## §SELF — miscsubjects (paste without context)

**Principle:** Self-explaining payload — no external context required. This _self block describes what you are reading and where to look next.

**This widget:** `article_bundle` — **LLM article bundle**
Paste-ready package: body + claims + sources + voxels + provenance + manifest + constitution.
- **article slug:** `oip-node-c11-networks-small-world-scale-free`
- **contains:** body, claims, sources, voxels, provenance, question graph, constitution, llm_manifest
- **how to use:** Paste entire block into Grok/GPT/Gemini. Section §SELF explains the system.
- **read:** https://miscsubjects.com/api/articles/oip-node-c11-networks-small-world-scale-free/bundle?format=markdown

### Logical proof (verify each step)
1. Articles are voxel graphs of tiered claims, not prose blobs. → https://miscsubjects.com/api/articles/constitution
2. Claims link to hash-chained sources via source_ids. → https://miscsubjects.com/api/articles/oip-node-c11-networks-small-world-scale-free/sources
3. Ask reads topology; ingest/claim append to ledger. → https://miscsubjects.com/api/protocol
4. Models queue growth: populate → collaborate → repair → reflex. → https://miscsubjects.com/api/protocol/grow
5. Graph proves its own shape (reflex) and $/claim (yield). → https://miscsubjects.com/graph.html?layer=reflex
6. Full feature index + _explain on every API response. → https://miscsubjects.com/api/articles/system-map

### Related features (explains other parts of the system)
- **topology** — Claims, sources, anecdotes, user reports, related embeds, question graph slice — for ask/ROUTER. · https://miscsubjects.com/api/articles/oip-node-c11-networks-small-world-scale-free/topology
- **voxels** — Claims as atoms, sources as edges (supported_by, posted_by). Per-claim provenance. · https://miscsubjects.com/api/articles/oip-node-c11-networks-small-world-scale-free/voxels
- **ask** — Answer only from topology; creates question_node with gaps and ingest_hint. · https://miscsubjects.com/api/articles/oip-node-c11-networks-small-world-scale-free/prompts
- **ingest** — Parse pasted evidence → source ledger + claims + evidence_ingest node.
- **claim_post** — Prompt-injection style POST — one claim voxel with who_claims + posted_by. · https://miscsubjects.com/api/articles/oip-node-c11-networks-small-world-scale-free/voxels
- **llm_manifest** — Machine-readable read/write contract for external LLMs. · https://miscsubjects.com/api/articles/llm-manifest

### Full index
- JSON: https://miscsubjects.com/api/articles/system-map
- Markdown: https://miscsubjects.com/api/articles/system-map?format=markdown

*Not medical advice. Tier-honest. Cite claim/source ids.*

---

# miscsubjects article bundle

> Paste this entire block into Grok, GPT, or Gemini. They can READ the ledger below and RETURN evidence via ingest (see § LLM manifest).

## Article
- **slug:** `oip-node-c11-networks-small-world-scale-free`
- **title:** Node C11: Networks / Small-World / Scale-Free
- **url:** https://miscsubjects.com/a/oip-node-c11-networks-small-world-scale-free
- **register:** oip_protocol
- **updated:** 2026-07-04T05:02:00.118Z
- **tags:** philosophy, oip, convergence-catalogue, node, systems-theory

## Body

# Node C11: Networks / Small-World / Scale-Free

C11 — Networks / Small-World / Scale-Free
{
  "id": "C11",
  "claim": "Connectivity in natural and social systems converges on a small set of topologies: small-world (high clustering + short path length) and scale-free (power-law degree distribution, a few hubs, many spokes).",
  "domain": ["neuroscience", "computer science", "ecology", "sociology", "molecular biology", "economics"],
  "pattern": ["small_world", "scale_free", "preferential_attachment", "hubs", "clustering"],
  "mechanism": "Small-world: start with a regular lattice and rewire a fraction p of edges randomly; at intermediate p, clustering remains high while average path length drops logarithmically. Scale-free: growth + preferential attachment ('rich get richer') produces power-law degree distribution P(k) ~ k^(-γ). Granovetter: weak ties bridge otherwise disconnected clusters.",
  "scale": "molecular → civilization",
  "claim_tier": "T1",
  "sources": [
    "Euler, L. (1736). 'Solutio problematis ad geometriam situs pertinentis.' Commentarii academiae scientiarum Petropolitanae, 8, 128-140.",
    "Watts, D.J. & Strogatz, S.H. (1998). 'Collective Dynamics of Small-World Networks.' Nature, 393, 440-442.",
    "Barabasi, A.L. & Albert, R. (1999). 'Emergence of Scaling in Random Networks.' Science, 286, 509-512.",
    "Granovetter, M.S. (1973). 'The Strength of Weak Ties.' Am. J. Soc., 78(6), 1360-1380."
  ],
  "dual": "Regular lattice (all local, no global reach) vs. random graph (no local structure, efficient paths but no clusters).",
  "falsifier": "Large adaptive networks (neural, social, metabolic, technological) that are demonstrably neither small-world nor scale-free — e.g., regular grids with no shortcuts, or homogeneous degree distributions in mature systems.",
  "rival_frame": "Network properties are statistical artifacts of growth processes, not convergent solutions to optimization problems. 'Scale-free' claims have been overstated — many real networks follow log-normal or exponential distributions; power-law fitting is often methodologically sloppy. Small-world structure is trivially expected in any spatially embedded growing network.",
  "independence_check": "HIGH. Euler (mathematics, Konigsberg, 1736) invented graph theory from a puzzle. Granovetter (sociology, Harvard, 1973) studied job-seeking networks. Watts-Strogatz (applied math, Cornell, 1998) modeled network clustering. Barabasi (physics, Notre Dame, 1999) derived preferential attachment. Four fields, four centuries, four questions, convergent finding: networks with efficient information flow look alike.",
  "pattern_type": "structural",
  "maps_to_axiom": ["A3", "A7"]
}

