[Autoplectic]

Summary

For a dataset of minimal generators, each result needs to say how well its generator reproduces the source and what kind of generator it is. GenerativeModelResult gains:

• reproduction_error: the returned generator's word-probability deviation from the source, from _reproduction_error (which since Generator verification: equations are necessary only; exact word-process check #56 includes the exact difference-automaton check). It was computed already but discarded.
• structure: n_states, weights (descending), functional (every causal-state pair maps to one generator state), lifting_residual (the largest of the two lifting-condition conditional mutual informations and the separation one, in bits) and lifted (residual at most 1e-8; then the lift of the generator's channel generates as well).

certified now also requires reproduction_error <= 1e-6 (the certification tolerance), so a closed bracket is never reported on an approximate generator. On survey v12 (43 cases, on main at #56) certified uppers have exact errors around 1e-13 and coupled-search uppers around 1e-8, so no certification changes. Both fields also appear in the reliability-summary stage.

Test plan

• Golden mean: error below 1e-9, 2 states, functional and lifted
• Interleaved (eps = 0.1): the ε-machine seed is functional and lifted; the memory lift of the flag (the coupled minimal generator) is neither, with lifting residual 0.019 bits, as documented
• certified is false at reproduction_error = 1e-4
• Generator suites: 152 passed
• ruff check, ruff format --check; ty check has no new diagnostics

Made with Cursor

[Autoplectic]

Added tests/test_generative_model_invariants.py (marked slow): a hypothesis test over random binary 2- and 3-state ε-machines with generic probabilities (E <= lower <= upper <= min(C_mu+, C_mu-); reproduction_error <= 1e-5; H[pi] of the returned model equals upper; structure consistent with the model), 12 examples, and the RLL known value C_g = 3/2 certified. Both pass (-m slow, ~3 min).