FUES bounded scan can accept a run of dominated points (n_points_to_scan default under-scans)

[hmgaudecker]

Summary

refine_envelope's bounded same-segment scan (_find_same_segment_point, src/_lcm/egm/upper_envelope/fues.py:400) inspects only n_points_to_scan candidates (default 10, src/lcm/solvers.py:102). When more than n_points_to_scan off-segment candidates interleave two points of the same segment in sorted-grid order, the scan never sees the segment's continuation, so the intervening dominated candidates are wrongly accepted onto the envelope.

This is finding F4 of the external adversarial FUES correctness audit. Full verification write-up: FUES_AUDIT_VERIFICATION_RESULTS.md (commit a72bb1a).

Reproduction

Upper line A(x)=x (anchors (0,0),(0.1,0.1),(12,12), p=x) plus eleven points 0.5 below it ((i, i-0.5) for i=1..11, p=x-100), at the shipped default n_points_to_scan=10, jump_thresh=2:

| n_points_to_scan | n_kept | max|dev| of interpolated value from A(x)=x |
| --- | --- | --- |
| 10 (default) | 14 | 0.50 |
| 11 | 3 | 0.00 |
| 14 | 3 | 0.00 |

All eleven below-envelope points survive and the interpolated value function sits a uniform 0.5 below the true envelope. Widening the window to cover all candidates recovers the exact envelope — so this is a genuine correctness defect at the shipped default, not just an approximation knob.

Locked as tests/solution/test_fues_upper_envelope_audit.py::test_f4_interleaved_segments_give_analytic_envelope_at_default_scan (xfail(strict=True)), with ::test_f4_failure_resolves_when_scan_window_covers_all_candidates pinning the boundary.

Reachability

Not exercised by the IJRS examples: every candidate row captured from a small IJRS worker-model DC-EGM solve is fully concave (segment_jumps = 0, nearest-same-segment-successor offset 0), so the multi-segment finely-interleaved input never arises there. Triggering F4 needs (a) genuine multi-segment non-concavity and (b) more than n_points_to_scan points of one segment falling between two consecutive points of another — a strong per-segment grid-density asymmetry inside an overlap region. Plausible for strongly non-concave targets (ACA's discrete-choice structure, the Laibson liquid/illiquid model) with the 200-node clustered savings grid; should not be assumed safe there.

Recommended fix

Either:

1. a correctness-critical mode that scans exhaustively (n_points_to_scan = n_candidates), or
2. carry explicit segment/bracket ids and jump directly to the next same-segment point (this also closes the related F5 missing-capability gap).

Raising the default n_points_to_scan only pushes the boundary out; it does not close the gap. A fix should remove the xfail(strict=True) marker on the F4 regression test.

[hmgaudecker]

Update from the ChatGPT 5.5 Pro EGM-pipeline audit (commit 7b61787 on feat/dcegm):

• Duplicate abscissae (audit F1 = prior F3): fixed. refine_envelope now collapses coincident-abscissa candidates to their max value before the scan (sort by grid asc / value desc, NaN the non-leading copies), so a dominated duplicate can no longer reach the index-keyed interpolation. Regression tests added, incl. the reviewer's [0,1,1,2] counterexample.
• jump_thresh robustness (audit F2): scope-documented + hook added. The fixed 2.0 default is now documented as a heuristic (must exceed the within-segment Lipschitz bound and lie below the jump signal; model/grid-dependent), and refine_envelope gained an optional segment_id channel (switch = policy-jump OR label change, with segment filtering in the bounded scan). segment_id=None is bit-identical to the policy-jump-only scan. No label is wired yet — the constrained/interior join is a continuous concave kink, not a value-segment switch, so the hook is reserved for a future notch/bracket model.

Still open (the core of this issue): the bounded n_points_to_scan=10 forward scan can still miss a same-segment witness when >10 off-segment candidates interleave (the test_f4_interleaved_segments_give_analytic_envelope_at_default_scan xfail remains strict=True). The exhaustive correctness-mode / label-driven jump for genuine interior non-concavity is the remaining work.