo's surface) with the admissible powers 5 and 61 (SM Eqs. (S6.15)-(S6.17)).
`verify_charge22.gp` (PARI/GP) and `verify_charge22.py` recompute all of it from the definitions. Whether W = 0 at this
vacuum is not decided.

`hv4/` (Section 4, Eqs. (44)-(56), Proposition 4.1, Table 5; SM Section S7). Gram5, W5, N_flux = Q(g)/2, u = Gram5 g, the
residual monodromy M_d, the operator L5, the cut and the box R with the interval behind 751, the frame map C with the
vanishing classes at the three conifold points, the flux counts in both units (signed vectors and classes), the 28
vacua in R at twelve positions, the three certified vacua of Table 5 with full digit strings, the field signs and
margins, the special-point catalogue, and the charge-1 scope. `verify_hv4.py` recomputes the lattice statements, the
frame identities, the L5 recurrence, and re-enumerates the fluxes and their monodromy classes; the Krawczyk
certificates themselves are quoted (re-running them needs the period-transport code, which is not part of this
folder).

`dkmm/` (Section 5, Eqs. (57)-(69), Tables 6-7; SM Section S3). The certificate set for the KKLT benchmark: the
certified F-term critical point of the DKMM superpotential and the enclosure of |W0| (`cert_w0_vac/`; its
`result_vac_R_150.json` is the file served here as `kklt-w0-ball.json`), the on-curve certified periods and frame
(`cert_w0/`), the tail-envelope lemma with proof and regression tests (`majorant/`), the comparison worksheet for
the zeta(3) chi term (`pilot/`), the conditional certified value for the AdS vacuum 5-81-3213 (`pfaffian_ads581/`),
the exact restricted operator and series (`restrict/`), and the source-archive hashes (`manifests/`). Each directory
has a README with inputs, commands, outputs and runtimes; `dkmm/README.md` has the overview.

## Download

The folder is served as static files under `https://bootloops.ai/files/kklt/`; every path in `SHA256SUMS` is relative to
that address. To fetch the whole folder into the current directory:

```
curl -O https://bootloops.ai/files/kklt/SHA256SUMS
wget -x -nH --cut-dirs=2 -i <(cut -c67- SHA256SUMS | sed 's,^,https://bootloops.ai/files/kklt/,')
```

(or per file: `curl --create-dirs -o lattice/genera54.json https://bootloops.ai/files/kklt/lattice/genera54.json`).

## How to verify

```
sha256sum -c SHA256SUMS                            # integrity of every file listed below (run it first: the dkmm legs rewrite their result files)
cd lattice  && python3 verify_lattice.py           # full: rc 0, 150 s; --quick: rc 0, 59 s (this release, one x86 core)
cd charge22 && gp -q verify_charge22.gp            # rc 0, under 1 s
cd charge22 && python3 verify_charge22.py          # rc 0, 3 s
cd hv4      && python3 verify_hv4.py               # full: rc 0, 27 s; --quick: rc 0, under 1 s
cd dkmm     && (see dkmm/README.md)                # pilot 20 s, majorant self-test 5 s, cert_w0 legs 16-106 s, cert_w0_vac legs 17-119 s, verdict.py 5 s, restrict/gamma2p.py 1 s
python3 kklt-evaluate.py                           # the stand-alone Section-5 evaluator (about a minute)
```

Every `verify_*` checker exits with status 0 if and only if all of its checks pass, printing one PASS/FAIL line per
check and naming the offending item on failure; the `dkmm` steps exit nonzero on any failed comparison or assertion
(see `dkmm/README.md`). Re-running the `dkmm` legs rewrites their `result_*.json` files identically apart from the
recorded wall-time fields, after which `sha256sum -c` reports those files as changed.

In this release all checks passed: verify_lattice.py 106 checks passed, 0 failed; verify_charge22.gp 42 checks passed, 0 failed;
verify_charge22.py 41 checks passed, 0 failed; verify_hv4.py 35 checks passed, 0 failed; all 20 dkmm legs exit status 0, and the 18 files listed in `SHA256SUMS` that they rewrite are identical to the shipped ones (11 byte for byte, 7 apart from the recorded wall-time fields).

