Reproduction

These instructions accompany the grade. The mathematical files under review/ preserve the settled mathematical delivery; the source-excerpt locator and editorial filing changes are disclosed in the index. The original reproduction account describes the reviewer's executions; this account records the grader's two reruns on 2026-10-15 UTC. Neither stored output nor a previous successful exit replaces a fresh execution.

Inputs and relocation

The 34-file public bundle under review/ preserves the computational inputs and the examination, with a bibliographic locator replacing its source excerpt: the report, three derivations in one file, reproduction account, independent diagnostic, exact diagnostic JSON, statement, eight-section proof, evidence description, full checker, source locator, runtime modules, project specification, lockfile text, API capture, and identity wrapper. The runtime's uv.lock.txt is preserved in its delivered safe name. Neither it nor the copied project specification was used to install an environment.

The grader first reconstructed those files in private scratch with their original relative hierarchy, then preserved identical bytes in the settled grading bundle. The public filing replaces only the copyrighted source excerpt by its locator and makes the disclosed path and citation edits. Every path is mapped in the private reconstruction receipt. The only execution substitutions were the enclosing directory, explicit interpreter selection, and the frozen runtime import path. No mathematical source, constant, input, or assertion was edited. The public reproduction paths include /review in review_dir; use the value below when reproducing this package.

The full checker has no separate data file or quick-mode option. It begins with thirteen small-parameter boxes and 300 larger-parameter seed intervals, then adaptively encloses the latter. The diagnostic reads twelve exact Gaussian-rational root cases from diagnostic_inputs.json, with five prescribed points per local input box, and the retained boundary/rejection instances. It imports helper functions from the full checker without calling its main().

Environment and bounded execution

Use an already installed repository-local environment. The observed grader runs used CPython 3.14.6, python-flint 0.9.0, typer 0.27.2, and PyYAML 6.0.3. The checker sets 64-bit arb precision and one flint thread; the diagnostic compares 64-bit tested boxes with 128-bit reference calculations, also with one thread. It is a different root construction, not a different ball library.

Before execution the grader verified sys.prefix, tools.__file__, typing.__file__, the installed package versions, safe-path mode, and every loaded tools module location. The prefix was the local environment, tools came from the reconstructed permitted runtime, and typing came from the interpreter's standard library. Both mathematical programs also print their commissioned runtime identities. Inspect those identities on a rerun.

The commands below are the inner mathematical commands used by the recorded supervisor, with portable path substitutions. The supervisor imposed a 900-second wall limit on the full checker and a 60-second wall limit on the diagnostic, stopped only its own process group if necessary, and retained stdout, stderr, return code, and elapsed time. These are enforced execution limits, not claims that the algorithms have a proven runtime below those limits on every machine. Both observed runs finished within their limits. A timeout or missing required enclosure is not a pass. Apply the corresponding wall limit when using another execution supervisor.

The extra --no-project, --no-config, --offline, and --no-python-downloads flags prevent project discovery, configuration reads, network resolution, and interpreter acquisition. The already installed interpreter is explicit. uv reported that --no-sync is redundant alongside --no-project; no synchronization or installation occurred.

Full checker

From the repository root after filing the package at its commissioned home:

review_dir=wiki/theory/polynomials/L144_cubic_lemniscate_length/evidence/verify/review
env -u VIRTUAL_ENV -u UV_PROJECT -u UV_PROJECT_ENVIRONMENT \
  -u UV_WORKING_DIR -u UV_NO_PROJECT \
  PYTHONPATH="$PWD/$review_dir/assets/subject/runtime" \
  PYTHONDONTWRITEBYTECODE=1 OMP_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 \
  MKL_NUM_THREADS=1 VECLIB_MAXIMUM_THREADS=1 NUMEXPR_NUM_THREADS=1 \
  uv run --no-sync --no-project --no-config --offline --no-python-downloads \
  "$PWD/.venv/bin/python" -P -u \
  "$review_dir/assets/operating/run_frozen_evidence.py" \
  "$review_dir/assets/subject/evidence/main.py"

The grader's run exited 0 after 251.65 seconds, with all 22 obligations passing. It reproduced 13 small-parameter boxes, 591 accepted larger-parameter boxes, and respectively 1,930,449 and 2,581,149 regular integration pieces. Printed enclosures included

largest small-regime integral upper bound $[-0.216023\pm1.23\cdot10^{-7}]$, and reported smallest large-regime margin $[0.0114301\pm4.80\cdot10^{-8}]$. The control at $\beta=1/2$ implies the conservative scalar bracket $[8.1746135,8.1829017]$. The checker must establish its individual accepted-box inequalities and complete covers; these printed summaries alone do not certify them.

The original reproduction account lists concrete failing inputs for the tiling, graph, far-branch, gamma-consistency, negativity, regime-join, unresolved-cover, margin, and control predicates. Those interfaces were inspected; their hypothetical modifications were not executed or applied to the frozen code.

Independent finite diagnostic

Using the same review_dir and repository root:

env -u VIRTUAL_ENV -u UV_PROJECT -u UV_PROJECT_ENVIRONMENT \
  -u UV_WORKING_DIR -u UV_NO_PROJECT \
  PYTHONPATH="$PWD/$review_dir/assets/subject/runtime" \
  PYTHONDONTWRITEBYTECODE=1 OMP_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 \
  MKL_NUM_THREADS=1 VECLIB_MAXIMUM_THREADS=1 NUMEXPR_NUM_THREADS=1 \
  uv run --no-sync --no-project --no-config --offline --no-python-downloads \
  "$PWD/.venv/bin/python" -P -u "$review_dir/independent_check.py"

The grader's run exited 1 after 0.324 seconds. Exactly 44 of 48 reported predicates passed. All sixty prescribed-root comparisons and the specified exact/rejection instances behaved as recorded. The same four predicates failed as in the original review:

• finite depth cap retains rectangle bounds [2,4];
• negative rectangle bound uses correct width endpoints;
• positive rectangle bound uses correct width endpoints;
• sign-changing rectangle bound contains both extremes.

These failures remain part of the retained result. The exact discrepant endpoints were not printed, so their magnitudes and individual causes were not measured. The assertions demand exact ideal endpoints, whereas the required mathematical argument uses enclosing inequalities. The grade gives these four predicates no successful-calibration weight and explains why the written signed-rectangle argument supplies the mandatory warrant independently. Do not repair the code merely to reproduce a successful exit, or report this leg as a pass.

The exact retained negative cases include a wrong origin-density factor, indeterminate integrand at depth zero, invalid critical window at $\beta=0$, unresolved cover $[0,2^{-41}]$, and the singular point $2i$. They test the specified error paths. The finite root route can expose a Cardano branch/normalization error on its cases; it cannot certify the whole parameter family or the ball arithmetic implementation.

Scope of the record

Exactly two mathematical checks were run in this grading. Administrative byte comparisons, static code/history parsing, and identity probes are separate and introduce no further mathematical execution. The unchanged programs, JSON, source, runtime support, and wrapper above are the inputs needed for mathematical reproduction. The exact administrative scripts, bounded supervisor, commands, stdout/stderr, timings, identity receipts, and primary isolation records are retained privately beside the grade for intake. They are not needed as cached mathematical data.

The uniform integral certificate relies on the mathematical argument in the report and derivations. The existence reduction, gamma identity, source interfaces, and equality proof remain written mathematical obligations and are assessed in the grade. Reproducing either program alone supplies no grade of those obligations.