Automata and shift ideas ported to processes (4/4)

[Autoplectic]

Stacked on #25 (base sofic-literature-gaps); retarget to main after #23–#25 merge.

Implements the ports D1–D10 from the correctness-and-coverage plan, each with docstring citations, a docs page, and property/metamorphic tests.

Ports

• D1 SlidingBlockCode.apply_to_process / image_process, and HiddenMarkovModel.higher_block(k). h_μ never increases under factor maps; E and C_μ are not conjugacy invariants (E(β_k X) = E(X) + (k−1)h_μ, asserted exactly).
• D2 Process-preserving HMM out-/in-splitting (split_state) and amalgamate (Lind & Marcus §2.4; Upper 1997).
• D3 minimal_quasi_realization and process_rank (Schützenberger 1961); dimension equals the brute-force Hankel rank.
• D4 bisimulation_partition / coarsest_lumping (Larsen & Skou 1991); lump(partition=None) is the coarsest lumping.
• D5 learn_epsilon_machine_active + ProcessOracle (Angluin 1987; Shalizi & Crutchfield 2001): exact on golden mean, even, nemo, butterfly and random machines with polynomial queries.
• D6 Public support_nfa, support_includes, is_absolutely_continuous, support_equal.
• D7 condition_on_language via the Doob h-transform; the uniform i.i.d. process conditioned on an irreducible SFT recovers its Parry measure.
• D8 omega_probability for deterministic Büchi properties and regular_language_probability (Baier & Katoen 2008).
• D9 renyi_entropy_rate (α ∈ [0, ∞]), pressure, rate_function (Rached et al. 2001; Dembo & Zeitouni 1998).
• D10 Experimental canonical_residual_hmm (requires experimental=True; Denis et al. 2002; Maarand & Tamm 2022; Löhr & Ay 2009): strictly smaller than the ε-machine on a constructed 4-symbol example.

Fixes found along the way

• EpsilonMachine.from_hmm split causal states that differed only by belief-update round-off (a fair-coin HMM gave 33 states, C_μ ≈ 2.46); numeric probabilities now compare within the mixed-state tolerance. Its docstring documents that numeric merging can close a converging infinite belief set at a finite approximation.
• to_support_dfa accepted only terminal recurrent subsets and rejected words of positive probability (e.g. 1 for the even process).
• entropy_rate/state_entropy with mixed int/tuple state labels; is_equal_process on sympy HMMs; DFA.add_transition with a new source state.

Gates

pytest -n 8: 2246 passed, 17 skipped. ruff check / ruff format --check clean. Fresh sphinx-build -W clean.