Pith Number

pith:DJAS5RYE

pith:2013:DJAS5RYENEJSYJMORRQINS3LCL

not attested not anchored not stored refs pending

Phase transition in the two star Exponential Random Graph Model

Sumit Mukherjee

arxiv:1310.4164 v1 · 2013-10-15 · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DJAS5RYENEJSYJMORRQINS3LCL}

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	2026-05-18T03:10:24.913890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a412ec70469132c258e8c6086cb6b12ca57a31b716af3361d8e3fb0ca5e9b1d

Aliases

arxiv: 1310.4164 · arxiv_version: 1310.4164v1 · doi: 10.48550/arxiv.1310.4164 · pith_short_12: DJAS5RYENEJS · pith_short_16: DJAS5RYENEJSYJMO · pith_short_8: DJAS5RYE

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/DJAS5RYENEJSYJMORRQINS3LCL \
  | 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: 1a412ec70469132c258e8c6086cb6b12ca57a31b716af3361d8e3fb0ca5e9b1d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d2e567469ce07de5a18868f8b7b36c0fc8a66f3594820da9b145fb7210df436",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2013-10-15T19:52:19Z",
    "title_canon_sha256": "1b71c7375ee08b31f98a82900d7c6d58a31ebd7ef5d46689f6bb3aa6e83fe429"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.4164",
    "kind": "arxiv",
    "version": 1
  }
}