[Autoplectic]

Summary

EpsilonMachine.from_hmm (and so infer_reverse_epsilon_machine and the bidirectional preflight) failed on processes whose hidden state no finite word reveals, such as a period-2 process whose phase stays uncertain. Their beliefs converge to the causal states without reaching them, and:

• either rounding closed the mixed-state presentation on hundreds of beliefs within round-off of the simplex boundary (rounding acts as a reflecting barrier for the posterior's log-odds random walk, so a transient walk became a recurrent class with geometrically decaying mass), giving e.g. 255 "causal states" instead of 3;
• or the presentation exceeded max_states and raised MixedStateExplosionError, so the process was classified as having an infinite reverse machine.

Now build_epsilon_machine seeds a second mixed-state presentation from a limit belief (the heaviest recurrent belief when the recurrent beliefs have entries below 1e-8, or the belief after Bayes-filtering a 4096-symbol sample when the first presentation explodes), with sub-1e-8 entries set to zero. It minimizes the result and accepts it only if it generates the source process (_equivalence_error at most 1e-9). A finite unifilar presentation of the process minimizes to its ε-machine, so an accepted result is correct; otherwise the old behaviour is unchanged.

Evidence

• Period-2 example (A, B0, B1, flip probability e): 3 reverse states with C_mu = 1.5 at e = 0.4 (was 255 states), 0.1 and 0.45 (were explosions); equivalence errors around 1e-16.
• All 142 binary 3-state survey topologies: explosions 35 → 26; the 9 rescued are 3-state reverse ε-machines with equivalence errors at most 6e-13. Finite/infinite now agrees with reverse_epsilon_machine_is_finite on all 138 minimal topologies. One topology the criterion calls infinite returns 827 states instead of 893; both are finite approximations, and the existing truncation warning still fires.

Test plan

• tests/test_asymptotic_synchronization.py: both failure modes (e = 0.4 closure, e = 0.1 explosion)
• Full suite: 2290 passed, 19 skipped
• ruff check, ruff format --check, ty check

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