Hunt r_f7cd45: which structural properties of ζ actually discriminate

Publishes the artifact queued by issue #21 (https://github.com/teal-sea/zeta-lab/issues/21): a partial computation established that three commonly-cited structural properties of ζ are satisfied by every RH-violating look-alike in zeta.epstein.battery, and it was recorded as an observation without the probe, the data or the writeup. This hunt runs it end to end and lands those three files.

The question

For each of six claimed structural properties of ζ, does the property distinguish ζ from functions that share its analytic structure and violate RH? Gate #3 of docs/09-new-ontologies.md: a property the Davenport–Heilbronn function and the discriminant −23 Epstein zetas also satisfy cannot be the load-bearing step of an RH proof, because it is ungrantable to nothing.

Five of the six were reported in issue #21. The sixth, "in a box strictly off the critical line the completed function has no zeros", ran to a 50-minute timeout there and is the open part.

Scope

• Writes only inside hunts/r_f7cd45/, plus one case-log line in hunts/README.md.
• Nothing here is evidence for or against RH (docs/08-why-it-is-hard.md). The subject is which properties discriminate, not where the zeros are.
• Gate #3 is eliminative, never probative. "Distinguishes" means "not yet eliminated", not "proves anything".

Preregistration for the sixth property

Issue #21 warns that the box parameters must be chosen before any truth value is seen, because choosing after is choosing the answer. These were fixed, and this file committed, before the first box was counted.

The property "the completed function has no zeros in box B" is not scale-free: its verdict is a function of B. A single box would let the choice of B decide the gate verdict, so two boxes are run and both are reported:

The real extent is issue #21's, unchanged. Only the imaginary extent is narrowed, 10 → 1, and the working precision is dropped to dps = 15. Both changes are the ones issue #21 names ("narrow the box or lower dps"). Cost drove the size: one epstein_completed evaluation was measured at ~1.0 s before the boxes were chosen, and the issue's 10-unit box needs of order 10³ of them per rival.

The wall-clock cap is 600 s per (function, box). A box that exceeds it is reported as timeout, not guessed.

id: r_f7cd45
question: For each of six claimed structural properties of zeta, does the property distinguish zeta from the RH-violating look-alikes of gate #3, or is it shared with them?
frontier: five properties reported unpublished in issue #21 (3 vacuous, 2 discriminating); the sixth, a box zero count over Re in [0.6,0.9] Im in [80,90], unfinished at a 50-minute timeout
proposed_attack: run all six through zeta.epstein.battery against Davenport-Heilbronn and both discriminant -23 Epstein forms, with the sixth narrowed to two preregistered unit-height boxes at dps 15
dead_routes:
  - the sixth property at Im in [80,90] and default precision - it exhausted 50 minutes without finishing in issue #21
  - reading a passing property as evidence about RH - gate #3 is eliminative, never probative (docs/09 section 5.1)
required_oracles:
  - argument-principle winding number over the box boundary, required to come out an integer to within 1e-6
  - exact integer representation counts of the binary quadratic forms
  - the published Davenport-Heilbronn off-line zero 0.8085171824566373855 + 85.6993484853775921719i, pinned in zeta/epstein.py against its literature digits
  - sign changes of the real Hardy-style Z on the critical line
kill_conditions:
  - a winding number fails to be an integer to 1e-6, making that box count ill-posed
  - the property verdict for a rival flips under a change of box, precision or tolerance that was not preregistered
  - zeta itself fails a property it is supposed to have, indicating a defect in the probe rather than a result
agents_may:
  - run the battery and record its verdicts
  - narrow the sixth property's box within the preregistered parameters
  - report a property as unsettled at this cost
agents_may_not:
  - choose box parameters after seeing a truth value
  - read a vacuous verdict as evidence for or against RH
  - claim the reserved word that belongs to zeta/rigor.py and the Lean arm
  - widen the gate verdict beyond the four functions actually run

Kill conditions, in prose

Stop and report if the winding number is not an integer (a zero on the contour makes the count ill-posed), if ζ fails a property it demonstrably has (the probe is wrong, not the mathematics), or if the sixth property exceeds 600 s per box per function. "Not settled at this cost" is the result in that case.