Research disposition: unresolved. No resolution of RH, no novelty assertion, and no outside mathematical review. The proof text is an ordinary derivation with named classical dependencies. Numerical and exact checks are separate.
Environment: Python 3.14.0, mpmath 1.3.0, SymPy 1.14.0, python-flint 0.9.0. The repository backend check reported python-flint and both installed backends, python-flint and mpmath.iv. This hunt's Arb computation uses only python-flint; it is not the repository's two-backend cross-check.
Observed results
- Two numerical runs, at 50 and 80 decimal digits, each compare 8 moments from central derivatives and theta quadrature and 8 matrix determinants. All 8/8 determinants are positive in each route and precision.
- Maximum relative moment differences: 4.61716e-48 and 4.72664e-78.
- Two Arb runs, at 256 and 384 bits: 8/8 strictly positive determinant enclosures each. Serialized bounds were checked, and a separate Arb matrix-determinant algorithm recomputed signs from saved moment intervals.
- The independent symbolic/rational checker passes one symbolic identity, three negative determinant witnesses, and eight positive determinants for a function with explicitly known off-axis zeros. Its checks also compare both floating-point routes with the Arb results.
- Hunt/document checks: 29 passed, 5 slow tests deselected. Generated context is current. Python compilation and git whitespace checks passed.
- A separately invoked doors run included slow tests: 26 passed, one failed. The failure was the existing bloch evaluation smoke command exceeding its 180-second timeout. The learn and refute commands passed. No code in that environment or in those tests was changed. This is not an all-green suite.
The broad fast suite was launched in the original shared checkout at fd04f1fa, before this hunt's edits: 2990 passed, 3 failed, 56 skipped, 6 expected failures, in 1022.65 seconds. The failures were a stale dated HardyZ proof observation, a missing case-log entry for jensen_newton, and a reserved-word occurrence in rh_resolve/MISSION.md. The latter two hunt paths were not in this session's initial status and are not this hunt's files; the shared checkout was not a stable isolated baseline. No files in those hunts or the HardyZ dossier were edited by this attempt. The research worktree starts from the newer origin/main 783307c8; the broad run is not a full-suite validation of this worktree. The 29 focused checks above were run in the isolated research worktree and passed. The single HardyZ staleness test was then rerun in the isolated worktree: it also fails there, comparing the recorded 2026-08-13 observation with a 2026-09-28 file-change date. This is a pre-existing failing check outside the changed files, not a result to suppress or repair within this hunt.
Reproduce
.venv/bin/python hunts/central_moments/probe.py .venv/bin/python hunts/central_moments/ball_check.py .venv/bin/python hunts/central_moments/check_exact.py .venv/bin/python -m pytest -q -o addopts='' -m 'not slow' tests/test_huntspec.py tests/test_docs_numbering.py tests/test_doors.py tests/test_hunt_probe_discipline.py .venv/bin/python scripts/make_context.py --check
id: central_moments-2026-10-02-checkpoint1
hunt: central_moments
started: 2026-10-02, local calendar date; exact start time not recorded
finished: 2026-10-02, local calendar date
ran:
- .venv/bin/python hunts/central_moments/probe.py
- .venv/bin/python hunts/central_moments/ball_check.py
- .venv/bin/python hunts/central_moments/check_exact.py
- .venv/bin/python -m pytest -q -o addopts='' -m 'not slow' tests/test_huntspec.py tests/test_docs_numbering.py tests/test_doors.py tests/test_hunt_probe_discipline.py
- .venv/bin/python scripts/make_context.py --check
outcome: RH unresolved; eight finite positive matrix enclosures and exact counterexamples to generic positivity transfer preserved
artifacts:
- hunts/central_moments/MISSION.md
- hunts/central_moments/RESULTS.md
- hunts/central_moments/probe.py
- hunts/central_moments/results.json
- hunts/central_moments/control_extension.json
- hunts/central_moments/ball_check.py
- hunts/central_moments/ball_results.json
- hunts/central_moments/check_exact.py