TECHNICAL, Route-WVR v1 (leg 160): a different fitness DEFINITION, and P3 still does not move

Runner experiments/p2_route_wvr_v1_fitness.py; evidence experiments/p2_route_wvr_v1_fitness_evidence.py; data writeup/data/p2_route_wvr_v1_fitness.json; figure writeup/figures/fig64_route_wvr_v1_fitness.png (fig64); novelty pass writeup/novelty/leg_160.md; journal experiments/journal/leg_160.md. Every number below is in the JSON and is re-derived from it by the evidence script.

No GA compute ran, on either branch of this leg's gate. plan_of_record.py bans it on an unvalidated fitness; the runner imports nothing from ga/ and the evidence script asserts that by reading the runner's own source. The gate answered NO, so the ban's lift condition is not met and nothing about the ban changes.

1. The object, and what a "definition" means here

solver/weight_search.py scores a weight θ = (p, log10 L, q, log10 l, log10(w_l/X_max)) on BorderedCLM (the a = 0 CLM steady system bordered with (c_l, c_ω) as implicit unknowns, exact profile Ω_0(X) = −4X/(1+4X^2)) by

f_0(θ) = log10( Y_0(θ) / budget(θ) ),   budget = (1−Z_1)^2/(2 Z_2),
Y_0(θ) = max_i w_i |(A F(z))_i|,        A = DF(z)^{-1} in float64,

in the weighted sup norm on z = (Ω, c_l, c_ω), same weight on domain and codomain.

Legs 46/49/50/59 all score f_0 and differ only in the box the search runs in. This leg changes f_0 itself. Both candidates were written into the runner's module docstring, with their predicted failure modes, before any number was computed (leg 111's pre-naming discipline; the runner's first commit is the record).

2. What was frozen, and the mechanism that guarantees it

FROZEN, untouched, and identical to leg 59's list: all six thresholds (P1_SPREAD_MIN 1.0, P2_FINITE_FRAC 0.90, P3_MONO_VIOLATIONS 0 and slope-error 0.05, P4_RANK_RHO_MIN 0.90 / P4_TOP3_OVERLAP 2, P5_BAND_MIN 2.0, P6_INTERIOR_FRAC 0.05), the roster construction (2 controls + 6 degenerates + 32 random, seed 0), the resolutions (n = 201 / 401), the search settings (per_gene=9, refine=4), the defect grid DEFECT_EPS_DEFAULT, the window constant DEFECT_WINDOW_C = 0.1, DEFECT_MIN_WINDOW = 3, the probe direction, and the 2-D wall model.

solver/weight_search.py is read-only under this leg (DIRECTION.md leg 160 territory) and is not edited. The gate is not reimplemented: six_property_gate is executed unmodified, and a context manager substitutes the class the name weight_search.FitnessEngine resolves to for the duration of the call. Consequence worth stating plainly: not one frozen threshold is copied into this leg as a literal, so a constant cannot drift here without drifting in the module, and the evidence script re-reads the thresholds out of the module to confirm.

CHANGED: only the score. Four modes, two of them controls.

3. The three definitions, as run

τ is computed by each engine at its own state, so WVR-2 needs no reference state and is usable by a searcher. hiprec is labelled a realization control throughout (standing discipline 70) and is not offered as an answer to the gate.

4. The identity control, run before anything was believed

The substitution must reproduce leg 59 bit-for-bit. It does, on all six banked quantities:

5. THE GATE, at the frozen configuration n = 201 / 401

The gate answers NO. P3 is the only property that fails in three of the four modes, and it has now survived three different kinds of repair:

the BOX          leg 50 (1-D wall), leg 59 (2-D wall)   P3 moved by  0.0000000000
the DEFINITION   this leg, WVR-1 and WVR-2             P3 moved by +0.6579, +0.6918
the REALIZATION  this leg, hiprec control              P3 moved by −0.0102288110805537

−0.0102 is the first movement toward the threshold since leg 49, and it closes 3.5% of the 0.2921 gap to the frozen 0.05 ceiling. It comes from the control, not from a candidate.

