Pith Number

pith:HANTPSD7

pith:2011:HANTPSD7ECRXF6TNMK36WY5TFG

not attested not anchored not stored refs pending

Phase transitions in exponential random graphs

Charles Radin, Mei Yin

arxiv:1108.0649 v3 · 2011-08-02 · math.PR · cond-mat.stat-mech · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HANTPSD7ECRXF6TNMK36WY5TFG}

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	2026-05-18T03:05:28.670441Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

381b37c87f20a372fa6d62b7eb63b3299d4d8e333cf125cde0dd77f73dbfafe9

Aliases

arxiv: 1108.0649 · arxiv_version: 1108.0649v3 · doi: 10.48550/arxiv.1108.0649 · pith_short_12: HANTPSD7ECRX · pith_short_16: HANTPSD7ECRXF6TN · pith_short_8: HANTPSD7

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/HANTPSD7ECRXF6TNMK36WY5TFG \
  | 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: 381b37c87f20a372fa6d62b7eb63b3299d4d8e333cf125cde0dd77f73dbfafe9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57afc17309a6044f79ca8375af997536be62b24f64a65070f5973e299b51ea48",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-08-02T19:18:12Z",
    "title_canon_sha256": "5bb74d507d99dd5d515cac85bd851d175f78532c1324e43c607360f4bf6ef963"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.0649",
    "kind": "arxiv",
    "version": 3
  }
}