Pith Number

pith:YNZNODS3

pith:2010:YNZNODS3YXLTHZJ35FSNRONAUA

not attested not anchored not stored refs pending

Mixing times for random k-cycles and coalescence-fragmentation chains

Nathana\"el Berestycki, Oded Schramm, Ofer Zeitouni

arxiv:1001.1894 v3 · 2010-01-12 · math.PR · 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{YNZNODS3YXLTHZJ35FSNRONAUA}

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	2026-05-18T01:09:24.159948Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c372d70e5bc5d733e53be964d8b9a0a00e6f8dc900462d4d3eaf7a13f5f3ee49

Aliases

arxiv: 1001.1894 · arxiv_version: 1001.1894v3 · doi: 10.48550/arxiv.1001.1894 · pith_short_12: YNZNODS3YXLT · pith_short_16: YNZNODS3YXLTHZJ3 · pith_short_8: YNZNODS3

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/YNZNODS3YXLTHZJ35FSNRONAUA \
  | 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: c372d70e5bc5d733e53be964d8b9a0a00e6f8dc900462d4d3eaf7a13f5f3ee49

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "93354f471a817c0dfc7272328263f4d3b96174eb5f36e408c0efd60bdc119495",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-01-12T14:58:12Z",
    "title_canon_sha256": "fbc69146c572511a01430159ebc407bb6d2f8a1b28c5dbc44ea16ad2b17121b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.1894",
    "kind": "arxiv",
    "version": 3
  }
}