[Autoplectic]

Summary

Add quantized_filter for known, positive-transition MooreHMMs, following Feng & Meng, Recursive memory for prediction and generation (arXiv:2611.13760, Theorems 3.1/4.3 and Appendix A.4).

• Enumerate only the reachable log-odds-grid labels, retaining the exact initial belief and reporting full-grid/reachable counts and allocated memory bits.
• Select precision for future-event log error, uniform-word log error, or total forward KL; all public loss budgets are in bits.
• Separate event queries, recursively rounded unifilar generation, and posterior-initialized private-state simulation, reusing existing HMM sampling/word/YAML APIs.
• Add documented examples, literature citations, static-IB/exact-MSP cross-references, and 55 focused regression tests.

Scope and numerical guarantees

The bounds are theorem-derived in real arithmetic, not formal interval certificates: bounds.rigorous is explicitly False, and unresolved float64 precision is rejected. Arbitrary edge-emitting Mealy HMMs are deliberately rejected; positivity of the summed transition matrix alone does not establish the required contraction. Zero emissions and nonstationary/boundary initial beliefs are supported.

This does not optimize the smallest state machine, change exact mixed-state enumeration, add a scalar-quantization solver, or conflate label capacity with statistical complexity/IB rate. Fixed total forecast loss is distinguished from a per-symbol allowance.

Validation

• Full non-slow suite, Python 3.12: 2,345 passed, 19 skipped.
• Focused new tests: 55 passed, 99% coverage of the new module.
• Python 3.11 without SymPy: 115 passed across the new module and HMM/mixed-state/relative-entropy regressions.
• Repository-wide ruff check . and ruff format --check .: pass.
• Repository-wide ty check: exits 0 with existing warnings; targeted checks of the new module/tests are clean.
• sphinx-build -q -W --keep-going -b html docs docs/_build/html: pass; the documented Python example was executed separately.
• Reproduces Table 3's three log-grid state counts; checks Hilbert/event bounds on exhaustive short histories, total KL against the source-prefix chain rule, generated word probabilities/YAML round trips, private simulation, zero emissions, initial-law handling, and resource/numerical guards.