euler_defect_axis: run manifests

id: euler_defect_axis-2026-09-09-entitlement
hunt: euler_defect_axis
started: 2026-09-09T23:00-05:00
finished: 2026-09-10T00:10-05:00
ran:
  - .venv/bin/python hunts/euler_defect_axis/probe.py
outcome: a(1) is exactly 1 on the 14 principal forms and exactly 0 on the other 27; the identity residual is machine zero on the entitled rows and bounded away from zero on the rest, worst 189.6888; no non-principal form represents only multiples of its least represented value; the class-number-one control c(n) = Lambda(n)(1 + chi_d(n)) agrees with the recursion to 2.8e-30
artifacts:
  - hunts/euler_defect_axis/artifacts/axis.json

id: euler_defect_axis-2026-09-10-audit
hunt: euler_defect_axis
started: 2026-09-10T00:20-05:00
finished: 2026-09-10T00:35-05:00
ran:
  - an independent adversarial audit by a separate agent, given the write-up and the repository and told to break the claim rather than review it
  - .venv/bin/python -c "recount the forms, check R against |1 - a(1)| max|c|, check the 1 + Z_Q reading, re-measure the axis at cutoffs 61, 121, 201, 401"
outcome: verdict survives-with-corrections after eight attacks; eleven overclaims found in the write-up; the three carrying numbers recomputed here before the corrections were accepted (41 forms not 44, R = |1 - a(1)| max|c(n)| to 0.0 on 40 of 41 rows, the published non-principal numbers are the composite defect of 1 + Z_Q(s) to 0.0 on all 27); the axis has no scale, the band running 2.9608-5.0847 at cutoff 61 and 5.0196-10.5748 at cutoff 401 with the ordering unchanged
artifacts:
  - hunts/euler_defect_axis/AUDIT.md
  - hunts/euler_defect_axis/artifacts/cutoff.json
  - hunts/euler_defect_axis/RESULTS.md
  - hunts/euler_defect_axis/PROPOSAL.md

Notes

• The audit is the reason this hunt's write-up changed, and the claim did not. It ran with the repository in front of it and no part in producing the result. It attacked a(1) from the definition rather than from the artifact, derived the identity from -f'/f itself, checked the Kronecker symbol against an independent implementation, and searched by least squares for any integer-indexed c solving the identity for a non-principal form (residual 2.18 to 5.79, so none exists). Nothing moved the claim. Eleven sentences moved.
• The corrected axis is not this hunt's own reading of the family. It is the smallest statement the entitled rows support, and the audit's cutoff sweep is the reason it is stated as an ordering rather than as a range.

id: euler_defect_axis-2026-09-10-ordering
hunt: euler_defect_axis
started: 2026-09-10T04:05-05:00
finished: 2026-09-10T04:10-05:00
ran:
  - .venv/bin/python hunts/euler_defect_axis/ordering.py
outcome: the ordering claim in RESULTS.md section 5 was false and is corrected; the nine discriminants do NOT rank identically at cutoff 61 and 401, -23 and -24 transpose; six of nine positions are fixed at every cutoff and all movement is inside the -20/-23/-24 block; Spearman against cutoff 61 is 0.9500 at 121 and 0.9833 at 201 and 401; the ordering settles by 201, where 201 and 401 agree at rho = 1.0000
artifacts:
  - hunts/euler_defect_axis/ordering.py
  - hunts/euler_defect_axis/artifacts/ordering.json

• Correction, 2026-09-10. The outcome: line of the audit manifest above, and five sentences derived from it, said the axis runs from one band to another "with the ordering unchanged". That is false. The manifest is left as recorded because it is the record of what that run reported; ordering.py and the manifest directly above this note are the correction, and the five sentences are fixed in place in RESULTS.md, PROPOSAL.md and hunts/README.md.

Two things about how it got in are worth more than the number itself. The claim entered during the rewrite the audit prompted, which means it was written after the adversary had finished and was never attacked by anything. An audit fixes the sentences it read; it does not cover the ones its own findings cause you to write. And the false version was the stronger and tidier claim, "exactly the same order" against "six of nine positions hold", which is the direction a summary drifts when nobody is checking. The true statement is also the more useful one: the tail of the list is rigid, the head is not, and the quantity needs a couple of hundred composites before it orders anything reliably.

• Renumbered #119 to #124, 2026-09-16. main landed lambda_dh_exact as Hunt #119 on 2026-09-10, the same day this hunt took #119 from a base that was by then 130 commits behind. The landed number wins and this one moved. tests/test_hunt_numbering.py exists on main and is the right guard, and it structurally cannot catch this: it checks that the numbers printed in one copy of the case log are unique, and both copies were internally consistent. The collision existed only in their union, which nothing reads until a merge. Its own docstring already records the same failure twice, once from "a session working from a branch 101 commits behind". This is the third instance.

Worth the contrast: the docs/ numbers this branch took the same day, 37 through 40, did not collide, because scripts/science_preflight.py reports the next free doc number rather than validating the file you already have. A guard that computes the next free value survives a stale base. A guard that checks the current file for internal consistency does not.

id: euler_defect_axis-2026-10-10-landing
hunt: euler_defect_axis
started: 2026-10-10T12:55+00:00
finished: 2026-10-10T13:55+00:00
ran:
  - .venv/bin/python hunts/euler_defect_axis/probe.py
  - .venv/bin/python hunts/euler_defect_axis/ordering.py
  - .venv/bin/python -m pytest -q hunts/euler_defect_axis
outcome: axis.json and ordering.json reproduce byte for byte; cutoff.json, which had no script behind it, reproduces to the last bit from the principal forms at cutoffs 61, 121, 201 and 401; every number RESULTS.md and docs/40 state is pinned by test_euler_defect_axis.py (23 tests, about 8 s) except one count, "0.0 exactly on 40 rows and 1.6e-30 on the remaining one" in RESULTS.md section 2, which does not reproduce (0.0 on 33 rows, R itself between 7.9e-31 and 3.2e-30 on 8 principal rows) and is marked there; the permutation p = 0.113 is a Monte Carlo estimate of the exact 0.1124; docs/40 section 3 still carried the false sentence "the ordering is identical at both cutoffs" and is corrected in place with the original quoted
artifacts:
  - hunts/euler_defect_axis/test_euler_defect_axis.py
  - hunts/euler_defect_axis/RESULTS.md
  - hunts/euler_defect_axis/PROPOSAL.md
  - docs/40-one-form-per-discriminant.md

• Landed on main and renumbered #124 to #127, 2026-10-10. By the time this directory reached main, #124 there was qrh_class_number and #125 and #126 were taken as well, so it takes the next free number above every heading in the case log. The front door, numbered 38 on the branch, is docs/40: main had meanwhile used 37 for the methods index, 38 for the quasi-Riemann claim and 39 for the results built on it. The issue #93 comment of 2026-09-10 still calls it hunt #119 with its front door at number 38, and is left as written.

That corrects the contrast the note above draws. The doc numbers this branch took on 2026-09-10 did not collide that day, because the preflight reported the next free number; they collided later, when main took 37 to 39 while the branch sat unmerged. A guard that computes the next free value is right at the moment it runs and says nothing about a merge weeks later. Both numbers are labels, and the directory name is the stable reference.

• The repair landed before the hunt did. #296 applied PROPOSAL.md to docs/34, the zeta_temperament probe and its test on 2026-10-10; PROPOSAL.md's closing note records what it did differently.