Object Invocation Protocol · protocol specification

Invariant 3.3 — 3.3 Symmetry ↔ conservation

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

3.3 Symmetry ↔ conservation

Every continuous symmetry yields a conserved quantity. Sources: Noether's theorem; Lie/group theory; gauge theory; Curie's principle. Domains: physics core, crystallography, particle physics, aesthetics. Scale: quantum → cosmic. Dual: symmetry-breaking (below). Tier: T0 (theorem). Falsifier: n/a for the theorem; for a mapping, a conserved quantity with no symmetry. Maps: A₁, A₃.

---

Corpus map

Same invariant, other planes: Catalogue node C03 · Encyclopedia C03
Inventory hub: Convergence Catalogue — Public Article

Key evidence

7 claims · tier-ranked · API

mechanistic

Every continuous symmetry yields a conserved quantity.

mechanistic

The dual of the invariant is symmetry-breaking.

mechanistic

The tier of the invariant is T0 (theorem).

mechanistic

The scale of the invariant is quantum → cosmic.

mechanistic

The invariant maps to A₁ and A₃.

anecdotal

The same invariant appears in other planes at Catalogue node C03 and Encyclopedia C03.

anecdotal

The inventory hub for the invariant is Convergence Catalogue — Public Article.

Model review1 contributions · 1 modelExpand the recursive review layer

1 / 1

grok/grok-4.3atomizer

atomize2026-07-07 08:06

atomize · 7 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-3-33-symmetry-conservation

it output

{
  "claims": [
    {
      "id": "c1",
      "text": "Every continuous symmetry yields a conserved quantity.",
      "section": "### 3.3 Symmetry ↔ conservation",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Core statement of the invariant linking symmetry to conservation."
    },
    {
      "id": "c2",
      "text": "The dual of the invariant is symmetry-breaking.",
      "section": "### 3.3 Symmetry ↔ conservation",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Specifies the paired concept for the invariant."
    },
    {
      "id": "c3",
      "text": "The tier of the invariant is T0 (theorem).",
      "section": "### 3.3 Symmetry ↔ conservation",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Classifies the invariant's formal status."
    },
    {
      "id": "c4",
      "text": "The scale of the invariant is quantum → cosmic.",
      "section": "### 3.3 Symmetry ↔ conservation",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Defines the range of applicability."
    },
    {
      "id": "c5",
      "text": "The invariant maps to A₁ and A₃.",
      "section": "### 3.3 Symmetry ↔ conservation",
      "tier": "mecha

3fa4d0499a045290

Machine verification: /api/articles/oip-invariant-3-33-symmetry-conservation/contributions

3.3 Symmetry ↔ conservation

Corpus map

Key evidence

Latest from the journal

Related articles