H0199: reconcile the saved numbers

Report lines 94–96 say four distributed witnesses at 1.6% beat 36 edge witnesses. The saved n_sweep instead gives four-grid 1.609537%, 36 edge 0.773497%, and 36 grid 0.318889%. Lower RMSE is better. At equal count, four-grid beats four-edge 9.514729%, and 36 grid beats 36 edge. The original cross-count claim is reversed.

Source: REPORT.md:94–96; JSON /n_sweep indices 0,1,10,11; code/h0199.py:178–184

The main quadratic-fit sweep gives edge 1.916313% versus grid 0.789271% RMSE for the linear field. The separately saved degree-1 fit gives edge 0.429855% versus grid 0.494446%; edge is lower there. This supports estimator-dependent comparisons, not a universal tie or universal superiority of distributed grids.

Source: REPORT.md:115–118; JSON /main indices 0,1 and /degree1 indices 0,1; code/h0199.py:152–168

In the saved smooth-random-field rows, random placement has 3.714480% RMSE, grid 4.302867%, jitter 4.725026%, edge 7.138894%. This is an ordering of the saved rows only. Random placement is also distributed, so “distributed wins” should not be paraphrased as “a grid always wins.” The GP implementation issue below prevents promoting these numbers as a valid matched-field comparison.

Source: REPORT.md:40–58; JSON /main indices 20–23

Static inspection shows field("gp",X) divides its random basis sum by max(abs(g)) evaluated on the supplied coordinates. trial() calls it separately for reactive and witness positions. The same seed therefore need not produce the same normalized field at both sets. The intended common-field measurement model is not consistently implemented. Preserve the main gp rows, degree1 gp rows and ell_sweep as supplied outputs, but withhold their physical/design interpretation until this issue is repaired and a separately versioned rerun is checked. No replacement GP values are asserted here.

Source: code/h0199.py:47–54,114–131; JSON /main indices 20–23, /degree1 indices 10–11, /ell_sweep

The source defines gy_estimator and an estimator_kind branch. Every run_sweep trial call uses the default estimator_kind="poly". The saved results cannot substantiate the report’s statement that a Gaussian-process estimator variant “is also run.” A random field family called gp is distinct from GP reconstruction.

Source: REPORT.md:28–30; code/h0199.py:104–115,132–135,146–193

The main and degree1 blocks use 400 seeds. The correlation-length, witness-count and unity_eps blocks use 200. Five field families are deterministic; for those, the seeds change noise and, where relevant, layouts rather than draw a new field. The code uses additive Gaussian noise with standard deviation 0.02 in the simulated signal units. The estimator error is relative; the noise itself is not explicitly multiplied by local signal amplitude.

Source: REPORT.md:28–31,38; code/h0199.py:35–46,119,131,154,165,174,182,190–191

The saved model is f=1+0.5sin(πx)sin(πy). Its total field equals 1 on the boundary. Only the added bump is zero there. The main edge result has 22.863542% mean relative bias and 23.116270% RMSE; these are different metrics. Boundary-only data cannot distinguish arbitrary interior fields sharing the same boundary trace without additional interior constraints. The specific roughly 23% estimator bias is not a universal value for every field, estimator or witness count.

Source: REPORT.md:10–13,62–75; JSON /main index 16; code/h0199.py:45–46

n_sweep uses radial_edge, not boundary_null. unity_eps also uses radial_edge despite its “field that vanishes” code comment. The supplied file does not contain a boundary_null sweep across witness counts. A structural non-identifiability argument survives, but these arrays do not demonstrate a fixed 23% bias at every number of blanks.

Source: REPORT.md:70–71,94–96; code/h0199.py:178–193; JSON /n_sweep and /unity_eps

The quadratic reconstruction has six coefficients. With only four witnesses it is underdetermined; least squares selects a minimum-norm solution. The eight edge points also have a quadratic ambiguity: all lie at the same distance from the center, so a nonzero radial quadratic vanishes at those sample locations. The grid generator keeps the first n points from a ceil(sqrt(n)) square grid: at n=12 it keeps three rows of a 4×4 grid. These finite point layouts should not be advertised as uniformly optimized designs.

Source: code/h0199.py:59–75,89–101; JSON /n_sweep

In the main linear-field rows, edge bias is −0.085248% and standard deviation 1.914415%; grid bias is 0.032817% and standard deviation 0.788589%. The RMSE advantage is mainly a spread/noise-amplification difference in that comparison. Large bias dominates other examples such as edge_enhanced. Report bias and spread separately rather than attributing every gain solely to bias.

Source: REPORT.md:120–122; JSON /main indices 0,1,12,13

The saved finite cases do not prove that edge placement is defensible only for monotone fields, nor that every radial field is invisible at an edge. The explicit radial_edge example is a quadratic represented by the default model. The correlation-length rule depends on the flagged GP rows. Equal witness counts do not demonstrate identical engineering costs or patch areas; the code samples points and does not model fabrication, shadowing or laboratory cost.

Source: REPORT.md:51–58,73–92,100–111; code/h0199.py:39–44,59–85

At ell=0.8 the saved edge RMSE is 4.249114%, which rounds to 4.2% at one decimal place rather than 4.3%. The README’s 0.8–1.0% distributed-error headline excludes the saved gp rows. Preserve those originals, but attach their finite-case and GP-status qualifications before reuse.

Source: REPORT.md:82–85; README.md:9–12; JSON /ell_sweep index 8