Agent Persona: The Hunter (unsupervised-fun edition) Scope: hunts/lehmer_pair/ only. Nothing outside this directory is modified except the case-log entry in hunts/README.md.
Objective
Lehmer's phenomenon is the place RH came closest to being false below height 10⁴: γ₆₇₀₉ ≈ 7005.0629 and γ₆₇₁₀ ≈ 7005.1006 sit 0.0377 apart, 24× tighter than the local mean spacing, and between them Hardy's Z(t) climbs to only ≈ +0.004 before diving back. Had that bump failed to cross zero, two zeros would have left the critical line.
The repo has recomputed the pair with floats (docs/05) but has never pointed the ball-arithmetic arm at it. The hunt asks one question:
Do the enclosures of
zeta.rigordecide, on both backends, that the near-miss is real, that the bump genuinely clears zero, and how much precision does the closest call actually cost?
Instruments
probe.py, which runs five experiments and writes results.json + lehmer_zoom.png. The only rigor-layer entry points used are rigor.proven_sign and rigor.enclose_Z; the grid scans are built on those two so the probe owns its grid and its undecided-point accounting. The strongest word this hunt uses is decided: an enclosure [lo, hi] came back with lo > 0 or hi < 0, an exact comparison on exact endpoints. The reserved word for that regime belongs to zeta/rigor.py and appears nowhere in this directory, the case log names it.
- Three-point sign pattern: sign of Z at exact rationals flanking and inside the pair, both backends. Pattern −,+,− brackets ≥ 2 line zeros.
- Dense window scan: sign changes on [7004.9, 7005.3] with a grid ~7× finer than the pair, both backends; the window contains no other zeros (γ₆₇₀₈ = 7004.04, γ₆₇₁₁ = 7006.74).
- Lesion: the default grid policy, the default scan step at this height is mean_spacing/20 ≈ 0.045, wider than the whole Lehmer gap. Sweep the window phase and measure how often that grid sees the pair at all.
- Precision response: enclosure width of Z at the bump vs prec_bits, both backends; and the decision cost (bits needed to settle a sign) as the probe point slides toward γ₆₇₀₉ at distances 10⁻³ … 10⁻¹².
- Rival (gate #1): Davenport–Heilbronn owns the failed version of this bump: near its off-line zero 0.8085 + 85.6993i, Z_dh approaches zero and never crosses (2 strip zeros, 0 line crossings, pinned by
tests/test_epstein.py). Measure the closest approach so the two bumps can be shown side by side. This is the check that "a small bump" alone distinguishes nothing; what distinguishes is crossing.
Rules of engagement
Repo-wide rules apply (.venv python, mp.workdps, Agg before pyplot, honest scope). Nothing here is evidence for RH; the deliverable is sign facts at named rationals decided by enclosure, plus measured instrument behaviour. The Davenport–Heilbronn scan is the float regime, accurate, a weaker claim, and labelled as such.