Reproduction

Reading: the complete frozen checker and evidence description, the copied runtime interface, the supplied installed API reference, and the independently written diagnostic. These instructions accompany the report and derivations; they do not turn a stored output into a check.

Retained inputs

assets/subject/ contains exact copies of the supplied statement, proof, evidence description, checker, and individually supplied runtime files. The copyrighted source excerpt is identified by its exact bibliographic locator instead of reproduced. No executable mathematical input was changed. The runtime lockfile is named uv.lock.txt, preserving its delivered safe name and original bytes. It is not an installation target.

The independent finite diagnostic is independent_check.py. Its exact Gaussian-rational cases and rejection inputs are assets/diagnostic_inputs.json. It reads the retained checker as a module to test its functions; it does not run the checker's main() a second time. Its reference density comes from a prescribed root and quadratic division, not Cardano. The mathematical rationale and scope are in derivation 3.

The operating wrapper assets/operating/run_frozen_evidence.py is preserved exactly as executed. It prints and checks environment identities, sets the original single-script argument list, and executes the unchanged checker through runpy.run_path. It introduces no mathematical check or changed constant. The supplied installed API text is retained as assets/operating/flint_api_reference.txt; no example from it was executed.

Environment and path substitution

The observed mathematical runs used the checkout-local .venv, CPython 3.14.6, python-flint 0.9.0, the supplied runtime's tools package, and the interpreter's standard-library typing. Each running process printed the four commissioned identities: sys.prefix, tools.__file__, typing.__file__, and python-flint version. Both used Python safe-path mode. The author's checker sets ctx.prec=64 and ctx.threads=1; the independent diagnostic uses one thread with 64-bit tested boxes and 128-bit reference calculations.

The original documented command, from the repository root, is:

uv run --no-sync python wiki/theory/polynomials/L144_cubic_lemniscate_length/evidence/main.py

The closed examination authorized replacing that live mathematical path by the supplied frozen copy and replacing the package import by its supplied runtime. The original live path was not executed. The commands below apply that same substitution to the retained copies, plus the transparent identity wrapper used in the observed full run. Set review_dir to the directory containing this report; after filing at the commissioned home it is as shown. Use an already installed repository environment. Do not install or synchronize from the copied runtime project or lockfile.

Full frozen checker

From the repository root:

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 python -P -u \
  "$review_dir/assets/operating/run_frozen_evidence.py" \
  "$review_dir/assets/subject/evidence/main.py"

This is a full mathematical rerun, not an output parser. The observed run exited 0 with 22 successful obligations in approximately 288 seconds. It reproduced all thirteen small-parameter boxes and 591 accepted larger-parameter boxes. Detailed numerical findings are in the report. The identity prefix is operating information, not a mathematical check. A rerun must inspect its own outputs and exit status; the recorded result is not a substitute.

The driver has no input data file and exposes no quick-mode argument. Its failure interfaces are its fixed constants, computed candidate bounds, and parameterized helper functions. The following are concrete negative witnesses for its obligation types, established by reading their predicates; they are not additional executed tests or edits to the retained source.

Independent diagnostic and its retained failures

From the same repository root, with review_dir set as above:

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 python -P -u "$review_dir/independent_check.py"

The observed run completed in less than a second and exited 1, with 44 checks passing and these four of 48 failing:

• 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.

Despite their labels, their predicates require exact equalities to ideal endpoints. The ball-constructor contract permits outward radius rounding, so these predicates are stronger than the required enclosing inequalities. The actual endpoint values were not printed. The driver is retained unchanged and is not a successful whole certificate. Its observed root-comparison and rejection-case results have the finite scope stated in the report. The analytical signed-rectangle argument does not rely on the four failed tests.

Meaningful failing inputs include the wrong origin density $4/3$, an indeterminate integrand at depth zero, the invalid critical window at $\beta=0$, and an unresolved cover of $[0,2^{-41}]$. Their exact forms are in the JSON and code. The failure to reject any one of them would make the corresponding diagnostic check fail. Replacing an enclosing constant interval by its midpoint would fail for the endpoint members of that constant family; the retained exact-equality tests did not properly encode that weaker requirement.

The diagnostic has not been repaired, rerun, or retroactively relabeled as a pass. If the four calibration assertions are corrected and instrumented, the result must be retained as a new diagnostic record. Only the two described mathematical executions were performed. Further execution is not claimed by this record.

Coverage and limitations

The full checker verifies the uniform integral bounds and their parameter cover. The written reductions, gamma identity, source interfaces, and equality classification are checked mathematically in the report and derivations. The independent root route can detect branch, coefficient, or normalization mistakes on its exact cases, but shares the arb/acb implementation and makes no statistical or universal inference from those cases.

The supplied source is cited by locator and the operating references are retained for the assessment; they do not imply PDF inspection or reconstruction of the underlying external books. Raw environment receipts, process transcripts, subscription outputs, and communication receipts remain private operating records. They are not mathematical inputs to either program. The earlier excluded-package import is disclosed in the report and still requires the distinct grader's materiality ruling.