Pith Number

pith:EL3TANYK

pith:2009:EL3TANYKJMDAPHYIB7HP3BX4UU

not attested not anchored not stored refs pending

Mixing time of near-critical random graphs

Eyal Lubetzky, Jian Ding, Yuval Peres

arxiv:0908.3870 v2 · 2009-08-26 · 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{EL3TANYKJMDAPHYIB7HP3BX4UU}

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	2026-05-18T03:55:03.031172Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

22f730370a4b06079f080fcefd86fca5250721df789cde34aa365fb6be5df896

Aliases

arxiv: 0908.3870 · arxiv_version: 0908.3870v2 · doi: 10.48550/arxiv.0908.3870 · pith_short_12: EL3TANYKJMDA · pith_short_16: EL3TANYKJMDAPHYI · pith_short_8: EL3TANYK

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/EL3TANYKJMDAPHYIB7HP3BX4UU \
  | 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: 22f730370a4b06079f080fcefd86fca5250721df789cde34aa365fb6be5df896

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b78384b8477eebf756f74fa8ea03e4ee190b41bd999507c0aa95bc59a96185a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-08-26T17:41:16Z",
    "title_canon_sha256": "88626ca8c95ab82360738089d21563231f57f94b4c3fa9e73a5d2dcb57725027"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.3870",
    "kind": "arxiv",
    "version": 2
  }
}