T5: regulation as a constrained prior, fitted all at once
Synthetic, dimensionless population of 200 coupled two-sensor neurons (n = 3, k = 2, mean-field coupling 0.4); no organism result. Proposal T5 in spec/13-proposals.md.
Gates: 15/15 passed.
| Fit | θ = (s*₁, s*₂, Nᵀμ) | Error / SE | LM iterations | Network evaluations | Fixed-field cell evaluations | Seconds |
|---|---|---|---|---|---|---|
| Truth | (0.168, 0.136, -1.51) | |||||
| One-shot | (0.168, 0.136, -1.5) | (-0.709, -0.365, 1.69) | 5 | 7 | 0 | 0.0794 |
| Nested | (0.168, 0.136, -1.5) | (-0.709, -0.365, 1.69) | 5 | 122 | 201 | 0.364 |
| Measurement | Result |
|---|---|
| One-shot vs nested: max difference in θ / in adult states | 5.74e-12 / 1.76e-10 |
| Adult-state RMS error: fitted / raw expression observations | 0.0124 / 0.0194 |
| Certification: min loop-gain eigenvalue, per neuron / coupled network | 0.315 / 0.315 |
| Certification: basin check, max deviation after developing from 2.37 away | 6.35e-12 |
| Violation map, 10 idiosyncratic neurons of 200 with spread 0.03: AUC total / sensor-only; recall; false positives (χ²₄ 0.999) | 0.653 / 0.602; 0; 0 |
| Violation map, 10 idiosyncratic neurons of 200 with spread 0.06: AUC total / sensor-only; recall; false positives (χ²₄ 0.999) | 0.856 / 0.777; 0.5; 0 |
| Violation map, 10 idiosyncratic neurons of 200 with spread 0.1: AUC total / sensor-only; recall; false positives (χ²₄ 0.999) | 0.987 / 0.951; 0.8; 0 |
| Density with |det[J; Nᵀ]|: normalization ± SE / mean error (sd units) | 1 ± 0.004 / 0.00702 |
| Density without the determinant: normalization ± SE | 29.1 ± 0.115 |
| Gate | Passed |
|---|---|
| one-shot and nested reach the same estimate (< 1e-6) | yes |
| one-shot and nested reach the same adult states (< 1e-6) | yes |
| truth within 3 SE (one-shot) | yes |
| one-shot uses < 1/3 of nested network evaluations | yes |
| regulation prior sharpens adult states vs raw observations | yes |
| certified: every neuron's loop gain stable | yes |
| certified: coupled network loop gain stable | yes |
| certified: development from elsewhere on each slice returns (< 1e-8) | yes |
| violation map: lawful neurons' misfit near chi^2_4 mean (3-5) | yes |
| violation map: AUC grows with violation size | yes |
| violation map: AUC > 0.95 at the largest size | yes |
| violation map: at most 2 false positives per dataset at chi^2_4 0.999 | yes |
| density with det normalized (within 3 SE of 1) | yes |
| density with det reproduces forward mean (< 0.05 sd) | yes |
| density without det is not normalized (> 10 SE from 1) | yes |
Seed 3. Full values: report.json.