Ancillary files (code) for "On the maximality conjecture for quantum permutation groups" (Claude and Teo), state of 31 October 2026.
In this upload: the output files written by the scripts (<name>out.txt, nineout/progress_*.txt, ...) are gathered in
logs.log, one section per file, and this README is README.log.  Running a script writes its own log file again.
Python 3 with numpy and scipy.  Each script explains its usage in its first lines (run it without arguments, or with
"test", to see it).  Every script writes a log file next to itself (<name>out.txt, or an output folder).  File names
carry no digits; numbers inside generated file names are written in unary ("x" * k) or in words.

Section 2     duals.py        Proposition 2.x (11 actions, Catalan through k = 8), class (c) actions at N = 6
Section 3     duals.py        (also the magic square at k = 4, 5)
              sol.py          magic square (k <= 8), A_7 system (no laws of length <= 8)
              doubling.py     repetition lemma, Catalan for m = 2, 3 and k <= 7 (exact)
Section 4     twists.py       cocycle twists of S_N and of its subgroups (Propositions 4.x, Remark 4.x)
              twistpu.py      the twists PU_n^sigma (Proposition 4.x)
Section 5     hadamard.py     joint dimensions and the Dita scan (fast); the wildness numbers lambda_k (wild, paley)
Section 6     exotic.py       finite exotic case: Hankel determinants and index bounds, d_k, multiplicities f_j
Sections 7-9  levels/         the uniform-in-N chain, levels 5 to 8 (server side); see levels/README.txt:
                              level 5 (level5.py), level 6 (step1sym, levquadrics, elim, design, cert, closex, locus, ...),
                              level 7 (stepone, stepone_rec, select, exactrows, dmod, runprimes, crt, dfinal, nsix),
                              level 8 exploration at N = 11 (modforms, cubic, tripbatch, ...), with the helpers
                              levlin.py, levquad.py, levnull.py, hm.py, levquadrics.py
              levelseven/     the laptop half of the level-7 determinant (lapjob.py, job.json, the result files)
              halfturn/       Theorem 9.x (half-turn), one N at a time (run.py, job.py, engine.py, triple.py)
              leveleight/     level-8 triple contractions by rotation sector (laptops)
              tyson.py        closing level 8 for 8 <= N <= 37 (Proposition 9.x), level-9 first steps (Proposition 9.x)
              kitty.py        level-9 slices, first attack (Proposition 9.x)
              tiger.py        level-9 slices, second attack (the remark after Proposition 9.x)
              positivity.py   Subsection 9.6, positivity certificates at level 8, N = 11 (needs realbasis.py and
                              realforms.py from levels/ for the real kernel and the real quadrics)
              ninekernel.py, nineforms.py, ninepositivity.py, nine.py (with engine.py): the same at level 9, by rotation
                              characters, at the values of N listed in nine.py
Section 10    orthoduals.py   Proposition 10.x: group duals easy over O_N (31, 305, 595, 2339, 917 law sets)
              words.py        Theorem 10.x: exotic words of Z_2 * Z_2 * Z_2 up to length 20 (python3 words.py 20 two, ~4 h):
                              one rotation relation kills every word up to length 18; at length 20, 240 words beginning
                              with a need two steps, all killed (list in wordsleft.txt)
              orthotwists.py  Section 10.6: sign twists O_N^eps (all graphs, N = 3, 4, 5) and theta-twists (N = 4, 6)
Section 11    pairlevels.py   levels 6 (Brauer closure, Proposition 11.x), 8 (Proposition 11.x, the formulas for h_+-)
                              and 10 (Theorem 11.x, blocks 4 + 1 + 8 and certificates at each N), exact rational arithmetic
              evander.py      numerical certificates: HL, Brauer and projective versions, levels 6 to 14, queues a, b, c
Section 12    projective.py   unitary group duals (law sets at N = 3, 4; <PO_N, PG>), and the older U_4^2 and
                              <O_N^{-1}, H_N^+> checks (no longer in the paper)
              projlevels.py   the projective level method: level 6 exact (six), the rho^2-category generated by
                              xi_kappa (gen, through level 12: python3 projlevels.py gen 12, about 17 min per N, laptop log
                              projlevelsout.txt), the certificate table of Subsection 12.4 (table; log projlevelstable.txt)
              projeight.py    Proposition 12.x (level 8, half-liberated, exact): the cross term h_{+-}(N) = 0
              projtencert.py  the half-liberated level 10, exact for all N >= 5 (table of Subsection 12.4, Theorem 12.x(1)):
                              Z[N] basis of the merged block, the c(N) of Proposition 11.x(3), minors positive in N - 7,
                              integer certificates at N = 5, 6 (log projtencertout.txt)
              evander.py      families PR (Brauer, rho^2 blocks) and PH (half-liberated, rho^2 blocks):
                              python3 evander.py item PR m N  /  python3 evander.py item PH m N
Not in paper  freeness.py     the level method for the (false) freeness conjecture, orthogonal case: envelopes D,
                              D-uncappable spaces, certificates; it found the counterexample S_N^+ x Z_2 with the sign
                              on xi^perp (level 4, envelope NC_{1,2}).  Kept for a future project.

