Define the falsifiable question
Translate the idea into state variables, observables, assumptions, and an outcome that can fail.
METHOD / REPRODUCIBILITY / CLAIM CONTROL
Methodology
The purpose of a numerical study is not to obtain an attractive plot, but to construct a testable chain in which a favourable regime survives required controls and failure modes remain visible.
01 / EVIDENCE LADDER
Claim levels are not interchangeable
Every study page states what type of result is presented and what it does not establish.
| Level | What it means | Boundary |
|---|---|---|
| Hypothesis | A proposed mechanism | No result yet |
| Numerical result | An observable from one calculation | Requires robustness checks |
| Simulation study | A documented series under one model | Bounded by equations and parameters |
| Numerical PoC | A linked chain of controls and stress tests | Supports a mechanism at model level |
| Laboratory validation | An independent physical experiment | Tests correspondence with reality |
| Experimentally confirmed result | A reproducible physical measurement | Not automatically industrial readiness |
02 / WORKFLOW
Six required transitions
The exact tests change with the physics of the problem; the verification logic remains stable.
Build the smallest defensible model
Choose equations, discretisation, boundaries, initial conditions, and diagnostics appropriate to the question.
Establish controls and balance checks
Add passive, null, negative, ablation, conservation, and numerical-validity controls before interpreting a favourable branch.
Run a structured experiment campaign
Sweep parameters, seeds, perturbations, and resolutions; retain negative and failure results.
Audit robustness and claim boundaries
Separate model-level evidence from assumptions, artefacts, untested extrapolation, and laboratory claims.
Package evidence and the next test
Deliver reproducible methods, diagnostics, limitations, and an explicit laboratory or engineering follow-up.
03 / CONTROL SET
Typical control set
Not every project needs every item, but omissions must be justified.
Balance and invariants
Mass, energy, fluxes, constraints, and numerical error.
Passive and null baselines
What happens without the claimed mechanism or controller.
Negative control
A configuration expected to destroy the target effect.
Mechanism ablation
Removal of a term, channel, or feedback pathway.
Seeds and initial states
Dependence on a specific realisation.
Grid and timestep
Discretisation, resolution, and timestep dependence.
Noise and perturbations
The range before degradation or collapse.
Metric triangulation
A coherent observable set rather than one convenient score.
Extrapolation boundary
What cannot be transferred to hardware without experiment.
STANDARD DISCLAIMER
This work is a numerical proof-of-concept. It establishes model-level behaviour under the stated assumptions and does not replace independent laboratory validation.