Pith Number

pith:JK7WNMMZ

pith:2025:JK7WNMMZ6ZLN3AGDVFKVWGZFTK

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Finding the right path: statistical mechanics of connected solutions in constraint satisfaction problems

Damien Barbier

A new statistical mechanics ensemble reveals a stable cluster of connected solutions in the symmetric binary perceptron that persists up to a critical threshold.

arxiv:2505.20954 v5 · 2025-05-27 · cond-mat.dis-nn · cond-mat.stat-mech

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\usepackage{pith}
\pithnumber{JK7WNMMZ6ZLN3AGDVFKVWGZFTK}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

We unveil the presence of a cluster composed of delocalized connected solutions. In particular, we demonstrate its stability until a critical threshold κ^{no-mem}_{loc. stab.} (dependent on α).

C2weakest assumption

The local entropy bias is assumed to correctly identify the manifold of connected solutions whose stability governs algorithmic success in the symmetric binary perceptron.

C3one line summary

A new ensemble for connected solutions in CSPs reveals a stable cluster of delocalized solutions in the symmetric binary perceptron up to a critical threshold κ_no-mem_loc.stab. that conventional approaches miss.

Receipt and verification

First computed	2026-06-30T01:16:23.499742Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4abf66b199f656dd80c3a9555b1b259abc33bd941ffc7288446102f60416f170

Aliases

arxiv: 2505.20954 · arxiv_version: 2505.20954v5 · doi: 10.48550/arxiv.2505.20954 · pith_short_12: JK7WNMMZ6ZLN · pith_short_16: JK7WNMMZ6ZLN3AGD · pith_short_8: JK7WNMMZ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JK7WNMMZ6ZLN3AGDVFKVWGZFTK \
  | 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: 4abf66b199f656dd80c3a9555b1b259abc33bd941ffc7288446102f60416f170

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6919c771b88ecd6a0c5cfe21a87110f08c527198227e2f76c956767267431176",
    "cross_cats_sorted": [
      "cond-mat.stat-mech"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.dis-nn",
    "submitted_at": "2025-05-27T09:50:00Z",
    "title_canon_sha256": "23daad944e2c0abda28397542a76a225eb81716e3805e7977d970105401d50e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.20954",
    "kind": "arxiv",
    "version": 5
  }
}