Pith Number

pith:NHRWGG3G

pith:2026:NHRWGG3GXFY72MJHLKAXNVVYWS

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Composite-Operator Scaling on Triadic Hypergraphs: Formation Transitions in Multi-Agent Architectures with Three-Body Coupling

Eduardo Salazar

Multi-agent AI architectures with k-body spin correlations exhibit composite-operator criticality, yielding vanishing susceptibility for k greater than or equal to 3.

arxiv:2604.27038 v2 · 2026-04-29 · cond-mat.stat-mech

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\pithnumber{NHRWGG3GXFY72MJHLKAXNVVYWS}

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Record completeness

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4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Multi-agent AI architectures whose dominant collective observable is a k-body spin correlator O_k ≡ ⟨ϕ^k⟩ over a Z_2-symmetric order parameter exhibit composite-operator criticality with effective exponents β_k = k/2 and γ_k = 2-k, thereby producing a finite susceptibility for k≥2 and a vanishing susceptibility for k≥3.

C2weakest assumption

That the dominant collective observable in the AI architectures is the k-body spin correlator and that the formation transition reduces exactly to a triadic Ising model under controlled universality and mean-field arguments.

C3one line summary

Multi-agent AI systems with k-body correlations exhibit composite-operator criticality with exponents β_k = k/2 and γ_k = 2-k, producing vanishing susceptibility for k ≥ 3 and reducing to an exactly solvable triadic Ising model for k=3.

Receipt and verification

First computed	2026-06-19T16:12:20.414378Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69e3631b66b971fd31275a8176d6b8b4b5f075101f728d0e565193f8a8fe17c3

Aliases

arxiv: 2604.27038 · arxiv_version: 2604.27038v2 · doi: 10.48550/arxiv.2604.27038 · pith_short_12: NHRWGG3GXFY7 · pith_short_16: NHRWGG3GXFY72MJH · pith_short_8: NHRWGG3G

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/NHRWGG3GXFY72MJHLKAXNVVYWS \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 69e3631b66b971fd31275a8176d6b8b4b5f075101f728d0e565193f8a8fe17c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb60c2dcbed1d4abab090e5c0d0a0fedb0a2fe0cf6e25a372c6f8ad0ec73fe13",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-04-29T17:06:42Z",
    "title_canon_sha256": "45a05d2f4fd52ea7b8cf130ac58087079ddd736eda08898022772a081100bb0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.27038",
    "kind": "arxiv",
    "version": 2
  }
}