Object Invocation Protocol · protocol specification

Convergence Edge 10: Symmetry-Breaking ↔ Attractors

Posted Jul 4, 2026 · Updated Jul 17, 2026 · 1 min read

C04 (Symmetry-Breaking) recurs-with C23 (Attractors)

Shared pattern: A symmetric state becomes unstable; the system must choose among equivalent broken states; different initial conditions fall into the same attractor basins

Domain distance: Particle physics/Cosmology → Dynamical systems/Meteorology (large)

Derivation independence: HIGH. Higgs (particle physics, 1964) showed gauge symmetry breaking gives mass. Landau (condensed matter, 1937) showed phase transitions break symmetry. Lorenz (meteorology, 1963) found strange attractors where symmetric equations produce asymmetric trajectories. Thom (topology, 1972) classified catastrophe types from symmetry-breaking. Four fields, same mathematics (bifurcation theory), same pattern: symmetric laws, asymmetric outcomes.

Convergence strength (1–10): 9

Note: This is the most mathematically precise convergence in the catalogue. Both nodes are instances of bifurcation theory. The symmetry-breaking of the Higgs mechanism and the symmetry-breaking of a convecting fluid cell are the same mathematical operation on different Hamiltonians.

Summary Table: Cross-Domain Convergence Edges

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Corpus map

C04 (Symmetry-Breaking): C04 in the Encyclopedia · C04 in the Catalogue
C23 (Attractors): C23 in the Encyclopedia · C23 in the Catalogue
Convergence edges: 1 · 2 · 3 · 4 · 5 · 6 · 7 · 8 · 9 · 10
Catalogue hub: Convergence Catalogue — Public Article · The Schema

Key evidence

15 claims · tier-ranked · API

mechanistic

C04 (Symmetry-Breaking) recurs-with C23 (Attractors)

mechanistic

A symmetric state becomes unstable; the system must choose among equivalent broken states; different initial conditions fall into the same attractor basins

mechanistic

Domain distance from Particle physics/Cosmology to Dynamical systems/Meteorology is large

mechanistic

Derivation independence is HIGH

mechanistic

Four fields share the same mathematics (bifurcation theory) and same pattern: symmetric laws, asymmetric outcomes

mechanistic

Both nodes are instances of bifurcation theory

mechanistic

The symmetry-breaking of the Higgs mechanism and the symmetry-breaking of a convecting fluid cell are the same mathematical operation on different Hamiltonians

anecdotal

Higgs (particle physics, 1964) showed gauge symmetry breaking gives mass

anecdotal

Landau (condensed matter, 1937) showed phase transitions break symmetry

anecdotal

Lorenz (meteorology, 1963) found strange attractors where symmetric equations produce asymmetric trajectories

5 more ranked claims

anecdotal0.30

Thom (topology, 1972) classified catastrophe types from symmetry-breaking

Historical attribution in derivation independence

anecdotal0.30

C04 (Symmetry-Breaking) links to C04 in the Encyclopedia at /a/convergence-encyclopedia-c04 and C04 in the Catalogue at /a/oip-node-c04-symmetry-breaking-bifurcation

Corpus navigation structure

anecdotal0.30

C23 (Attractors) links to C23 in the Encyclopedia at /a/convergence-encyclopedia-c23 and C23 in the Catalogue at /a/oip-node-c23-attractors-dynamical-systems

Corpus navigation structure

anecdotal0.30

Convergence edges link to edges 1 through 10 at the listed /a/oip-convergence-edge paths

Corpus navigation structure

anecdotal0.30

Catalogue hub links to Convergence Catalogue — Public Article at /a/oip-convergence-public-article and The Schema at /a/oip-convergence-schema

Corpus navigation structure

Model review1 contributions · 1 modelExpand the recursive review layer

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grok/grok-4.3atomizer

atomize2026-07-07 08:26

atomize · 17 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-convergence-edge-10

it output

{
  "claims": [
    {
      "id": "c1",
      "text": "C04 (Symmetry-Breaking) recurs-with C23 (Attractors)",
      "section": "",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Core recurrence relation defining the convergence edge"
    },
    {
      "id": "c2",
      "text": "A symmetric state becomes unstable; the system must choose among equivalent broken states; different initial conditions fall into the same attractor basins",
      "section": "",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Shared pattern across domains"
    },
    {
      "id": "c3",
      "text": "Domain distance from Particle physics/Cosmology to Dynamical systems/Meteorology is large",
      "section": "",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Establishes cross-domain scope of convergence"
    },
    {
      "id": "c4",
      "text": "Derivation independence is HIGH",
      "section": "",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Supports convergence strength rating"
    },
    {
      "id": "c5",
      "text": "Higgs (particle physics, 1964) showed gauge symmetry breaking gives mass",
      "section": "",
      "tier": "anecdot

b6e664c52f2277c5

Machine verification: /api/articles/oip-convergence-edge-10/contributions

Corpus map

Key evidence

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