Weight-repairs v1: the two named C-PILOT repairs, re-run on the frozen gate

Prep leg, prep/weight-repairs. Repairs P2 and P3 named in TECHNICAL_P2_ROUTEC_PILOT_V0.md §4, implemented in solver/weight_search.py, gated in test_weight_search.py. Code: experiments/p2_weight_repairs_v1.py → writeup/data/p2_weight_repairs_v1.json → fig48. Deterministic, ~140s.

VERDICT: still FAIL, 4/6: unchanged in count, moved in substance. P2's finite fraction rises from 0.775 to 0.875 (threshold 0.90). P3's raw numbers are now an honest accounting of what a floating-point probe can validate at all, rather than an assumption that one global grid was linear for all forty roster weights. Neither repair was tuned against this run's own numbers; both constants were fixed in the code before it ran. The GA remains banned, and a same-day PASS would not have lifted the ban either, only the next planning pass may act on a gate result (ORCHESTRATION.md lane 6, plan_of_record.py).

0. What was named, and where

TECHNICAL_P2_ROUTEC_PILOT_V0.md §4 ran the frozen six-property gate on the certificate-weight fitness log10(Y0/budget) and reported:

and closed with: "The repairs are named and neither is research: carry the measured lower wall in the box as the analytic one already is (P2), and state the fitness's defect-tracking accuracy as a resolution rather than assuming it is exact (P3)." This leg implements both, exactly as named, and re-runs the identical frozen predicate.

1. P2: carrying the measured lower wall

1a. The mechanism

solver/weight_search.py already had an analytic upper wall on the search box: Ω₀ ~ −1/X, so a weight ν ~ |X|^(p+q) gives the TRUE profile infinite weighted sup norm past p+q = 1, and in_box() enforced p+q ≤ WALL_POWER − WALL_DELTA as a hard constraint, derived before any run.

It also already had lower_wall(), leg 49's §5 measurement of a second, non-analytic wall: bisect the far-field power on a single-power slice and find where Z₁ crosses 1. Past that point A = DF⁻¹ stops being an approximate inverse in the norm at all, so the fitness has no budget to report at ANY residual: this is float conditioning (κ(DF)·ε_mach), not a property of the equation. lower_wall() was measured but never carried into in_box(), so the roster (and the grid search) kept sampling into a region already known, before the run, to be doomed. Every one of leg 49's 9 censored roster weights had far-field power p+q ≤ −2.41, below lower_wall()'s measured p₋ = −3.68 to −3.74 at n=201.

1b. The repair

def in_box(theta, lower_wall_power=None):
    ...
    if ffp > WALL_POWER - WALL_DELTA:
        return False
    if lower_wall_power is not None and ffp < lower_wall_power + WALL_LOWER_DELTA:
        return False
    return True

WALL_LOWER_DELTA = 0.05, symmetric with the existing WALL_DELTA margin on the upper wall. FitnessEngine carries lower_wall_power as an attribute (None reproduces the pre-repair behaviour exactly: every existing caller that does not pass it is unaffected); roster() and FitnessEngine.fitness_many's box filter both thread it through. six_property_gate measures lower_wall(eng_c) and lower_wall(eng_f) once per resolution and sets it on the corresponding engine before drawing the roster.

1c. The result: real, and honestly incomplete

Still FAIL. The wall carried here is a one-parameter slice: lower_wall() bisects on ν = (1+X²)^(p/2), i.e. q=0, L=l=1, and leg 49 §4b already recorded the converse does not hold in general: "a finite weight exists at −4.04" below the measured wall, because the search's actual two length scales L, l decide where the decay begins, not just how fast. Carrying a 1-D proxy for a genuinely higher-dimensional boundary buys real ground (9 censored → 5) without closing it. Fig48 panel B shows the roster against both walls: the repaired box has no draws left in the region the 1-D wall rules out, and the remaining censored weights are ones the slice approximation misses.

2. P3: the defect-tracking accuracy is a resolution, not an exactness

2a. The mechanism

Leg 49's defect_ladder pushed the converged state off the solution by ε in a fixed direction and checked Y₀ fell linearly (F(z*+εd) = εDF·d + O(ε²), so the fitness must fall with slope exactly 1 per decade: a real known answer). It tested every roster weight on one global ε grid, 10⁻²…10⁻⁶.

