Pith Number

pith:5BR3MY7E

pith:2012:5BR3MY7EI2AOZFT2KWXSQ2EZL7

not attested not anchored not stored refs pending

A cluster expansion approach to exponential random graph models

Mei Yin

arxiv:1202.5587 v3 · 2012-02-24 · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5BR3MY7EI2AOZFT2KWXSQ2EZL7}

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	2026-05-18T03:56:33.766792Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e863b663e44680ec967a55af2868995fe4003180bb32febc7eaf50eae90381f0

Aliases

arxiv: 1202.5587 · arxiv_version: 1202.5587v3 · doi: 10.48550/arxiv.1202.5587 · pith_short_12: 5BR3MY7EI2AO · pith_short_16: 5BR3MY7EI2AOZFT2 · pith_short_8: 5BR3MY7E

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/5BR3MY7EI2AOZFT2KWXSQ2EZL7 \
  | 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: e863b663e44680ec967a55af2868995fe4003180bb32febc7eaf50eae90381f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87dad8d432c29e687cbb6939d80b3abd01a126840ef0780836b32d31a927bd53",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-02-24T23:58:58Z",
    "title_canon_sha256": "bf718ff962db0988e1b2b416b9a02bb3d15f7fcd49f0d1ab8b942f8ca6dc117b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.5587",
    "kind": "arxiv",
    "version": 3
  }
}