Pith Number

pith:ECV4MFVH

pith:2024:ECV4MFVHXVJ3SCU7JL2ACV5BQT

not attested not anchored not stored refs pending

The thermodynamic limit in mean field neural networks

Adriano Barra, Alberto Fachechi, Diego Pallara, Elena Agliari, Pierluigi Bianco

arxiv:2409.10145 v1 · 2024-09-16 · cond-mat.dis-nn · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ECV4MFVHXVJ3SCU7JL2ACV5BQT}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

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.

Receipt and verification

First computed	2026-07-05T09:07:35.794688Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

20abc616a7bd53b90a9f4af40157a184db538367348f28f07912bd88f635759c

Aliases

arxiv: 2409.10145 · arxiv_version: 2409.10145v1 · doi: 10.48550/arxiv.2409.10145 · pith_short_12: ECV4MFVHXVJ3 · pith_short_16: ECV4MFVHXVJ3SCU7 · pith_short_8: ECV4MFVH

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/ECV4MFVHXVJ3SCU7JL2ACV5BQT \
  | 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: 20abc616a7bd53b90a9f4af40157a184db538367348f28f07912bd88f635759c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8406fab4a25318e9776563d6f5b31f63f9f30c608d2a4483ccb7ce6520df14d",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.dis-nn",
    "submitted_at": "2024-09-16T10:15:14Z",
    "title_canon_sha256": "0176f20ddf566125de51069b531465866b49435828da1324cc229f81b1f54c27"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.10145",
    "kind": "arxiv",
    "version": 1
  }
}