All runs are single-process Python on the swarm box (32 vCPU, 115 GiB, shared), started at nice 10, with the 1-minute load average between 56 and 100 during the session (other workflows' Lean builds and numerics). Times below are wall-clock under that load, so they are upper estimates for an idle box.
Estimate written before the full run (2026-10-21, 17:40 box time)
Unit timings, from the exploratory runs of this session (same code paths, single process):
| unit | size | measured time |
|---|---|---|
| Davenport-Hasse by brute force, q = 7, n = 3, deg c <= 3 | 34,202 Gauss sums | 23 s |
| the same, q = 7, n = 6 | 85,505 | 73 s |
| the same, q = 13, n = 4, deg c <= 2 | 85,683 | 81 s |
| structural against brute-force Gauss sums, q = 7, n = 3 | 319,200 | 164 s |
| three routes to F(s, A, H) | 30,576 | 138 s |
| K against the product of local summands | 12,642 tuples | 48 s (3.8 ms per tuple) |
| probe triples of total degree at most 5, three representations | 13 triples | 300 s, slowest 210 s |
| n = 4 relations at q = 13 (C sums up to degree 5) | about 40 coefficients | over 40 minutes, not finished when stopped |
Estimate for the full run, by part (each part writes results_<part>.json when it ends, and steps 2 and 3 checkpoint every unit to results_<part>.partial.json, so a restart resumes after the last finished unit):
| part | estimate |
|---|---|
| step1 (sources formulas, q = 7, n = 3 brute force to degree 3) | 10 minutes |
| step2 (the probe and Lemma 7.1; K on about 130,000 tuples; three large triples) | 90 to 150 minutes |
| step3 (biquadratic theta at q = 13, degree-4 samples) | 60 to 120 minutes |
| ledger (prime classes to degree 6; two balanced probes) | 15 minutes |
| rival (210 characters; principal row to degree 3 in X and 1 in W) | 5 minutes |
The parts run as four concurrent single-process jobs, inside the cap of 8 processes, with MemAvailable above 90 GiB throughout (each job stays under 2 GiB).
Estimate written before the second session's runs (2026-10-21, 22:40 box time)
A second session resumed this hunt after the first stopped (nothing ran in the worktree for three hours). It added step2b (the remaining probe triples of total degree at most 6, through vectorized D_s = 0 routes) and crosscheck.py (the second implementation reproducing every exact number). Unit timings, from validation runs of this session under a load average of 50 to 110:
| unit | measured time |
|---|---|
| a D_s = 0 triple with D_A = 3, all five routes (direct, Poisson, Euler, and the two vectorized ones) | 1 s to 370 s (the slow routes dominate) |
| one PARI symbol table entry (resultant in GP) | about 10 microseconds |
| one PARI local coefficient by definition, small t | about 10 ms |
| one PARI F(s, A, H) by enumeration, deg T A = 3 | about 3 ms |
Estimates: step2b 30 to 60 minutes (the frequency sum of (0,0,5) dominates: about 13,000 indices A against 14,406 frequencies, one symbol table per A); crosscheck.py 60 to 120 minutes, dominated by the K check (164,591 tuples, 3 to 4 ms each on each side), the structural check (319,200 Gauss sums by enumeration) and the n = 4 coefficients of degree 4 (C sums over 371,293 moduli). Both checkpoint per unit (per triple, per item) and run as single processes at nice 10.
Manifests
Run manifests are appended below as each part ends.
id: ff_probe-2026-10-21-rival
hunt: ff_probe
started: 2026-10-21T17:40Z
finished: 2026-10-21T17:41Z
ran:
- .venv/bin/python hunts/ff_probe/ffprobe.py --part rival
outcome: 210 characters modulo T^3 scanned in 16 s; 66 rivals with zeros off the circle; the principal-row local identity fails for the rival first at X^2 and holds for chi to X^3 W
artifacts:
- hunts/ff_probe/results_rival.jsonThe next four manifests were written by the second session from the results files and their modification times (box clock); the first session ended before writing them.