6. Why WVR-1 fails, and it is a statement about P3

Pre-registered before the run and confirmed: dropping Y_0 makes the score nearly independent of the injected defect, so the ladder's fitted slope is ≈ 0 and |slope−1| ≈ 1. That is not under-tuning. P3, as frozen, hard-codes that the fitness must be a defect-magnitude proxy: it admits only scores of the form log10(c·‖z − z*‖ + …). Any definition that scores the norm's quality rather than the state's residual is rejected by construction, including the one leg 49's own gauge ablation argues for (its whole 5604× lives in Y_0's border rows, i.e. in preconditioning, not in the choice of space).

So the space of definitions P3 can accept is far narrower than "a fitness for a searched certificate norm", and within it the only free choices are the norm and a prefactor: neither of which touches the floor. This is the structural reason the definitional route was always thin, and it is measured here rather than argued.

7. Why WVR-2 fails, measured

WVR-2 subtracts the state's own arithmetic floor componentwise and adds it back once as an anchor. The failure is in the estimator, not the idea. The floor a single-state definition can compute is

τ = 8 · |A| @ |F_float64(z) − F_longdouble(z)|      (absolute values: NO cancellation)

while the floor actually present in the ladder is

ρ = A F(z*)                                          (signed: it cancels)

Measured at n = 201 (over_subtraction in the JSON):

||tau||_inf                         1.2999035590373247e-09
||rho||_inf                         4.790972900601766e-11
ratio                               27.132350485097742
median componentwise tau/|rho|      27.138837074030103
fraction of components over-subtracted   0.9950738916256158

So the estimator over-subtracts by 27× on 99.5% of components. ‖τ‖_∞ = 1.30e-09 sits inside the probe window, the window's top is C/‖A‖_w ≈ 2.8e-08, so roughly two of its ~3.4 decades are annihilated before any floor is removed, and the score goes defect-blind (P3 = 1.0339015518487575). At n = 101, where there is signal to spare, the same definition leaves some (P3 = 0.2744581497130689): still 3.8× worse than doing nothing, and the ratio there is 44.6×.

The idea of subtracting is not what fails. The estimator does, and it fails for a reason that is structural rather than tunable: any floor estimate a single-state fitness can build has to bound a signed quantity by an absolute-value expression, and the cancellation it throws away is exactly the factor that makes it useless as a subtrahend.

8. What P3 actually measures, reconstructed, not correlated

Credit first. Leg 59 banked this mechanism for this exact object and deliberately left it out of the frozen gate: its D_probe_window block carries per-weight eps_min_noise_floor = Y_0 / max_i w_i|d_i|, reports Spearman(window width, |slope−1|) = −0.8779220779220779 over 21 weights, and its reading field already says "this is a defect in the FITNESS's definition, not in the box the wall model draws". The general principle is older and belongs to Moré–Wild (ECnoise) and the Berahas–Byrd–Nocedal / Shi–Xie–Xuan–Nocedal derivative-free-optimization interval literature: a finite-difference probe has a two-sided window, capped above by truncation and floored below by the function's own noise. defect_ladder has the upper cut (leg 50's DEFECT_WINDOW_C = 0.1/‖A‖_w) and no lower cut: the grid runs to eps = 1e-11. This leg claims neither.

What is this leg's. Writing A F(z* + eps d) = eps d + ρ + O(eps^2) with ρ = A F(z*), the ladder can be rebuilt from ρ alone, with no PDE evaluation at any perturbed state, and each weight's fitted slope predicted in the same frozen window. Over the 21 resolved weights:

max |predicted − measured| slope   0.058
median                             0.021
predicted worst |slope−1|          0.3057   vs measured 0.3421  (under by 0.0365, 11%)

The 11% is the first-order model's own missing O(eps^2) term and is reported as its error, not absorbed. A correlation of −0.878 is consistent with several mechanisms; a reconstruction is consistent with one.

