deform_v1

The height dimension of the map is flat. Across all seventeen arms the median per-seed peak on unseen_mismatch sits between 99 and 100, so no single-parameter deformation moves the ceiling; the peak is saturated in every direction. Even driving the bursts down to a uniform valley still brings 19 of the 20 replicates through the 95 mark at some point in training. What the map is made of, then, is the other two objectives: how many seeds reach that mark, and how soon.

The first of those, coverage, barely moves. Coverage here is the fraction of seeds whose own peak reaches 95, seed coverage, which is a different quantity from the report's replicate-coverage check that only confirms every arm ran the same 20 seeds. It holds at 19 or 20 of 20 for every arm but two, and both of those weaken the burst structure: a burst made too shallow (v_1.3, whose valley α is 1.3) covers 16 of 20, and a single tooth (teeth_1) covers 18 of 20 and reaches the band late, at a mean of 492 iterations over its reached seeds. Phase 2 had already found that removing the bursts is how coverage is lost, and these two arms are the nearest ways to remove them.

The two cliffs the hypothesis expected did not appear on the reach objective. The valley approaching 0.4 was expected to interfere destructively, but v_0.4 reaches the band on all 20 seeds and v_0.0 still on 19; the floor approaching 0 was expected to collapse coverage, but the floor, tested down to 0.7, holds 19 of 20. Where the deep valleys do their damage is in speed and in what happens after the peak, which the next paragraphs take in turn, not in whether the band is reached at all.

Speed is where the deformations separate, and the envelope start moves it the most and most simply.

Valley depth trades speed against coverage. Making the burst shallower (v_1.3) buys no speed, 259.1 iterations against the incumbent's 259.9, and costs coverage, 16 of 20. Making it deeper buys full coverage, 20 of 20 at both v_0.4 and v_0.7, at the cost of onset, which slows to 313.7 and 293.9 iterations. Driving it to a uniform valley (v_0.0) is the slowest of the valley settings at 356.4 and does not hold what it reaches. The incumbent valley of 1.0, the continuous burst ladder carried over from Phase 2, sits near the knee of that trade at 259.9 iterations and 19 of 20.

Tooth count and duty are mostly sloppy, with speed the only thing that moves. From two to six teeth, coverage is 19 or 20 of 20 and onset sits between 265 and 295 iterations; the single tooth is the lone outlier, slow at 492 and one seed short at 18 of 20. Duty behaves the same way: at 0.75 it is sloppy, 286 iterations at 20 of 20, but at 0.25, which leaves each cycle down in the burst valley three quarters of the time, onset slows to 447 while coverage stays full.

The envelope floor is sloppy for the map's objectives, and it doubles as a check on what those objectives measure. The three floor settings, 0.7, 1.0, and 1.6, reach the band about as early as the incumbent, between 263 and 271 iterations over their reached seeds against its 260, and each holds 19 of 20 coverage, because the 95 band is crossed during the first descending pass from α = 3 toward 1, before the floor is ever in play. What the floor moves is the endpoint: at 900 iterations the mean unseen_mismatch falls with it, 83.7 at 0.7, 88.6 at 1.0, and 92.6 at 1.6. The floor-toward-0 cliff the hypothesis expected was not reached, because the floor was tested only down to 0.7.

Phases 4 and 5 carry that lead forward, testing the combined shape, a higher start with a coverage-safe valley of 1.0 or below and two to four teeth, at shortened budgets, to find how early the band can be reached at full coverage and to confirm that this region is the optimum. The per-arm trajectories are in images/curriculum_comparison.png and each arm's α over training is in images/schedules.png.