Pith Number

pith:TGW3AELS

pith:2006:TGW3AELSZ2BDHLXQOA324RHAIO

not attested not anchored not stored refs pending

The mixing time of the giant component of a random graph

Gady Kozma, Itai Benjamini, Nicholas Wormald

arxiv:math/0610459 v2 · 2006-10-15 · 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{TGW3AELSZ2BDHLXQOA324RHAIO}

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	2026-05-18T01:10:11.537768Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

99adb01172ce8233aef07037ae44e0438ae073204885b404fd8f55feb1dde93b

Aliases

arxiv: math/0610459 · arxiv_version: math/0610459v2 · doi: 10.48550/arxiv.math/0610459 · pith_short_12: TGW3AELSZ2BD · pith_short_16: TGW3AELSZ2BDHLXQ · pith_short_8: TGW3AELS

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/TGW3AELSZ2BDHLXQOA324RHAIO \
  | 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: 99adb01172ce8233aef07037ae44e0438ae073204885b404fd8f55feb1dde93b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8b882e28925417973db7c50635afe4fc6d17d90d0c5b266f0beeb0c300829a3",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2006-10-15T21:01:33Z",
    "title_canon_sha256": "8d7181db8887f0d582873855121d0653bb147dfe4cb4fad520605f8d624dfbc9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0610459",
    "kind": "arxiv",
    "version": 2
  }
}