Fresh rerun | synthetic evidence
The k(L) trend does not survive its strongest control
We reran the 8-scale NSGA-II model with seed 42 after fixing a reversed robustness score and removing wall-clock noise from the objective. The original scale-specific bounds reproduce the familiar line. Giving every scale the same admissible k range reduces the fit and leaves only the Planck point away from zero.
Original scale-specific bounds
R^2 = 0.7096
k = -0.0137 log10(L) + 0.1585
Diagnostic fit only. Four lower bounds are 0.8, 0.5, 0.3, and 0.2, so this run partly prescribes the pattern it reports.
Common-bounds control: 0 <= k <= 1.5
R^2 = 0.4370
k = -0.0051 log10(L) + 0.0249
The model's own linear-pattern test fails. This refutes use of the archived formula as a validated physical lookup rule.
Fresh selected k values
Both runs use 40 generations, population 25, and the same deterministic seed 42.
| Scale | Encoded bounds | Common bounds |
|---|---|---|
| Planck | 0.8000 | 0.3973 |
| Femto (Nuclear) | 0.5000 | 0.0000 |
| Pico (Atomic) | 0.3000 | 0.0000 |
| Nano (Molecular) | 0.2000 | 0.0000 |
| Micro (Mesoscopic) | 0.0000 | 0.0000 |
| Macro (Human) | 0.0000 | 0.0000 |
| Solar System | 0.0000 | 0.0000 |
| Cosmological | 0.0000 | 0.0000 |
What remains useful
This is a reproducible synthetic stress test for how chosen objectives and admissible regions select k. It is useful for optimizer diagnostics and sensitivity analysis.
What is not established
The runs are not measurements from nature, validation against 16 independent papers, evidence that the universe chooses a calculus, or a physical prediction for an arbitrary length scale.
The k(L) lookup tool is retired
An earlier page offered a k-for-any-length-scale lookup built on the encoded-bounds fit. The common-bounds control above removes that trend, so the lookup no longer has a basis and has been withdrawn.
Reproduce it
python -m meta_calculus.multiscale_moo run --gen 40 --pop 25 --save
python -m meta_calculus.multiscale_moo run --gen 40 --pop 25 --common-bounds --save
Artifacts: results/multiscale_moo_results.json and results/multiscale_common_bounds_control.json