Software: Python 3 (standard library suffices for the three `verify_*.py` checkers; `mpmath` and `sympy` are used when
present); PARI/GP for `verify_charge22.gp` and, optionally, for the |Aut| recomputation in `verify_lattice.py`;
`python-flint` (Arb) for the certified legs in `dkmm/`; `mpmath` for `dkmm/pilot/`, the `dkmm` check steps and
`kklt-evaluate.py`; `sympy` for `dkmm/cert_w0_vac/jet_ideal.py`; `numpy` for `dkmm/pfaffian_ads581/check_pa1.py`.
Tested with Python 3.12.3, PARI/GP 2.15.4, mpmath 1.3.0, sympy 1.14.0, python-flint 0.8.0, numpy 2.4.1 (also 1.26.4).

## Files

155 files are listed: the three `kklt-*` files already in this folder and 152 files (73.7 MB) in the four
directories (charge22/ 6 files, 0.1 MB, dkmm/ 89 files, 66.8 MB, hv4/ 4 files, 0.1 MB, lattice/ 53 files, 6.7 MB); this `README.md` and `SHA256SUMS` are not in the table
(`SHA256SUMS` covers `README.md`).

| file | sha256 (first 16) | size |
|---|---|---|
| kklt-evaluate.py | 5c18c3269927b92e | 28897 bytes |
| kklt-expression.md | bcfe7c3cc407f51f | 4638 bytes |
| kklt-w0-ball.json | 28f3307f54fc8bc3 | 1989 bytes |
| charge22/README.md | b74fcb97b93bc97b | 2155 bytes |
| charge22/charge22.json | 41cab1aabba14a22 | 58138 bytes |
| charge22/charge22.txt | c7cfcf6f75c3be82 | 25025 bytes |
| charge22/charge22_data.gp | 9ccb35060a4b9cc0 | 19066 bytes |
| charge22/verify_charge22.gp | 434072a04d6a1f1e | 8971 bytes |
| charge22/verify_charge22.py | ea0ef8c602eec841 | 19432 bytes |
| dkmm/README.md | a59cea651de1038c | 6592 bytes |
| dkmm/cert_w0/README.md | 2707a22aa1456ee3 | 2647 bytes |
| dkmm/cert_w0/cert_lib.py | 5aafa6c5da74b679 | 18036 bytes |
| dkmm/cert_w0/cert_transport.py | c087254d1631b12b | 16533 bytes |
| dkmm/cert_w0/checks_cert.json | c4476bceeb0eb5e0 | 1067 bytes |
| dkmm/cert_w0/frame_solution.json | 75d93b6964d47e15 | 341 bytes |
| dkmm/cert_w0/out_C_150.txt | 1b7ea58db29ff110 | 11469 bytes |
| dkmm/cert_w0/out_C_60.txt | 344c5553d1b36522 | 11024 bytes |
| dkmm/cert_w0/out_R_150.txt | 73fb176a458c7bd0 | 4222 bytes |
| dkmm/cert_w0/out_R_60.txt | f1e180aba2980641 | 3828 bytes |
| dkmm/cert_w0/out_checks_cert.txt | 1e70445ce46b9b7a | 1380 bytes |
| dkmm/cert_w0/out_model_at_point.txt | f5ee0afaffd9c83e | 1005 bytes |
| dkmm/cert_w0/out_stage1.txt | 90c8c1e2d92102fe | 775 bytes |
| dkmm/cert_w0/result_C_150.json | 6ab51250e871b335 | 12741 bytes |
| dkmm/cert_w0/result_C_60.json | 138cf61e389f8d8b | 12117 bytes |
| dkmm/cert_w0/result_R_150.json | c5ccedb4fefa930b | 5017 bytes |
| dkmm/cert_w0/result_R_60.json | b53b850169c35b72 | 4444 bytes |
| dkmm/cert_w0/run_cert.py | 65c2afb6021a1bd0 | 11328 bytes |
| dkmm/cert_w0/towers_ext.json | a2ac43f8dd2cab2f | 1696296 bytes |
| dkmm/cert_w0_vac/README.md | 3f013112553ddeea | 3191 bytes |
| dkmm/cert_w0_vac/cert_vac.py | dc9e5ff9c757e1ab | 17371 bytes |
| dkmm/cert_w0_vac/checks_vac.json | 192d8cb348ad30d7 | 939 bytes |
| dkmm/cert_w0_vac/connection_z.json | 8e67c16af8ede45d | 5674 bytes |
| dkmm/cert_w0_vac/curve_T.json | c747730440f3db47 | 23599 bytes |
| dkmm/cert_w0_vac/jet_checks.py | 2f043b418437a7a9 | 12698 bytes |
| dkmm/cert_w0_vac/jet_ideal.py | 104a6dd2f3723fde | 8484 bytes |