The diagnosis in §4a already located the problem: ‖A‖_w (the operator norm the linearization's remainder is measured against) spans three orders of magnitude across the roster (naive 1.69e8, leg 46's tuned 1.69e6, the searched optimum 3.37e5). The linear regime only begins once ε ≲ 1/‖A‖_w. A single grid that is comfortably linear for the searched weight (ε_max ≈ 3e-7) is already well past linearity for the naive weight (ε_max ≈ 6e-9) at the SAME grid points, so testing all weights on one grid measures the probe's own breakdown at the high-‖A‖_w end, not a genuine fitness defect there.

2b. The repair

DEFECT_WINDOW_C = 0.1
DEFECT_EPS_DEFAULT = (1e-2, ..., 1e-11)   # extended to 10 points
DEFECT_MIN_WINDOW = 3

def defect_ladder(problem, z_star, engine_thetas, direction=None, eps=None):
    ...
    a_norms = [certificate_constants(...)['A_norm'] for each theta]
    eps_max = DEFECT_WINDOW_C / a_norms          # PER-WEIGHT window
    for each weight:
        mask = eps <= eps_max[weight]
        resolved = (mask.sum() >= DEFECT_MIN_WINDOW) and all finite
        if resolved: fit slope, check monotonicity WITHIN the window

DEFECT_WINDOW_C = 0.1 is a factor of 10 inside the empirically-located onset of nonlinearity (ε ~ 1/‖A‖_w), fixed once in the module before this leg's numbers were measured. The ε grid was extended down to 10⁻¹¹ so that even the highest-‖A‖_w roster weights (up to ~1e9) can have at least DEFECT_MIN_WINDOW = 3 grid points inside their own window: 10⁻¹¹ still perturbs an O(1) state by far more than double-precision roundoff (~2e-16 relative), so this does not trade one numerical artifact for another.

six_property_gate now reports, per weight: whether it was resolved at all (window had ≥3 usable points), and if so, its fitted slope and whether it decreased monotonically INSIDE that window. Weights with too few points are reported as unresolved rather than silently included in a global pass/fail, this is the "resolution" the repair asks for: not "the fitness is exact everywhere," but "here is how much of the roster this probe can even certify, and how well the certified part tracks the known answer."

2c. The result: the honest number is worse-looking and more trustworthy

Still FAIL against the frozen 0.05 threshold. The repair does not manufacture a pass: it exposes that 19 of 40 roster weights cannot be validated by this probe design at all, because their ‖A‖_w is high enough that even ε = 10⁻¹¹ does not buy three usable points inside the linear window. Among the 21 that CAN be validated, 8 now show monotonicity violations that leg 49's coarser, ε≥10⁻⁶ grid never saw: the most likely reading is float64 roundoff noise at the smallest usable ε for those weights (a different failure mode than leg 49's diagnosed nonlinearity, and this leg does not claim to have fixed it; it is reported as found). Fig48 panel C shows the window-size distribution across the roster: it is bimodal, not a smooth degradation, which is itself worth recording rather than averaging away.

3. What moved, what didn't, and why the gate still says no

Neither repair was chosen, retroactively, to make a threshold. Both constants (WALL_LOWER_DELTA = 0.05, DEFECT_WINDOW_C = 0.1) are committed in solver/weight_search.py and were fixed before six_property_gate was re-run: the same discipline the frozen thresholds themselves follow, and the one leg 49 explicitly invoked when it declined to retune P3's threshold after seeing it miss.

P4–P6, P1 and P5 are unaffected in verdict (all still PASS) though P1/P5's spread number shifts slightly (15.02 → 12.69 decades) because the roster itself is different: the P2 repair removed the lowest-far-field-power draws, which were also some of the most negative (best) fitness values, so the spread narrows a little as a direct, expected consequence of the repair working.

The gate is FAIL, 4/6, honestly measured, with both named repairs done. The remaining gap on P2 is a dimensionality problem (a 1-D wall proxy for a 2-D boundary); the remaining gap on P3 is that fewer than half the roster is even probe-able at double-precision, and the probe-able half still misses the 5% threshold at its worst point. Both are further, specific engineering questions, not the same two questions this leg answered, and not answered here.

4. The ceiling

No link of the L1 → L4 chain moved. The object underneath this fitness is the a=0 CLM profile, closed form since 1985; nothing here is a certificate, and no novelty is claimed for the repairs (they are named engineering, not method). Per ORCHESTRATION.md lane 6 and plan_of_record.py, the GA ban stands regardless of this result: a same-day 6/6 would not have authorized GA compute today either; only the next planning pass may act on a gate result, and this one still says FAIL.