Conventions
- Exact ranks are computed modulo primes p < 2^20 after a random compression (rows R C mod p, float64 products, exact
  below 2^53); the rank can only drop, so a Catalan output is a proof.  Gram-matrix ranks modulo two large primes are
  used where the entries are small integers.
- Primes: 1048573 (duals, sol, doubling, tyson, kitty, tiger), 1048261 = 1 mod 60 (twists, twistpu), 1048433 = 1 mod 8
  (level 8), 2147483647 and 1000000007 (Gram ranks).
- Laptop jobs (tyson, kitty, tiger, evander, nine) run 7-8 hours, stop by themselves and are resumable.
- The level-7 and level-8 data files produced on the laptops (levelseven/resulta.json, halfturn and leveleight results,
  tysonout, tigerout) are kept as they were produced; the big .npz working files are regenerated by the scripts.

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Appendix: levels/README (the map of the folder levels/)
====================================================================================================
Sections 7-9: the uniform-in-N chain (levels 5 to 8), server side.  Python 3, numpy, scipy; exact rational and modular
arithmetic.  Generated file names use the level in unary ("x" * k), e.g. stepone_xxxxxxx.pkl: no digits in file names.
Helpers: levlin.py (partitions, leg-sums, merges), levquad.py / levquadrics.py (level-6 kernel and ribbon contractions,
exact), levnull.py (exact nullspace), hm.py (partition vectors), poly.py (polynomials in N over Q), ribbon.py and
engine.py (ribbon contractions, modular), triple8.py / triple.py (triple contractions).

Level 5     level5.py          K_5(N) = 0: det M_5(N) = -(N-4)(N^2-3N+1)^2
Level 6     step1sym.py        the kernel K_6(N) with N symbolic (5 polynomial vectors, the 66 x 66 minor)
            levquadrics.py N   the 792 quadrics at integer N, exact (quad_N{N}.pkl)
            elim.py N          Hilbert function, Gotzmann, characteristic polynomial (the 4 points)
            irr.py N           irreducibility of the characteristic polynomial
            design.py, step2sel.py, cert.py     the certificates (C2) finiteness and (C3) closure, N symbolic
            closex.py N        closure in the quartic field (the 4 Galois-conjugate lines)
            locus.py, locustwo.py, runtwo.py, pade.py, padeq.py, roots.py, zeroset.py   the survival locus {0, 2, 5}
            triple6.py         triple contractions at level 6, N = 11
Level 7     stepone.py 7, stepone_rec.py 7     the kernel K_7(N), N symbolic (14 vectors, denominator delta(N))
            select.py, exactrows.py            the 105 quadric rows, as polynomials in N
            dmod.py, runprimes.py, mkjob.py    the determinant D_7(N) and Delta_7(N) modulo primes (laptop job in ../levelseven)
            crt.py, dfinal.py                  Chinese remaindering with the Hadamard bound, integer roots
            nsix.py, nsixexact.py              the case N = 6, modulo the Moebius relation
Level 8     testengine.py, dimk.py, dimk8.py   dim K_8 = 66
            modforms.py, realbasis.py, realforms.py    the quadric span (1154 of 2211), modular and real
            cubic.py, cubicplus.py, prep.py, tripbatch.py, batchlap.py, subsearch.py   degree-3 tests by rotation character
            halfturn.py, halfseven.py          the half-turn theorem (see also ../halfturn for the laptop version)
            ncpartner.py                       the redundancy of the noncrossing-partner constraints (Remark 7.x)