Reproduce the technical investigations

Synthetic investigations for edition 2026.10.7. These are original, neutral teaching cases. They contain no native protocol or product implementation. Authored material retains the publication's reserved-rights terms; no separate code or patent license is implied.

Use CPython 3.12.14 from the public source package. The case runner and public evidence validator use only the standard library. The successor check suite additionally requires the pinned public build dependencies described in BUILD.md; those dependencies are not needed to run a teaching case:

python examples/investigations/check.py
python tools/public_evidence.py
python tools/successor_checks.py

The first command computes positive cases and deliberate faults. There are twelve independent cases. Use --case approval to select one, or --case approval --mutant to run the deliberately wrong consumer; the mutant exits one. All other named cases have the same interface. The fault must violate the promised condition; syntax errors and unavailable interpreters do not count.

The code defines every enumerated population. The founding waiting cycle is an explicit liveness counterexample without fairness, not an unbounded model check. The construction case exhausts three Boolean functions, not any cryptographic identity construction. Calibration uses exact rational arithmetic. None of the cases qualify production behavior or proprietary algorithm equivalence.

The public evidence catalog records author execution on 12 October 2026. External reproducibility means the disclosed cases can be run without private inputs. It does not mean an outside reviewer has run them. Submit scoped objections through the publication review guide.