Literature gaps: zeta functions, conjugacy invariants, decisions, regex, entropy rates, correlations, predictive RD (3/4)

[Autoplectic]

Stacked on #24 (base sofic-property-tests); retarget to main after #23 and #24 merge.

Implements the literature gaps C1–C10 from the correctness-and-coverage plan, each with docstring citations, a docs page, and tests against known values or brute force.

Shifts

• C3 periodic_points(n) and zeta_function() for TMCs, SFTs and sofic shifts (Manning's signed-subset formula; Lind & Marcus §6.4). Exact integer counts; reproduces L&M Example 6.4.10 (even shift: (1+t)/(1−t−t²)).
• C7 In-/out-state splitting and amalgamation with division and edge matrices (A = DE, A′ = ED; §2.4); bowen_franks_group (pure-integer Smith normal form, checked against sympy) and jordan_form_away_from_zero (§7.4). Splitting preserves h_top, periodic points, zeta, BF group and Jordan form in property tests.

Automata

• C8 is_empty, accepted_word, is_universal, includes on LabeledAutomaton (antichains, De Wulf et al. 2006). BuchiAutomaton overrides with ω-semantics (is_empty, new accepted_lasso); Büchi universality/inclusion raise NotImplementedError.
• C2 parse_regex / regex_to_nfa / NFA.from_regex (Thompson 1968); fixes automaton_to_regex ambiguity for multi-character symbols. Round-trip property tests.
• C10 learn_dfa_k_testable (García & Vidal 1990).

Generators

• C1 entropy_rate(method="auto"|"exact"|"bounds"|"blackwell") for non-unifilar HMMs; Cover & Thomas Thm 4.5.1 bounds and a Blackwell-measure estimator. SNS bounds bracket the exact renewal value 0.677867181.
• C9 statistical_complexity_dimension (Jurgens & Crutchfield 2021); reproduces the Cantor (log 2/log 3) and Sierpinski (log₂ 3) examples.
• C4 autocorrelation, power_spectrum, mutual_information_function in closed form (Riechers & Crutchfield 2018); Wiener–Khinchin and brute-force checks.
• C5 predictive_rate_distortion (Still et al. 2010; Marzen & Crutchfield 2016; Tishby et al. 2000).
• C6 relative_entropy_rate(p, q) (exact for unifilar q, ∞ without absolute continuity) and relative_entropy_rate_bounds (Gray 1990 §3.5).

Also

• EpsilonMachine.from_hmm(max_states=...) (kwargs were silently ignored).
• entropy_rate_hmm / state_distribution handle MixedState labels.
• Fixed the riechers2017spectral2 citation (its DOI resolved to an unrelated paper).

Gates

pytest -n 8: 1983 passed, 17 skipped. ruff check / ruff format --check clean. Fresh sphinx-build -W clean.