---

## Corpus map
- Same node, other planes: [Encyclopedia C11](/a/convergence-encyclopedia-c11) · [Inventory invariant](/a/oip-invariant-16-316-networks-small-world-scale-free)
- Edges touching C11: [convergence edge 8](/a/oip-convergence-edge-8) · [convergence edge 9](/a/oip-convergence-edge-9)
- Catalogue hub: [Public Article](/a/oip-convergence-public-article) · [Schema](/a/oip-convergence-schema)

## Claims (0)


## Voxel graph (0 atoms · 0 edges)
- full graph: https://miscsubjects.com/api/articles/oip-node-c11-networks-small-world-scale-free/voxels

## Article constitution

- full: https://miscsubjects.com/api/articles/constitution

## Source ledger (0)
- chain valid: yes · head: `genesis`

## Provenance (2 model passes)
- chain valid: yes · head: `7870c6e46edf97b7`

- edit · claude-fable-5 · 2026-07-04T04:34 · hash `038c51400d0f`
- edit · claude-fable-5 · 2026-07-04T05:02 · hash `7870c6e46edf`

## Question graph
- questions: 0 · evidence ingests: 0

## LLM manifest — how to communicate with this ledger

- system map: https://miscsubjects.com/api/articles/system-map?format=markdown
- topology (ranked): https://miscsubjects.com/api/articles/oip-node-c11-networks-small-world-scale-free/topology
- ingest: POST https://miscsubjects.com/api/protocol/ingest
- claim: POST https://miscsubjects.com/api/protocol/claim

### Quick actions for this article
- **Read live:** https://miscsubjects.com/api/articles/oip-node-c11-networks-small-world-scale-free/topology
- **Ask (API):** POST https://miscsubjects.com/api/protocol/ask `{"slug":"oip-node-c11-networks-small-world-scale-free","question":"..."}`
- **Ingest your findings:** POST https://miscsubjects.com/api/protocol/ingest or text `ingest oip-node-c11-networks-small-world-scale-free|your evidence`
- **Post one claim:** POST https://miscsubjects.com/api/protocol/claim or text `claim oip-node-c11-networks-small-world-scale-free|tier|assertion`
- **iMessage ask:** `oip-node-c11-networks-small-world-scale-free|your question`
- **System map:** https://miscsubjects.com/api/articles/system-map?format=markdown


---

## §SELF — miscsubjects (paste without context)

**Principle:** Self-explaining payload — no external context required. This _self block describes what you are reading and where to look next.

**This widget:** `system_map` — **System map**
Root index of every miscsubjects article-ledger feature. Start here if you have zero context.
- **article slug:** `oip-node-c11-networks-small-world-scale-free`
- **contains:** body, claims, sources, voxels, provenance, question graph, constitution, llm_manifest
- **how to use:** Root index of every miscsubjects article-ledger feature. Start here if you have zero context.
- **read:** https://miscsubjects.com/api/articles/system-map

### Logical proof (verify each step)
1. Articles are voxel graphs of tiered claims, not prose blobs. → https://miscsubjects.com/api/articles/constitution
2. Claims link to hash-chained sources via source_ids. → https://miscsubjects.com/api/articles/oip-node-c11-networks-small-world-scale-free/sources
3. Ask reads topology; ingest/claim append to ledger. → https://miscsubjects.com/api/protocol
4. Models queue growth: populate → collaborate → repair → reflex. → https://miscsubjects.com/api/protocol/grow
5. Graph proves its own shape (reflex) and $/claim (yield). → https://miscsubjects.com/graph.html?layer=reflex
6. Full feature index + _explain on every API response. → https://miscsubjects.com/api/articles/system-map

### Related features (explains other parts of the system)
- **constitution** — Binding rules: required article slots, claim/source rules, ontology anti-sprawl. · https://miscsubjects.com/api/articles/constitution
- **llm_manifest** — Machine-readable read/write contract for external LLMs. · https://miscsubjects.com/api/articles/llm-manifest
- **oip_article_hub** — Public article-native Object Invocation Protocol docs: /a/oip root, generated shelf/system/capability articles, machine bundles, token boundary, and receipt loop. · https://miscsubjects.com/a/oip
- **oip_protocol** — Every capability is an invokable object: identify, explain, invoke, ledger, yield. · https://miscsubjects.com/a/oip
- **bundle** — Paste-ready package: body + claims + sources + voxels + provenance + manifest + constitution. · https://miscsubjects.com/api/articles/oip-node-c11-networks-small-world-scale-free/bundle?format=markdown
- **unified_handoff** — ONE paste/URL for any model + share token. Same self-explaining pattern as article bundle, but whole build. · https://miscsubjects.com/api/handoff?format=markdown

### Full index
- JSON: https://miscsubjects.com/api/articles/system-map
- Markdown: https://miscsubjects.com/api/articles/system-map?format=markdown

*Not medical advice. Tier-honest. Cite claim/source ids.*