Pith Number

pith:WRNBL6TA

pith:2010:WRNBL6TAODOSCCMI733EU6WWBC

not attested not anchored not stored refs pending

Phase transitions for the cavity approach to the clique problem on random graphs

Alexandre Gaudilliere, Benedetto Scoppola, Elisabetta Scoppola, Massimiliano Viale

arxiv:1011.2945 v1 · 2010-11-12 · math.PR · cond-mat.stat-mech · cs.SI · physics.soc-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WRNBL6TAODOSCCMI733EU6WWBC}

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	2026-05-18T02:04:48.284414Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b45a15fa6070dd210988fef64a7ad6088530f8174d35e623a879f522e0ecb100

Aliases

arxiv: 1011.2945 · arxiv_version: 1011.2945v1 · doi: 10.48550/arxiv.1011.2945 · pith_short_12: WRNBL6TAODOS · pith_short_16: WRNBL6TAODOSCCMI · pith_short_8: WRNBL6TA

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/WRNBL6TAODOSCCMI733EU6WWBC \
  | 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: b45a15fa6070dd210988fef64a7ad6088530f8174d35e623a879f522e0ecb100

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "438b91aba57ec2e2531b42ce838101ad0b6636a35bbb7c8cc90c639dc3587816",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "cs.SI",
      "physics.soc-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-11-12T15:26:35Z",
    "title_canon_sha256": "c713143a111a17817b0f07f47f09400465c8255c9539cb7cbd85f03618420954"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2945",
    "kind": "arxiv",
    "version": 1
  }
}