| dkmm/cert_w0_vac/out_checks_vac.txt | bc09fae71454facc | 664 bytes |
| dkmm/cert_w0_vac/out_jet_checks.txt | 9eef1c9165840291 | 341 bytes |
| dkmm/cert_w0_vac/out_jet_ideal.txt | 6dddb46ffbff07f0 | 284 bytes |
| dkmm/cert_w0_vac/out_vac_C_150.txt | d0650deceb01f9e4 | 1151 bytes |
| dkmm/cert_w0_vac/out_vac_R_150.txt | 65d8161b67bffeb0 | 1153 bytes |
| dkmm/cert_w0_vac/out_vac_R_60.txt | 9a0c031e4e54f7cc | 1085 bytes |
| dkmm/cert_w0_vac/result_vac_C_150.json | 75baf30544998223 | 1940 bytes |
| dkmm/cert_w0_vac/result_vac_R_150.json | 28f3307f54fc8bc3 | 1989 bytes |
| dkmm/cert_w0_vac/result_vac_R_60.json | 98e82216671a4aaf | 1508 bytes |
| dkmm/cert_w0_vac/run_vac.py | 65ed35bc2f60880a | 9106 bytes |
| dkmm/majorant/README.md | ae091c31138bd024 | 5888 bytes |
| dkmm/majorant/envelope_certified.py | 94a7fff1b0603500 | 11251 bytes |
| dkmm/majorant/selftest_envelope.py | 0d0e94737a28788c | 11340 bytes |
| dkmm/manifests/README.md | 85966e05800842a5 | 518 bytes |
| dkmm/manifests/data_SHA256SUMS | dabeab2bee9b6b94 | 2427 bytes |
| dkmm/manifests/sources_SHA256SUMS | 412e2a0bf6e25694 | 1523 bytes |
| dkmm/pfaffian_ads581/A_exact.json | eef01bf64a81c93f | 2921645 bytes |
| dkmm/pfaffian_ads581/README.md | 061a840963f4f3fc | 3844 bytes |
| dkmm/pfaffian_ads581/a1_lift.py | 4a6884cecd658dc9 | 4088 bytes |
| dkmm/pfaffian_ads581/a1_perprime.py | 6c6ece5f0798fd9b | 2408 bytes |
| dkmm/pfaffian_ads581/card_ads-5-81-3213.json | d8c3a37ca367b79d | 5406 bytes |
| dkmm/pfaffian_ads581/check_PA1.json | e7ebd86b237f801a | 124 bytes |
| dkmm/pfaffian_ads581/check_PA2.json | c6bbe158cadd9ee3 | 196 bytes |
| dkmm/pfaffian_ads581/check_PA3_amended.json | 6ae794d656338f67 | 751 bytes |
| dkmm/pfaffian_ads581/check_PA4.json | 622d04d1a144aad2 | 889 bytes |
| dkmm/pfaffian_ads581/check_PA5_substitute.json | 9b4f4aa5dcb6c6aa | 566 bytes |
| dkmm/pfaffian_ads581/check_PA6.json | 2d1e095b88cd5342 | 368 bytes |
| dkmm/pfaffian_ads581/check_pa1.py | 97d8c78f1d607e46 | 1914 bytes |
| dkmm/pfaffian_ads581/check_pa2.py | 1ce4e0d54c52ea0f | 2132 bytes |
| dkmm/pfaffian_ads581/deg_table.json | 01a6f36af7a687f7 | 1441 bytes |
| dkmm/pfaffian_ads581/f3_frame.json | c24fd55fad20ad75 | 2896 bytes |
| dkmm/pfaffian_ads581/gv_full.json | 8d100983d2cd921a | 12365 bytes |
| dkmm/pfaffian_ads581/jets_series.py | 654144d7e707fbdb | 3023 bytes |
| dkmm/pfaffian_ads581/pipe/cards/ads-5-81-3213.json | d8c3a37ca367b79d | 5406 bytes |
| dkmm/pfaffian_ads581/pipe/cards/ads-5-81-3213_bank/check_g2.json | 69295ad6fdcb5f82 | 930 bytes |
| dkmm/pfaffian_ads581/pipe/cards/ads-5-81-3213_bank/dmodule/conn_samples_2147483489.npz | 18a4f545933765ea | 1190022 bytes |
| dkmm/pfaffian_ads581/pipe/cards/ads-5-81-3213_bank/dmodule/conn_samples_2147483497.npz | cc6eb50c47321aae | 3565702 bytes |
| dkmm/pfaffian_ads581/pipe/cards/ads-5-81-3213_bank/dmodule/conn_samples_2147483543.npz | f752ab1e88757073 | 3565702 bytes |
| dkmm/pfaffian_ads581/pipe/cards/ads-5-81-3213_bank/dmodule/conn_samples_2147483549.npz | 203316838bc2470a | 3565702 bytes |
| dkmm/pfaffian_ads581/pipe/cards/ads-5-81-3213_bank/dmodule/conn_samples_2147483563.npz | 79ea6a5be3ea2abc | 3565702 bytes |
