Pith Number

pith:WARGR56V

pith:2014:WARGR56VE5AQXIZEKCLDGILE3A

not attested not anchored not stored refs pending

On the phase transition curve in a directed exponential random graph model

David Aristoff, Lingjiong Zhu

arxiv:1404.6514 v2 · 2014-04-25 · 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{WARGR56VE5AQXIZEKCLDGILE3A}

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	2026-05-18T00:20:18.090302Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b02268f7d527410ba3245096332164d80332a42ad0dbe24603c3614925172d6d

Aliases

arxiv: 1404.6514 · arxiv_version: 1404.6514v2 · doi: 10.48550/arxiv.1404.6514 · pith_short_12: WARGR56VE5AQ · pith_short_16: WARGR56VE5AQXIZE · pith_short_8: WARGR56V

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/WARGR56VE5AQXIZEKCLDGILE3A \
  | 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: b02268f7d527410ba3245096332164d80332a42ad0dbe24603c3614925172d6d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4170002bc7d0e2be59dfe672fbcf86fd3163f75eb120d01eb22b8cba5e924a36",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-04-25T19:49:14Z",
    "title_canon_sha256": "b2b7a2e8e4398e7ea2197db442dfe98a040edfc376ee3a583732b6487ac75767"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.6514",
    "kind": "arxiv",
    "version": 2
  }
}