id: ff_probe-2026-10-21-ledger
hunt: ff_probe
started: 2026-10-21T17:40Z
finished: 2026-10-21T17:55Z
ran:
- .venv/bin/python hunts/ff_probe/ffprobe.py --part ledger
outcome: 890 s; abs(F)^2 = 7 q_A in all 417 generic cases; the largest ratio to the template's bound is 7^(-1/2) over 63,870 nonzero cases; the principal correction stays within 0.199 of 1 on Re x = 7/8; the two balanced probe values agree in their direct and Euler representations
artifacts:
- hunts/ff_probe/results_ledger.jsonid: ff_probe-2026-10-21-step3
hunt: ff_probe
started: 2026-10-21T17:40Z
finished: 2026-10-21T18:01Z
ran:
- .venv/bin/python hunts/ff_probe/ffprobe.py --part step3
outcome: the n = 4 coefficients over F_13[T]; the final invocation resumed from a complete checkpoint, so the recorded 0.3 s is that invocation only; the census of the 2,028 squarefree cubics and the forced zeros of every component family are in S4.md
artifacts:
- hunts/ff_probe/results_step3.jsonid: ff_probe-2026-10-21-step1
hunt: ff_probe
started: 2026-10-21T17:59Z
finished: 2026-10-21T18:09Z
ran:
- .venv/bin/python hunts/ff_probe/ffprobe.py --part step1
outcome: 611 s; the cited formulas checked by brute force at q = 7, n = 3 (and n = 6, and q = 13, n = 4 where stated), with the corrections listed in SOURCES.md
artifacts:
- hunts/ff_probe/results_step1.jsonid: ff_probe-2026-10-21-step2
hunt: ff_probe
started: 2026-10-21T17:43Z
finished: 2026-10-21T18:26Z
ran:
- .venv/bin/python hunts/ff_probe/ffprobe.py --part step2
outcome: 2,582 s; the phase identities, F in three routes, C_p, the separation of K, Lemma 7.1 at 72 (prime, row) cases and the probe at 16 triples, all equal; the five triples on the selection-rule class are nonzero
artifacts:
- hunts/ff_probe/results_step2.jsonThe next manifest was written on 2026-10-26 by the resuming session, from results_step2b.json and its modification time (box clock); the second session of 2026-10-21 ended before writing it.
id: ff_probe-2026-10-21-step2b
hunt: ff_probe
started: 2026-10-21T22:24Z
finished: 2026-10-21T22:50Z
ran:
- .venv/bin/python hunts/ff_probe/ffprobe.py --part step2b
outcome: 1,612.5 s; the remaining probe triples of total degree at most 6 on the selection-rule class; nine have an empty frequency box and a zero direct sum; at the four D_s = 0 triples (0,0,5), (1,0,5), (3,0,5), (4,0,5) the direct, Poisson and Euler representations agree exactly, zero at the first two and nonzero at the last two
artifacts:
- hunts/ff_probe/results_step2b.jsonThe crosscheck run (2026-10-26, opened before launch)
Resumed by the owner's decision of 2026-10-26 and pre-approved by the coordinator as one single-process run. results_second.partial.json held 4 of 15 items (symbols, C_routes, F_routes, C_p) from 2026-10-21; crosscheck.py resumes after them. The estimate is the one above, 60 to 120 minutes on one process, which is under the coordinator's one-core-hour approval gate at its low end and was approved as written. At launch the 1-minute load average was 51 and MemAvailable 68 GiB.
id: ff_probe-2026-10-26-crosscheck
hunt: ff_probe
started: 2026-10-26T12:52Z
finished: 2026-10-26T16:02Z
ran:
- nice -n 10 .venv/bin/python hunts/ff_probe/crosscheck.py
- nice -n 10 .venv/bin/python hunts/ff_probe/crosscheck.py --item s4
outcome: resumed after the four items of 2026-10-21 (symbols, C_routes, F_routes, C_p, in results_second.partial.json); 10 items in 4,709 s (davenport_hasse 513.5, structural 519.1, pari_internal 38.0, rho0_relations 1,158.4, phase_identities 28.3, K 870.6, lemma 250.5, probe 977.2, ledger 331.7, rival 22.2, then s4 crashed at 15:14Z after about 50 min); the crash was a crosscheck.py bug (norm2 asked PARI for the degree of an exact zero, poldegree(0) = -oo), not a disagreement; fixed (test_norm2_of_zero) and s4 rerun alone from the checkpoint, 2,838.7 s, ending 16:02Z; all 15 items agree with the primary run (VERIFICATION.md section 2); about 3.2 core-hours of wall clock in all, against the 1 to 2 estimated, under a load average of 30 to 50; MemAvailable stayed above 65 GiB
artifacts:
- hunts/ff_probe/results_second.json