A bounded measurement run, opened 2026-08-14 by the operator. One number, at two precisions, plus the sweep needed to read those two numbers against a scale.
Why this hunt exists
zeta/epstein.py builds the rival interfaces that zeta.epstein.battery compares against ζ. Two of the entries in epstein_interface clamp the precision they were handed:
"zeros_on_line": Z_epstein(t, _f, dps=min(_d, 15)) # line 1073
"count_zeros_box": count_zeros_box(..., dps=min(_d, 20),
fn=lambda z: epstein_completed(z, _f, dps=min(_d, 20)))
# line 1092The clamps are a speed decision, and the question this hunt answers is what they buy and what they cost, on one concrete value rather than in principle.
The value chosen is abs(epstein_completed(0.8 + 85.7i, (2, 1, 3))). It is a fair stress point rather than a hostile one: count_zeros_box is an argument-principle contour integral, so it evaluates epstein_completed at whatever height its box reaches, and t = 85.7 is an ordinary height for a zero-counting box. The archimedean factor Gamma(s) decays like e^{-pi t / 2} there, which puts the true magnitude far below anything a 20-digit evaluation of a cancelling lattice sum can resolve.
Scope
This hunt measures. It does not change zeta/epstein.py, does not file the result as a defect, and does not decide whether the clamps should be raised: count_zeros_box only needs the sign of the winding, and whether the noise this hunt measures can flip that sign is a separate question this run did not ask. See README.md for what was and was not established.
id: dps_cap
question: What does the min(dps, 20) precision clamp in zeta/epstein.py's rival interfaces cost, measured on one value of the completed Epstein zeta at an ordinary zero-counting height?
frontier: at dps = 60 the value is 1.6174526323779715e-58; the clamped path evaluates the same object at dps = 20, where the routine returns 3.1063191101762651e-33
proposed_attack: evaluate the same point across a precision sweep and locate the precision below which no digit of the answer is correct
dead_routes:
- reading a small returned magnitude as a zero of Lambda_Q without first checking it against the routine's precision floor at that height
required_oracles:
- re-evaluation of the same quantity at higher working precision, converged when two adjacent precisions agree
- the archimedean envelope abs((sqrt(d)/pi)^s Gamma(s)) computed independently of the lattice sum, as a size bound the answer must respect
- an outside independent recomputation of the same number
kill_conditions:
- the dps = 20 and dps = 60 magnitudes agree to within an order of magnitude, so the clamp costs nothing at this point
- the dps = 60 value moves under further precision, so it is not the converged answer either
- the outside recomputation disagrees with the dps = 60 value by more than an order of magnitude
agents_may:
- measure
- sweep precision
- record raw magnitudes and timings
agents_may_not:
- edit zeta/epstein.py or any other file outside this directory
- promote this measurement into a defect report or a battery change
- declare novelty
- declare theorem statusid: dps_cap-2026-08-14-bounded-run
hunt: dps_cap
started: 2026-08-14T00:00-05:00
finished: 2026-08-14T00:00-05:00
ran:
- .venv/bin/python hunts/dps_cap/probe.py
outcome: the clamped precision returns 3.1e-33 where the converged value is 1.6e-58, a factor of 1.9e25 and no correct digit; dps = 30 returns exactly zero at the same point
artifacts:
- hunts/dps_cap/results.json
- hunts/dps_cap/README.md