All on the operator's 16 GB Mac, .venv/bin/python, HiGHS through scipy.optimize.linprog. Solve time grows like about X^2.7 in the truncation; the strip adds a few dozen rows and roughly doubles the cost at the wide rungs.
2026-09-05 to 06, first session
dual.py:
| grid | case | seconds |
|---|---|---|
| X=40, J=200 | control / strip 1.5 / strip 3.0 | 0.2 / 0.6 / 9.9 |
| X=80, J=320 | control / strip 1.5 | 1.0 / 4.3 |
| X=80, J=320 | strip 1.05 | about 1.5 |
Fine sweep at X=80, J=320, eight strip edges from 1.02 to 1.5: 1 to 4 s each.
ladder.py, 18 solves, checkpointed to artifacts/ladder-narrow-strip.json:
| X | J | control | width 0.05 | width 0.10 | width 0.20 |
|---|---|---|---|---|---|
| 40 | 200 | 0.2 s | 0.2 | 0.2 | 0.3 |
| 80 | 320 | 0.9 | 1.5 | 1.6 | 2.4 |
| 120 | 480 | 3.6 | 6.3 | 8.3 | 7.9 |
| 160 | 640 | 8.9 | 16.5 | 16.9 | 22.0 |
| 240 | 960 | 61.0 | 118.0 | 92.6 | not run |
| 320 | 1280 | 133.4 | 255.3 | 417.8 | not run |
Every control value matches hunt #110's artifacts where the rungs coincide (X = 40, 80, 240, 320). The X = 320 strip solves are the only ones that took longer than the session's foreground limit and finished in the background.
2026-09-06, second pass
Lattice ladder at X = 80, J = 320, strip 1.5: h = 1/16 (1 s / 3 s), 1/32 (2 s / 9 s), 1/64 (5 s / 15 s), and h = 1/32 at X = 160, J = 640 (33 s / 87 s): in-band 0.6749570, strip 0.6830328, gain +0.00808.
signed_window.py: L-BFGS-B over an even profile on [-S, S], ten starts, penalty on the strip sign condition. Control on [-1/2, 1/2] at step 0.005 lands at J = 1.32845 (Theorem D 1.32750): the Riemann-sum convolution misreads the window's edge discontinuity by about 1e-3, and the optimiser compensates with a spurious negative edge. Every strip start was rejected on the sign condition; the edge lemma in RESULTS.md section 5 says why. Kept as the record of the attempt, not as an instrument.
Counterexample check: K = sinc^2(x)(1 - c cos 4 pi x) on [-2000, 2000] at step 1e-3, FFT: min K = 0 (c = 1) and 5e-33 (c = 0.5); max Khat on 1 < |alpha| < 3.05 is 1.5e-6 and 7.4e-7; min Khat there -0.5 and -0.25; nothing beyond 3.05 above 6e-11.
Large-X lattice ladder, strip 1.5, planned as (1/16, X = 160), (1/64, 160), (1/16, 320), (1/32, 320), each in-band and strip. Landed: (1/16, 160): in-band 0.6764627 (14 s), strip 0.6833922 (123 s), gain +0.00693; with the earlier (1/32, 160) row, gain +0.00808. The run was killed by the operating system for memory on the (1/64, 160) rung (10,240 variables, dense constraint matrix, beside the rest of a 16 GB machine's load). The (1/16, 320) and (1/32, 320) rows are not run. They are plain scipy and belong on Modal, which is wired; not launched here because it spends the operator's Modal budget.
2026-10-10, replay of the cheap rows (issue #240)
The sessions above predate this hunt's manifests. They were not re-run in full here, and no manifest is back-filled for them from their prose: a block written from prose would look pinned and would not be. The block below records only what was re-run on 2026-10-10, on a shared four-core Linux container (scipy 1.18.1, numpy 2.5.3), not a laptop.
- Re-solved by
replay.py, which writes nothing: every row ofartifacts/ladder-narrow-strip.jsonat X <= 160, sixteen rows. Thirteen agree to within 2e-13; the three X = 160 strip rows agree to within 1.4e-8, inside HiGHS's tolerances (../outband_intake/RUNS.md, same date, sizes the solver's own spread). Every re-solved row rounds to the same seven decimals as its artifact value. - Reproduced from the artifact, not from re-solves:
pinned.pyprints the three width rows of the section 3 narrow-strip table in RESULTS.md (gains per rung, pinned-exponent limits, the control's fitted excess and the limit-to-error ratios) digit for digit. - Not re-run, so still unpinned: the X = 240 and X = 320 ladder rows (61 s to 418 s each, about a quarter of an hour together), the lattice ladders of the second pass,
dual.py,signed_window.pyand the counterexample check. Those rest on the original artifacts and the prose above.
id: outband_certificate-2026-10-10-replay
hunt: outband_certificate
started: 2026-10-10T01:32Z
finished: 2026-10-10T01:35Z
ran:
- .venv/bin/python hunts/outband_certificate/replay.py
- .venv/bin/python hunts/outband_certificate/pinned.py
outcome: all 16 narrow-strip rows at X <= 160 re-solved, 13 to within 2e-13 and the three X = 160 strip rows to within 1.4e-8, and pinned.py reproduces the section 3 table from the artifact; the X = 240 and 320 rows, the lattice ladders, dual.py and signed_window.py were not re-run and stay unpinned
artifacts:
- hunts/outband_certificate/replay.py