Invariant 3.9 — 3.9 Recursion / self-reference / strange loops

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-9-39-recursion-self-reference-strange-loops

{
  "claims": [
    {
      "id": "c1",
      "text": "Recursion, self-reference, and strange loops are structures that refer to and reproduce themselves.",
      "section": "## 3.9 Recursion / self-reference / strange loops",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Core definition of the invariant."
    },
    {
      "id": "c2",
      "text": "The sources of the invariant 3.9 are Gödel (incompleteness), Turing, von Neumann (self-replicators), Hofstadter (strange loops), the quine, and DNA.",
      "section": "## 3.9 Recursion / self-reference / strange loops",
      "tier": "anecdotal",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Explicit attribution of origins."
    },
    {
      "id": "c3",
      "text": "The domains of invariant 3.9 are math, logic, computation, mind, and biology.",
      "section": "## 3.9 Recursion / self-reference / strange loops",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Specifies scope of application."
    },
    {
      "id": "c4",
      "text": "The dual of recursion / self-reference / strange loops is flat hierarchy / no self-reference.",
      "section": "## 3.9 Recursion / self-reference / strange loops",
      "tier": "mechanistic",
      "source_ids": [],
      "so