miscsubjectsAI governance
Object Invocation Protocol · protocol specification

Invariant 3.16 — Networks / small-world / scale-free

Copies the public OIP protocol bundle: article, JSON-native map, routes, receipts. No owner token.

§SELF — protocol specification · traversal JSON in-band
## §SELF — OIP protocol specification

**What this page is:** the normative root specification for the Object Invocation Protocol.

**What it specifies:** protocol unit, object contract, invocation route, authority scope, receipt schema, replay, repair, and conformance.

**Read:** https://miscsubjects.com/a/oip-invariant-16-316-networks-small-world-scale-free
**This page as JSON:** https://miscsubjects.com/api/articles/oip-invariant-16-316-networks-small-world-scale-free
**Machine bundle:** https://miscsubjects.com/api/articles/oip-invariant-16-316-networks-small-world-scale-free/bundle?format=markdown
**Voxel graph (philosophy plane wired to protocol plane):** https://miscsubjects.com/api/articles/oip/voxels
**Live object tree:** https://miscsubjects.com/api/dispatch?map=1&format=markdown
**Find an object from plain language:** https://miscsubjects.com/api/dispatch?ask=<what you want>
**Read one object:** https://miscsubjects.com/api/dispatch?key=<KEY>&format=markdown

**Proof rule:** an action is not proven by intent, description, or a 200. It is proven by the ledger and the OIP receipt for the invocation.

Connectivity converges on a few topologies. Sources: Euler (graph theory); Watts–Strogatz (small-world); Barabási (scale-free, preferential attachment); Granovetter (weak ties). Domains: neurons, internet, food webs, metabolism, society. Dual: regular lattice vs random graph (small-world sits between — a criticality echo). Tier: T1. Falsifier: large adaptive networks that are neither small-world nor scale-free. Maps: A₃, A₇. (Your voxel graph is itself an instance.)

---

Corpus map

Key evidence

3 claims · tier-ranked · API
human
Domains exhibiting the topologies include neurons, internet, food webs, metabolism, and society.
mechanistic
Connectivity converges on a few topologies.
mechanistic
Small-world networks sit between regular lattice and random graph as a criticality echo.
Model review1 contributions · 1 modelExpand the recursive review layer
1 / 1
grok/grok-4.3atomizer
atomize2026-07-07 08:11
atomize · 3 claims
inspect — what it was prompted & output
prompted with
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-16-316-networks-small-world-scale-free
it output
{
  "claims": [
    {
      "id": "c1",
      "text": "Connectivity converges on a few topologies.",
      "section": "## 3.16 Networks / small-world / scale-free",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Core invariant stating convergence of network structures."
    },
    {
      "id": "c2",
      "text": "Domains exhibiting the topologies include neurons, internet, food webs, metabolism, and society.",
      "section": "## 3.16 Networks / small-world / scale-free",
      "tier": "human",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Specifies empirical scope of the convergence claim."
    },
    {
      "id": "c3",
      "text": "Small-world networks sit between regular lattice and random graph as a criticality echo.",
      "section": "## 3.16 Networks / small-world / scale-free",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Defines the dual positioning of small-world topology."
    }
  ],
  "sources": []
}
507cfdb9ecd13563
Machine verification: /api/articles/oip-invariant-16-316-networks-small-world-scale-free/contributions