AMR-050-0044: exact controls and optional numerical diagnostics

From the extracted source archive root, run with Python 3.9 or newer:
  python3 -I -B reproducibility/check_focal_inverted_area.py
  python3 -I -B reproducibility/check_exact_inverted_areas.py
  python3 -I -B reproducibility/check_repeated_six.py

All three required checks use only Python's standard library. The third
loads its adjacent check_exact_inverted_areas.py after verifying its SHA-256;
keep both files together. No external project or package is needed.

The algebra checker verifies polynomial identities and exact area values.
The geometry checkers directly verify ellipse incidence, reflected directions,
confocal tangency, internal contacts, finite focal inversion, and signed areas.
They include two primitive four-periodic phases, a primitive eight-periodic
fixture, and exact triangle/hexagon repetition obstructions to the stronger
listed-length interpretation. None is a proof by sampling of the general
theorem. The analytic argument is given in main.tex and the retained proof.

The geometry output includes an actual execution timestamp. Distribution
replays compare all fields except actual_execution_completed_at to the
accepted originating-researcher result. The timestamp is preserved in both
raw results and identified explicitly as the sole ignored volatile field.
The unchanged algebra output is also compared byte-for-byte. Script hashes
and all mathematical fields must match exactly.

Optional, not required and not rerun by the package builder:
  python3 -m pip install -r reproducibility/requirements-optional.txt
  python3 reproducibility/scout_focal_inverted_area.py
The optional diagnostic needs mpmath 1.3.0. The shipped script's project-local
dependency bootstrap has been replaced with a normal public-package import;
its numerical calculation body is unchanged. The included historical result
is from the original root rerun and names that original script's hash.
It sampled 33 families at 85 digits, including 27 genuine periods divisible
by four and six controls of other least periods. It is numerical evidence,
not exact proof or proof-assistant verification. No dependency is installed
by either the checkers or package builder.

Scope is the original polygon's signed area and unit focal-inverted signed
area for genuine least period divisible by four, admitted coprime stars, and
repetitions of those cycles; the circle is separate. Arbitrary repeated lists
of length divisible by four need not satisfy the conclusion. The known N4
case is credited. No unqualified source-row closure, independent human review,
formal verification, or absolute novelty/priority certification is asserted.
Source provenance lists URLs and checksums. Third-party PDFs, screenshots,
raw web pages and credentials are deliberately excluded from this archive.