Supporting magnitudes:

||F(z*)||_inf                6.661338147750939e-15      the converged residual
float64 evaluation noise     2.432759939677287e-15      |F_float64 − F_longdouble|
residual_floor(z*)           1.9462079517418296e-14     the module's own estimate
||rho||_inf   (n = 201)      4.790972900601766e-11      4.8x ABOVE the grid bottom
||rho||_inf   (n = 101)      4.640571829290985e-13      21x BELOW it
frozen grid bottom           1e-11                      does not move with n

16 of the 21 resolved weights are probed below their own floor at n = 201 (worst knee 7.89e-11, i.e. 7.9× the grid's bottom rung). And the arithmetic that produces the knee is checked against the predecessor rather than asserted: this leg's knee_eps and leg 59's eps_min_noise_floor are the same quantity, and they agree on all 21 shared weights to a worst relative difference of exactly 0.00e+00 (evidence check 8).

9. The resolution ablation: labelled, and NOT a second chance at the gate

Coarsening the grid lowers ‖A‖_w, lowers ρ by 103×, and leaves the frozen eps grid where it is. If the floor is what P3 measures, every defect-tracking mode must improve and the one defect-blind mode must not.

WVR-1 is the control that could have come out differently and did not. It dropped Y_0, so it is defect-blind by construction; a knob that moves every defect-tracking score by 3.8× to 34.9× and moves the defect-blind score by 0.99998× is acting on the defect's floor and on nothing else.

9a. The finding in this table that is not the gate answer

The unmodified, unrepaired leg-49 fitness passes the frozen six-property gate 6/6 at n = 101/151. Nothing was repaired to achieve it. plan_of_record.py's ban lifts on "a re-run of the six-property gate that PASSES on a repaired fitness", and that wording pins neither the resolution nor what "repaired" means, so as measured, the lift condition is reachable by coarsening the grid. That is a false pass in exactly Gate 4's sense.

This leg reports it and does not use it. The frozen configuration is n = 201/401; the gate answer is read off that alone and it is NO; no GA compute ran. Whether the ban's wording should pin the resolution is the user's call, not this leg's and not the DM's.

10. C3: the tension between P1/P5 and P3

P1 and P5 require ≥ 1 and ≥ 2 decades of spread at the converged state; P3 requires exact linearity in an injected defect down to eps = 1e-11. A fitness positively homogeneous of degree 1 in the defect vanishes at the converged state, so it has no spread there and fails P1/P5. Hence every fitness satisfying P1/P5 carries a nonzero floor at z*, and every floor saturates the ladder's small-eps end and costs P3. The two are jointly satisfiable only when the floor sits below the window's bottom decade: a statement about arithmetic and grid, not about the fitness's definition. WVR-2 is precisely the attempt to have both (subtract for P3, anchor for P1/P5); the anchor is what caps it. Nothing in the record states this; it is elementary once §8 is stated, and it is presented as an observation with a measured consequence, not as a named theorem.

11. A correction this leg owes on its own prediction

The runner's first docstring predicted that leg 59's ladder slopes would repeat identically to 16 digits across weights, cited 0.8378100167662509 as appearing twice, and invoked lesson 90. The data refutes it. Leg 59's 21 finite slopes have zero exact duplicates; the two entries are 0.83781001 and 0.83781002, differing in the 8th digit. Lesson 90's identical-numbers tell does not apply here.

The weaker, measured statement does hold and is what is claimed: the 21 slopes fall into 10 clusters at relative tolerance 1e-3 (12 at 1e-5, 17 at 1e-7). Weights whose weighted max selects the same component share a slope to about three significant figures; the residual spread is the O(eps^2) term plus the budget's own eps-dependence. The correction is in the docstring, in the JSON's slope_degeneracy note, and is asserted as evidence check (10) so it cannot quietly revert.

12. The ceiling

No link of the L1→L4 chain moved. This is a property check on a float fitness over the a = 0 CLM linearisation, whose profile has been closed form since CLM 1985: a rehearsal of a certificate, not a certificate. It says nothing about HL_S2_nonsymmetric. It does not reopen stage B, which leg 126 closed on the search space independently of the fitness. The GA ban stands, its lift condition is unmet, and lifting it was never this leg's to do.