Experiments: what breaks a PH W-oscillation cycle (sizes)

[DLWoodruff]

Self-contained research experiments (not a product feature, not wired into
CI) establishing which PH interruption actually breaks a W-vector oscillation on
the sizes model. This is the empirical evidence behind scaling #780 back to
slamming as the only interruption remedy.

What

examples/sizes/w_oscillation_experiments/ — a harness that reuses the merged
detection primitives (PR1, #778) and scores each would-be remedy by two metrics:

• zc — how many nonants the zero-crossings detector still flags. Scale-free
  (counts sign changes), so it can be fooled by anything that freezes W.
• primal gap sum_s p_s |x_s - xbar| — the ground truth: low only when the
  scenarios actually agree.

Run (needs a MIP solver; gurobi_persistent by default):

python run_experiments.py

Findings (sizes-3, 60 iters; see results/summary.md)

lever	outcome
plain PH / W-damping / W-reset / rho jitter	still cycling
rho reduction (geometric)	decoupled — primal gap explodes to ~24,000 while W freezes
fix (slam analogue)	converges (gap → 0 @ iter 35)
uniform rho ≥ 0.1	converges (rho ≤ 0.01 cycles)

• Only fix (changing the problem structure) and a larger rho converge the
  primal gap. Every state-perturbing move leaves the cycle intact, decouples the
  scenarios, or worsens it.
• Geometric rho reduction is the cautionary case: zc drops while the gap
  explodes — a detector false positive (driving rho → 0 freezes W).
• Root cause: the cycle is a small-rho artifact; sizes's _rho_setter
  uses rho = cost × 0.001, and rho ≥ 0.1 converges with no interruption at all.
• Metric lesson: a W-only oscillation detector can be gamed by anything that
  freezes W; confirming an interruption converged (vs decoupled) needs a
  primal-side check like the gap used here.

Relationship to #780

#780 ships the W-oscillation interruption with slamming as the only remedy —
these experiments are why (they showed the dual-side remedies do not break the
cycle). The extension's design doc (§9) points here for the evidence. Kept out
of CI because it needs a MIP solver.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 76.16%. Comparing base (a49f6f3) to head (f0b2ebb).
⚠️ Report is 6 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
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+ Coverage   76.00%   76.16%   +0.16%     
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  Files         169      169              
  Lines       22096    22224     +128     
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+ Hits        16794    16928     +134     
+ Misses       5302     5296       -6     

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