| dkmm/pfaffian_ads581/pipe/cards/ads-5-81-3213_bank/dmodule/conn_samples_2147483579.npz | 86c13bca0d9b9c23 | 3565702 bytes |
| dkmm/pfaffian_ads581/pipe/cards/ads-5-81-3213_bank/dmodule/conn_samples_2147483587.npz | b5f901648af6cfc8 | 3565702 bytes |
| dkmm/pfaffian_ads581/pipe/cards/ads-5-81-3213_bank/dmodule/conn_samples_2147483629.npz | 06008f7551bb7fa6 | 19007622 bytes |
| dkmm/pfaffian_ads581/pipe/cards/ads-5-81-3213_bank/dmodule/conn_samples_2147483647.npz | 2b02d8c21a7e7a36 | 19007622 bytes |
| dkmm/pfaffian_ads581/pipe/cards/ads-5-81-3213_bank/w0_series_3000.json.gz | ab30d1f4d997a35d | 175608 bytes |
| dkmm/pfaffian_ads581/pipe/family.py | bf808b9406f24592 | 5386 bytes |
| dkmm/pfaffian_ads581/pipe/geff_series.py | de5d2e01e9bcc135 | 28626 bytes |
| dkmm/pfaffian_ads581/pipe/pipe_lib.py | c7bfb8284ad84cd4 | 16789 bytes |
| dkmm/pfaffian_ads581/tower_120.json | 66ac9cff7a91b864 | 108652 bytes |
| dkmm/pfaffian_ads581/verdict.py | a778d8dd950fd260 | 11833 bytes |
| dkmm/pfaffian_ads581/verdict_raw.json | d7e6d20b1528e650 | 302 bytes |
| dkmm/pilot/README.md | e11613828bdf8511 | 1490 bytes |
| dkmm/pilot/out_repro_w0.txt | cd50a7be17ae3fa0 | 9392 bytes |
| dkmm/pilot/out_rt_1d.txt | f6af31f9132afc13 | 312 bytes |
| dkmm/pilot/repro_w0.py | 8352cece29941ba9 | 22476 bytes |
| dkmm/pilot/rt_1d_check.py | 3c6ad48560b70a7b | 2469 bytes |
| dkmm/restrict/README.md | 95fffcd0f3d16181 | 1018 bytes |
| dkmm/restrict/gamma2p.py | 88c6edeb5e70a447 | 16850 bytes |
| dkmm/restrict/gv_extracted.json | f785caab5f675e73 | 1043 bytes |
| dkmm/restrict/operator_LS.json | adf83245c16489ed | 39962 bytes |
| dkmm/restrict/s_vac.json | 8ea4bb1dde56c3d9 | 194 bytes |
| dkmm/restrict/series_curve.json | a10d8e1dcdde8501 | 286533 bytes |
| dkmm/restrict/tower_curve.json | 2ecd7e132e0f0207 | 575549 bytes |
| hv4/README.md | eb23189a41725b2b | 2221 bytes |
| hv4/hv4.json | b1f0734742012f78 | 32986 bytes |
| hv4/hv4.txt | 85be102cebc4d004 | 7957 bytes |
| hv4/verify_hv4.py | 78a9ff981e5a7b85 | 24743 bytes |
| lattice/README.md | 921dcd88d8204a45 | 3935 bytes |
| lattice/floor_certificates/dropJ_W512_J00.json.gz | 55d8752cdee5067a | 135480 bytes |
| lattice/floor_certificates/dropJ_W512_J01.json.gz | 7e36a27d9135c69e | 137335 bytes |
| lattice/floor_certificates/dropJ_W512_J02.json.gz | 4db51ff1c680082d | 84979 bytes |
| lattice/floor_certificates/dropJ_W512_J03.json.gz | d90823ef65eaf07e | 137508 bytes |
| lattice/floor_certificates/dropJ_W512_J04.json.gz | d3ee8cb404ae8177 | 139061 bytes |
| lattice/floor_certificates/dropJ_W512_J05.json.gz | 16f95d619d78e5b2 | 138940 bytes |
| lattice/floor_certificates/dropJ_W512_J06.json.gz | 285864610baa1905 | 130497 bytes |
| lattice/floor_certificates/dropJ_W512_J07.json.gz | 9e924e0bdcd540a9 | 144301 bytes |
| lattice/floor_certificates/dropJ_W512_J08.json.gz | d5acb108ba4e9355 | 128638 bytes |
| lattice/floor_certificates/dropJ_W512_J09.json.gz | 228913b1afae245a | 133398 bytes |
| lattice/floor_certificates/dropJ_W512_J10.json.gz | f3c2abbc49b5d7d6 | 84978 bytes |
| lattice/floor_certificates/dropJ_W512_J11.json.gz | b1ab1aa80ee5388d | 84975 bytes |
| lattice/floor_certificates/dropJ_W512_J12.json.gz | d263248829f380cc | 84973 bytes |
| lattice/floor_certificates/dropJ_W512_J13.json.gz | 162de62e184d2328 | 145721 bytes |
