Bloch certificate environment

A model gets read-only access to Frank Wikström's published Bloch certificate verifier. It must reproduce two archived certificate values, reproduce the published near-branch target, and find an accepted decimal target within 1e-10 below the shipped near-branch cutoff. Reward comes from the archive's own Arb verifier, not an LLM judge.

This is a public seed environment from Zeta Lab Hunt #80. It is deliberately small: four public calibration rows, no hidden test claim, no Lean rung, and no 24-sector away replay. The full environment product is the method across multiple targets and graders, not this free sample.

Trust boundary

Archive: Zenodo 10.5281/zenodo.21975862, version 1.0.0, MIT.
SHA-256 pinned: bdaa1ff347043a00733ca40d5db46c5418810d1f4e5c472d0bcb9de48ef408e7.
The same downloaded bytes are hashed and extracted into a fresh temporary directory before every uncached verifier mode.
Model inputs are exact JSON decimal strings. They are never passed to a shell, path lookup, Python evaluation, or upstream program.
Near-target queries have a 24-call episode budget. That is enough for the advertised 1e-10 bisection and prevents runaway tool/audit output.
Upstream code runs in a subprocess with a 90-second timeout and a minimal environment. This is process isolation, not a hostile-code sandbox. The code is hash-pinned and trusted as the grader.
Oracle failures raise an environment error. They never become a zero reward.
Each score records mode, digest, verifier log, elapsed time, target, verdict, and the exact scope of the check.

Tasks

Task	Acceptance
`fine-reproduce`	Exact (C) gain printed by the fine fixed-radius certificate
`coarse-reproduce`	Exact (C) gain printed by the coarse fixed-radius certificate
`near-reproduce`	A shipped near-branch target from `0.0153` up to its strict cutoff
`near-branch-cutoff`	An accepted target within `1e-10` below the near-branch cutoff

The near tasks do not replay the 24 away sectors. Hunt #80 previously replayed all sectors at 0.0153040536. That result is evidence behind the task calibration, not a computation this lightweight environment pretends to rerun.

For check_near_target, use goal="published" on near-reproduce and goal="cutoff" on near-branch-cutoff. The tool and final reward share the same positivity check, lower floor, and strict upper cutoff.

Run

Install the published Hub version:

prime env install thomas-lince/bloch-certificate@latest
bloch-prepare
bloch-smoke
vf-eval bloch-certificate --model <provider/model> -n 4 -r 1

Or, from either this standalone source directory or the package directory in the Zeta Lab repository:

python3.12 -m venv .venv
.venv/bin/pip install -e .
.venv/bin/bloch-prepare
.venv/bin/bloch-smoke
.venv/bin/vf-eval bloch-certificate --model <provider/model> -n 4 -r 1

bloch-prepare downloads once into ~/.cache/bloch-certificate/ and verifies the digest. load_environment() also prepares a missing default archive. bloch-smoke runs four positive and four negative controls without a model. Python 3.12 is intentionally required because that is the interpreter pinned by the upstream archive and exercised by this package's CI. Support is not claimed for an interpreter the certificate has not been replayed under.

What the evidence means

The fixed-radius rows check the finite certificate arithmetic. The near rows check the shipped near branch. They do not audit Bonk's theorem, the moment inequality, the three-atom reduction, or the centre-placement lemma. Acceptance is not by itself a theorem about Bloch's constant.

Sources: the upstream archive, its paper arXiv:2608.17660, and Zeta Lab's hunts/bloch_ceiling/RESULTS.md.