[Autoplectic]

Summary

These changes clear the last three 4-state survey timeouts. Each one was a single call that ignored the pipeline's deadline, or a computation that grew too fast with the size of the joint.

Stage deadlines

• Generator caps: branch-and-bound child LPs get the time left as a HiGHS time_limit. A cut-off LP keeps its parent's bound, so the cap stays valid; the root LP always runs to the end. One degenerate node LP had run more than 8 minutes past a 90 s deadline.
• dit fallbacks: dit's exact and Wyner optimizers take no deadline, so they are skipped above 30 causal-state pairs (logged as a skipped dit fallbacks stage). They had used 190–760 s of a 900 s budget on 30–70-pair joints. Every 3-state survey joint has at most 21 pairs, so the 3-state benchmark is unaffected.
• Memory lifts: memory_lift_search stops a start in progress at its deadline. Its first start used to run in full regardless (more than 14 minutes).
• Line-split polish: _optimize and _optimize_coupled take a deadline, and the pipeline's line-split stage passes it. One polish had run more than 10 minutes over budget. The targeted search and coupled_search are unchanged: by design they always finish one polish (or the ε-machine seed).

Builds

• Sparse stationary solve: stationary_distribution_hmm solves chains with more than 2,000 states sparsely. The dense matrix_rank and eig are $O(n^3)$ and never finished on a 50k-cap reverse machine. Symbolic weights, several closed classes, or a failed residual check fall back to the dense path and its warnings.
• No double build: the ladder and try_build_bidirectional reuse the machines the preflight built instead of building them twice, which roughly halves build time.
• max_reverse_states (off by default): a ladder build whose truncated reverse machine is larger than this is classified as an explosion. The survey driver sets it to 1,000, so such cases fall back to window bounds.
• Renamed the private exception to _DeadlineReachedError (lint rule N818).

Results

80-topology 4-state sample (cpfci survey4_v5.jsonl; ladder budget 300 s, pipeline budget 900 s, hard timeout 1500 s):

case	before	after
[[0,1],[2,None],[2,3],[1,0]] (95 pairs)	timeout	[0.932, 1.109] in 902 s
[[None,1],[2,1],[1,3],[3,0]] (144 pairs)	timeout	[1.073, 1.231] in 900 s
[[0,1],[0,2],[3,None],[1,None]]	timeout	50k build has 8,949 reverse states, so it is treated as an explosion; window bounds [1.872, 1.968] in 415 s

Totals: 32 brackets (10 certified), 35 window brackets, 13 skipped, 0 timeouts (was 3). The size cap reclassifies no other case.

Test plan

• New tests:
  • child LPs get the time left and keep the parent's bound (patched HiGHS);
  • dit fallbacks are skipped above the pair limit;
  • memory_lift_search stops inside a start (fake clock);
  • ALM polish returns at an expired deadline;
  • sparse vs dense stationary distributions agree (hypothesis), the sparse path declines two closed classes, and a 20,000-state chain solves in about 4 s;
  • an oversized ladder build is classified as an explosion.
• Generator, stationary and mixed-state suites: 157 passed
• ruff check, ruff format --check, ty check (no errors)

[Autoplectic]

Added: a sparse stationary solve for chains with more than 2,000 states (the dense matrix_rank + eig never finished on a 50k-state reverse machine), and the ladder and try_build_bidirectional now reuse the preflight's machines instead of building them twice. Together these take the last 4-state case's ladder build from never finishing to 354 s. That case still times out, because the pipeline then has to construct its problem from a truncated bidirectional machine with tens of thousands of reverse states; that is a policy question rather than a solver bug. Tests: 157 passed across the generator, stationary and mixed-state suites; ruff and ty clean.