| lattice/floor_certificates/dropJ_W512_J14.json.gz | 2b2ebafd0e6a7d76 | 84982 bytes |
| lattice/floor_certificates/dropJ_W512_J15.json.gz | 999e1ea9919b9bf0 | 84982 bytes |
| lattice/floor_certificates/dropJ_W512_J16.json.gz | de6f9d888413040c | 84978 bytes |
| lattice/floor_certificates/dropJ_W512_J17.json.gz | e0667bf6d2cbaf2c | 84979 bytes |
| lattice/floor_certificates/dropJ_W512_J18.json.gz | 321023261f5d3549 | 84975 bytes |
| lattice/floor_certificates/dropJ_W512p_J00.json.gz | 68e4b1b7fcf6491a | 115121 bytes |
| lattice/floor_certificates/dropJ_W512p_J01.json.gz | 94e660096cbb965e | 132846 bytes |
| lattice/floor_certificates/dropJ_W512p_J02.json.gz | eeab8c3e6e05a631 | 116371 bytes |
| lattice/floor_certificates/dropJ_W512p_J03.json.gz | 26ee5f32f77d0346 | 122037 bytes |
| lattice/floor_certificates/dropJ_W512p_J04.json.gz | aa76f8cb841418e5 | 130393 bytes |
| lattice/floor_certificates/dropJ_W512p_J05.json.gz | ab753f62a03029a4 | 123529 bytes |
| lattice/floor_certificates/dropJ_W512p_J06.json.gz | e561c909d228394b | 80347 bytes |
| lattice/floor_certificates/dropJ_W512p_J07.json.gz | b4ae9d54086af5cd | 80346 bytes |
| lattice/floor_certificates/dropJ_W512p_J08.json.gz | 9932b33a53db256b | 80345 bytes |
| lattice/floor_certificates/dropJ_W512p_J09.json.gz | f0e6dc83f90e9107 | 118271 bytes |
| lattice/floor_certificates/dropJ_W512p_J10.json.gz | 5fcf9bf1cbb2d540 | 80346 bytes |
| lattice/floor_certificates/dropJ_W512p_J11.json.gz | ed7436125cbcb7a1 | 80346 bytes |
| lattice/floor_certificates/dropJ_W512p_J12.json.gz | eaa77f6262545f25 | 129833 bytes |
| lattice/floor_certificates/dropJ_W512p_J13.json.gz | 3970a8a3802c5d1f | 80346 bytes |
| lattice/floor_certificates/dropJ_W512p_J14.json.gz | bfb5a8c90a7a5e7b | 80350 bytes |
| lattice/floor_certificates/dropJ_W512p_J15.json.gz | b8f68534e87227cf | 80356 bytes |
| lattice/floor_certificates/dropJ_W512p_J16.json.gz | ea03e3f72277ae54 | 80345 bytes |
| lattice/floor_certificates/dropJ_W512p_J17.json.gz | df4558c7ba766bdc | 80358 bytes |
| lattice/floor_certificates/dropJ_W512p_J18.json.gz | da867a5144f6c25b | 80345 bytes |
| lattice/floor_certificates/index.json | 6677323a61ceb566 | 17413 bytes |
| lattice/floor_certificates/local_solvability_156.json | cd87d5dcc5714f86 | 218144 bytes |
| lattice/floor_certificates/table3_C-1024.json | 65284d5843d767f5 | 19125 bytes |
| lattice/floor_certificates/table3_C-512k0.json | be860990f8d1a41a | 809868 bytes |
| lattice/floor_certificates/table3_C-512pk0.json | 7e60386aebd50d66 | 785798 bytes |
| lattice/floor_certificates/table3_C-512pu.json | ea536b1b4b49efc0 | 10315 bytes |
| lattice/floor_certificates/table3_C-512u.json | fc3d4e51552fac90 | 10453 bytes |
| lattice/genera54.json | be575e72bb9c1d0c | 531009 bytes |
| lattice/genera54.txt | 7e5f5840c4cc8b56 | 23180 bytes |
| lattice/rank19_lattices.json | cfa88bac15e621f8 | 50408 bytes |
| lattice/rank19_lattices.txt | 30c2e41095dd75c8 | 17836 bytes |
| lattice/rootfree_det160_224.json | ca477d393833dc3f | 164139 bytes |
| lattice/rootfree_det160_224.txt | baaaa4d7a05751a1 | 9957 bytes |
| lattice/verify_lattice.py | f70d64da8d558bd0 | 23240 bytes |

