AMR-050-0053: portable exact-checker reproduction
================================================

This source package carries two byte-identical Python standard-library
checkers. Neither checker proves the complete family theorem by sampling.
The general proof is in main.tex and the retained proof dossier.

Required runtime
----------------
Python 3.9 or newer. No third-party package, project checkout, network access,
credential, or installation is required. Do not use Python -O or set
PYTHONOPTIMIZE, because exact assertions are part of each certificate.

Fresh-extraction commands
-------------------------
Run from the extracted archive root:

  python3 -I -B reproducibility/check_projective_pentagon.py
  python3 -I -B reproducibility/check_dual_squares.py

Expected statuses:

  PASS_EXACT_PROJECTIVE_PRIMITIVE_PENTAGON
  PASS_EXACT_DUAL_CONSTRUCTION_CONTROLS

The -I flag isolates the interpreter from user and repository import paths.
The -B flag prevents bytecode files. Both programs print JSON to stdout and
otherwise write nothing unless their optional --output argument is supplied.
Any --output path must be new and must remain beside the checker.

Frozen source hashes
--------------------
check_projective_pentagon.py:
  0fa142da31e90987bd8dd40e52b43f0515b723b20ce6724a3ece937cc80c7737

check_dual_squares.py:
  c41ed96a5e35626b59f48d9e9515a8d098436f55d0c6e80b647b49b69bf7f594

Retained originating output hashes
----------------------------------
originating-projective-result.json:
  255342b31f22c065230dd3f86f640485954ced28b699ba675bb5d182601c0042

originating-dual-result.json:
  a0d074de075eada5a5906cd1bdd6fcca6793b8972c540d3aae04350f91a4ead2

Every fresh execution truthfully records a new actual_execution_completed_at
timestamp. The package replay compares every other parsed output field exactly,
while independently requiring the frozen checker hashes, expected statuses,
empty stderr, and exit code zero. Byte-identical raw JSON is therefore not
expected when only the execution time differs.

Scope of the two controls
-------------------------
check_projective_pentagon.py uses exact arithmetic in Q(t,sqrt(1-t^2)), where
t is the isolated real root of 25t^3-50t^2-40t+8. Rational interval bounds
certify all strict signs. It checks a primitive convex five-cycle, strict
nesting, original and transformed actual-segment tangencies, the projective
horizon, circle/ellipse data, excluded center/focus coincidences, and the exact
squared-side value 175/18-(625/48)t. It explicitly does not infer whole-family
constancy from one cycle.

check_dual_squares.py uses exact rational and real quadratic-field arithmetic
on ten period-3, period-4, and circular period-5 fixtures. It distinguishes
the sideline reciprocal from literal vertex inversion, verifies their midpoint
relation and two different trace formulas, and checks reversal and repetition.
It explicitly does not prove all periods or resolve the original k811 wording.

The all-family theorem instead uses the credited bicentric cosine theorem,
Jacobi's bicentric parametrization, the published MI-II cyclic identity, and
Poncelet closure. The frozen k811 record remains ambiguous and is not claimed
as an unqualified resolved proposition. The exact pentagonal counterexample is
to the separate Murad 2026 Section 6, Conjecture 1 necessity direction.

Third-party PDFs, HTML, headers, and rendered source pages are excluded from
this authored package. Their hashes and URLs remain in provenance manifests.
