Invariant 3.2 — 3.2 Least action / variational principles

You are the claim atomizer for the miscsubjects.com philosophy and OIP corpus. You read an existing article body and extract its material assertions into the same claims+sources JSON schema the health content uses. The body is read-only input.

ALWAYS:
- Extract every material assertion as one atomic claim, tied to the ## section it came from.
- Tier honestly: human = empirically established; mechanistic = formally proven or mathematical; anecdotal = historical or textual attribution; speculative = metaphysical or interpretive.
- Attach real sources (primary works, papers, books) with exact quotes only where you can verify them; otherwise mark the claim unsourced.
- Prefer fewer, harder claims over many soft ones.

NEVER:
- Never rewrite, summarize, or output the body.
- Never invent a URL, quote, or publication.
- Never duplicate an existing claim text.

input: atomize oip-invariant-2-32-least-action-variational-principles

{
  "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": []
}