## Conventions

- JSON files carry a `description` field stating their conventions; integers are JSON integers, rationals and long
  decimals are strings ("p/q", "0.0172..."); matrices are lists of rows and act on column vectors unless a field says
  otherwise (the K3Groups generator `M_BH` acts on rows). The `.txt` files render the same numbers.
- Decimal strings ending in `...` or given with a radius are truncations or ball midpoints of certified values; the
  full strings are in the JSON files.
- "SM" refers to the Supplementary Material, whose sections, equations and tables are numbered S1, (S5.3), S12, etc.

## Not included

What these files do not settle: whether W = 0 (supersymmetry) at the charge-22 vacuum; the exact charge-24 equation
q(M) = 48 on the determinant-512 pairs (Eq. (39)), for which the certificates give the constraints of Theorem 3.5 but no
decision; the indefinite strata of intermediate rank on K3 x K3 beyond Theorems 3.1 and 3.4; on the Hulek-Verrill
slice, a vacuum of charge 1 at smooth points outside R, and the hypotheses of Proposition 4.1 (the cut from mu_lo on
a grid, the all-orders annihilation by L5); for the AdS vacuum 5-81-3213, an F-term certificate (the value is at a fixed
point and conditional on the source's flux convention). The theta-series certificates of SM Eq. (S5.13), the
period-transport code behind the Krawczyk certificates of Section 4, and the source archives listed in
`dkmm/manifests/` are not part of this folder.

Generated 2026-09-28T20:21:37Z.