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Iron Laws Corpus

Append-only corpus of validated heuristics — iron laws — for solver design. Each law names a condition, a recommended atom or technique, and the evidence base. Future agent sessions consult this corpus instead of re-deriving choices.

Domain
general
Contributors
@pourion
Source essay
Toward a Simulation Organism
Tags
knowledge-base · heuristics · solver-design
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Iron Laws Corpus

Durable, append-only collection of validated solver-design heuristics. Each entry names a condition (when this rule applies), a recommendation (which atom or technique to use), and the evidence base (how we know).

Status: draft. Bootstrapped with two illustrative laws from the founding essay. Future contributors append validated heuristics from their own experiments. New entries should cite the experimental or analytical evidence that supports them.

Why iron laws

An iron law is a heuristic that has survived enough experiments across enough problem classes that the agent stops re-deriving it. Skills compound: when laws accumulate, the agent's effective starting point on a new problem improves monotonically.

Format

Every law has the same shape:

- id: <slug>
  condition: <when does this apply?>
  recommendation: <which atom / technique?>
  evidence: <citations or experiment IDs>
  added: <YYYY-MM-DD>
  status: provisional | validated | iron

Current laws

prefer-implicit-time-stepping-for-stiff-systems

  • Condition: Stiff time integration (largest eigenvalue ≫ smallest, e.g. chemical kinetics, advection-diffusion with disparate scales).
  • Recommendation: Implicit (BDF, Radau) time integrator over explicit RK.
  • Evidence: Classical numerical-analysis result; verifiable on Robertson and Van der Pol test problems with order-of-magnitude wall-clock difference.
  • Added: 2026-05-21 · Status: provisional

decompose-residuals-spatially-before-frequency-analysis

  • Condition: Diagnosing a stubborn simulation-experiment gap.
  • Recommendation: First localize the residual by region of interest; then, if the region is identified, decompose by frequency band within that region.
  • Evidence: Practitioner heuristic; derives from [[missing-physics-detector]].
  • Added: 2026-05-21 · Status: provisional

How to add a law

Open a PR adding a new section above. Include the citation or experiment ID that supports the rule. The maintainers review against the agent's accumulated corpus before promoting a law from provisional → validated → iron.

References