Pith Number

pith:QQQ5S4DR

pith:2013:QQQ5S4DR2TGJN3BQIDW7DE5WSP

not attested not anchored not stored refs pending

Phase transition for the vacant set left by random walk on the giant component of a random graph

Tobias Wassmer

arxiv:1308.2548 v2 · 2013-08-12 · 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{QQQ5S4DR2TGJN3BQIDW7DE5WSP}

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	2026-05-18T03:10:14.062328Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8421d97071d4cc96ec3040edf193b693ca35291ffb4cd94777581c7e4b6cc461

Aliases

arxiv: 1308.2548 · arxiv_version: 1308.2548v2 · doi: 10.48550/arxiv.1308.2548 · pith_short_12: QQQ5S4DR2TGJ · pith_short_16: QQQ5S4DR2TGJN3BQ · pith_short_8: QQQ5S4DR

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/QQQ5S4DR2TGJN3BQIDW7DE5WSP \
  | 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: 8421d97071d4cc96ec3040edf193b693ca35291ffb4cd94777581c7e4b6cc461

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3eee81d7278133aa643f79772f3183f41c329b30f64b1a7d409f6e1a12bb9b3f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-08-12T13:12:05Z",
    "title_canon_sha256": "d0050cd23d9207f1368ff288a086d5165e031e7a597902875a474197a2d7053e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.2548",
    "kind": "arxiv",
    "version": 2
  }
}