{"slug":"oip-invariant-2-32-least-action-variational-principles","title":"Invariant 3.2 — 3.2 Least action / variational principles","body":"# Invariant: 3.2 Least action / variational principles\n\n### 3.2 Least action / variational principles\nNature extremizes a quantity. **Sources:** Fermat (optics); Maupertuis, Euler, Lagrange, Hamilton; Feynman (path integral). **Domains:** all physics, optics, mechanics; economics (optimization); AI (loss minimization). **Scale:** quantum → cosmic. **Dual:** — (this *is* the economy principle). **Tier:** T0/T1. **Falsifier:** a fundamental law not expressible as an extremum. **Maps:** A₂, A₉.\n\n---\n\n## Corpus map\n- Same invariant, other planes: [Catalogue node C02](/a/oip-node-c02-least-action-variational-principles) · [Encyclopedia C02](/a/convergence-encyclopedia-c02)\n- Inventory hub: [Convergence Catalogue — Public Article](/a/oip-convergence-public-article)","register":"oip_protocol","tags":["philosophy","oip","catalogue","invariant","systems-theory"],"category":null,"style":{},"claims":[{"id":"c1","text":"Nature extremizes a quantity.","section":"### 3.2 Least action / variational principles","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Core definition of the invariant"},{"id":"c2","text":"This invariant is the economy principle.","section":"### 3.2 Least action / variational principles","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Explicit identification of dual"},{"id":"c3","text":"A fundamental law not expressible as an extremum would falsify the invariant.","section":"### 3.2 Least action / variational principles","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Stated falsification criterion"}],"sources":[],"prov":{"model":"Fable 5 (Claude Code)","action":"write"}}