[Autoplectic]

Summary

Ports the cpfci prototype gen_heaviest_bb.py, the first bound to certify C_g > G on a survey process with a full-support joint.

• heaviest_term_bound takes an optional weight_cap(box): an extra upper bound on the heavy term's weight over a box, or None to prune it. Without it the static bound is unchanged.
• generator_heaviest_term_bound(problem, ...): a generator's states are an exact decomposition whose heaviest term is its heaviest state, and that state satisfies the generator equations, so the weight cap is the one-explicit-state generator-cap LP (_HeaviestStatesRelaxation(problem, 1)) over the box of beliefs. The docstring records why the root's weight floor 1/(2^m - 1) (a cardinality bound on optimal decompositions) stays valid for generators with more states: a lighter heaviest state forces H[pi] >= log2(2^m - 1) >= min(C_mu+, C_mu-) >= C_g.
• Pipeline: generator_heaviest_term=False by default; when set, it runs after the static stage on joints with |S+| + |S-| <= 7 while the bracket is open, with a 0.3 share of the remaining budget.

Why opt-in

On ((0,1),(0,2),(0,1)) the LP excludes the G-optimal heavy term only in boxes of radius about 1e-4, so the bound passes G = 0.92433 after ~220k boxes (about 30 min) and plateaus at 0.928157 after 8 h. On RLL it stays at G for 40 s. Inside a default time budget it would rarely help.

Test plan

• A weight cap that admits nothing prunes every box
• On ((0,1),(0,2),(0,1)) (matrices embedded): the LP admits the G-optimal heavy term (t* = 0.6944) in a radius-1e-2 box and caps it below t* - 1e-3 at radius 1e-4
• The generator bound stays below a word-verified generator's entropy (0.96971)
• Pipeline smoke run with the flag on: the stage runs and logs
• Generator suites: 79 passed; ruff; ty has no new diagnostics

Made with Cursor