## §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:** `wilson-1971`
- **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/wilson-1971/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/wilson-1971/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/wilson-1971/topology
- **voxels** — Claims as atoms, sources as edges (supported_by, posted_by). Per-claim provenance. · https://miscsubjects.com/api/articles/wilson-1971/voxels
- **ask** — Answer only from topology; creates question_node with gaps and ingest_hint. · https://miscsubjects.com/api/articles/wilson-1971/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/wilson-1971/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:** `wilson-1971`
- **title:** Wilson 1971 — Renormalization Group and Critical Phenomena
- **url:** https://miscsubjects.com/a/wilson-1971
- **register:** source
- **updated:** 2026-07-04T20:40:50.750Z
- **tags:** source, grain, convergence, wilson

## Body

## The Source

Wilson, K.G. "Renormalization Group and Critical Phenomena. I." *Physical Review B* 4(9), 3174–3183 (1971). DOI: 10.1103/PhysRevB.4.3174.

Wilson, K.G. "Renormalization Group and Critical Phenomena. II." *Physical Review B* 4(9), 3184–3205 (1971). DOI: 10.1103/PhysRevB.4.3184.

## The Claim

At criticality, correlation length shoots to infinity. The system forgets its atoms. Symmetry alone picks the numbers.

## The Context

1971. Cornell. Magnets, fluids, and alloys share the same exponents. Landau's theory fails. Experiments defy prediction. Wilson takes Kadanoff's block-spin idea and builds the machine. Coarse-graining erases the small. The large survives.

## The Evidence

Wilson writes the renormalization group as a flow. Repeated rescaling drives the Hamiltonian toward fixed points. At those points, ξ → ∞. Finite scales wash away. Critical exponents emerge as eigenvalues. Part I maps Kadanoff scaling to field theory. Part II runs the phase-space cell analysis. The epsilon expansion debuts. The numbers match experiment.

## The Convergence

This instantiates **C05 — Criticality** and **C10 — Scale Invariance**.

Wilson proves that criticality and scale invariance are one face. No characteristic scale means power laws. The same exponents rule magnets, fluids, and sandpiles. The renormalization group is the bridge. It links Bak's avalanches [SOURCE:bak-1987|type:empirical] to fractal geometry to metabolic scaling. One engine. Many bodies.

GRAIN scores this edge at convergence strength 8. Four fields. Four methods. Same statistics.

## The Honest Limits

Wilson addresses equilibrium. He does not touch self-organized criticality. Bak's sandpiles find criticality alone. Wilson needs a dial.

The epsilon expansion lives near four dimensions. Low dimensions break it. The Kosterlitz-Thouless transition escapes his net.

Wilson gives math. He does not give the why. Why do brains, markets, and quakes sit near criticality? That waits for Beggs, Kauffman, and GRAIN.

Rival: power laws are fitting artifacts. Log-log plots make them appear. Finite systems show cutoff effects. Pure scaling is an idealization.

## The Receipt

> "At criticality, correlation length ξ → ∞; the system becomes scale-invariant."

This is Wilson's core payload. The Hamiltonian flows to H* under rescaling. Microscopic details vanish. Different systems land on the same fixed point. Same exponents. Same numbers. That is the proof.

## Related Sources

- [Bak, Tang & Wiesenfeld — Self-Organized Criticality (1987)](/articles/bak-1987): Wilson's math meets systems that tune themselves.
- [Schrödinger 1944 — What Is Life?](/articles/schrodinger-1944): Physics crosses into biology. Wilson's machinery follows.
- [Noether 1918 — Invariante Variationsprobleme](/articles/noether-1918): Symmetry begets conservation. Wilson's fixed points inherit this law.
- [Wiener 1948 — Cybernetics](/articles/wiener-1948): Feedback and control. The engineering cousin to scaling.
- [Barabási & Albert 1999 — Scale-Free Networks](/articles/barabasi-1999): Power laws in links. Wilson's math in graph space.
- [Prigogine 1977 — Dissipative Structures](/articles/prigogine-1977): Non-equilibrium order. The thermodynamic cousin to criticality.


## Claims (7)

- **c1** [system w=1] At criticality, correlation length ξ diverges to infinity, rendering the system scale-invariant.
  - sources: s1, s2
- **c2** [system w=1] The renormalization group describes critical phenomena as a flow of Hamiltonians under repeated rescaling toward fixed points.
  - sources: s1, s2
- **c3** [system w=0.95] Critical exponents emerge as eigenvalues of the linearized renormalization group at fixed points.
  - sources: s1, s2
- **c4** [system w=0.9] The same critical exponents govern magnets, fluids, and alloys — universality across different physical systems.
  - sources: s1, s2
- **c6** [system w=0.9] Wilson's framework addresses equilibrium critical phenomena but does not encompass self-organized criticality.
  - sources: s1, s2
- **c5** [system w=0.85] Wilson's epsilon expansion near four dimensions yields quantitative predictions matching experimental measurements.
  - sources: s1, s2
- **c7** [system w=0.85] The epsilon expansion breaks down in low dimensions, failing to capture phenomena such as the Kosterlitz-Thouless transition.
  - sources: s1, s2

## Voxel graph (7 atoms · 14 edges)
- full graph: https://miscsubjects.com/api/articles/wilson-1971/voxels

## Article constitution

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

## Source ledger (4)
- chain valid: no · head: ``

### s1 · primary
- title: Wilson, K.G. "Renormalization Group and Critical Phenomena. I." Physical Review B 4(9), 3174–3183 (1971).
- url: https://doi.org/10.1103/PhysRevB.4.3174
- summary: Introduces the renormalization group as a flow of Hamiltonians under rescaling, mapping Kadanoff's block-spin idea to quantum field theory.
- quote: At criticality, correlation length ξ → ∞; the system becomes scale-invariant.
- claim_ids: c1, c2, c3, c4, c5
- hash: ``

### s2 · primary
- title: Wilson, K.G. "Renormalization Group and Critical Phenomena. II." Physical Review B 4(9), 3184–3205 (1971).
- url: https://doi.org/10.1103/PhysRevB.4.3184
- summary: Develops the phase-space cell analysis and introduces the epsilon expansion, providing quantitative predictions for critical exponents.
- claim_ids: c1, c2, c3, c4, c5
- hash: ``

### s3 · adjacent
- title: Bak, Tang & Wiesenfeld — Self-Organized Criticality (1987)
- url: https://miscsubjects.com/articles/bak-1987
- summary: Empirical and theoretical work on systems that spontaneously tune themselves to criticality without external parameter adjustment.
- claim_ids: c6
- hash: ``

### s4 · rival
- title: Rival frame: Power-law fitting artifacts and finite-size effects
- summary: Challenges whether observed critical scaling is genuine or an artifact of log-log plotting and finite-size effects in real systems.
- quote: Log-log plots make them appear. Finite systems show cutoff effects. Pure scaling is an idealization.
- hash: ``

## Provenance (0 model passes)
- chain valid: yes · head: `genesis`


## 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/wilson-1971/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/wilson-1971/topology
- **Ask (API):** POST https://miscsubjects.com/api/protocol/ask `{"slug":"wilson-1971","question":"..."}`
- **Ingest your findings:** POST https://miscsubjects.com/api/protocol/ingest or text `ingest wilson-1971|your evidence`
- **Post one claim:** POST https://miscsubjects.com/api/protocol/claim or text `claim wilson-1971|tier|assertion`
- **iMessage ask:** `wilson-1971|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:** `wilson-1971`
- **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/wilson-1971/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/wilson-1971/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.*