Pith Number

pith:FNFPLCD3

pith:2010:FNFPLCD3F7UF7XMGOIKE5XD2WL

not attested not anchored not stored refs pending

The evolution of the cover time

Asaf Nachmias, Jian Ding, Martin T. Barlow, Yuval Peres

arxiv:1001.0609 v2 · 2010-01-05 · 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{FNFPLCD3F7UF7XMGOIKE5XD2WL}

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	2026-05-18T04:42:03.917676Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b4af5887b2fe85fdd8672144edc7ab2e091f034a45421bc79bf9551b74bac81

Aliases

arxiv: 1001.0609 · arxiv_version: 1001.0609v2 · doi: 10.48550/arxiv.1001.0609 · pith_short_12: FNFPLCD3F7UF · pith_short_16: FNFPLCD3F7UF7XMG · pith_short_8: FNFPLCD3

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/FNFPLCD3F7UF7XMGOIKE5XD2WL \
  | 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: 2b4af5887b2fe85fdd8672144edc7ab2e091f034a45421bc79bf9551b74bac81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e011afb2794c6baf18b676a02959da4cced4cdeeda04342f2777791e34ff5ad1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-01-05T01:01:31Z",
    "title_canon_sha256": "9cf60fa73f36aeaa8d6f0a7405e76f362652fb892530b5eaee4bde1d67ad3e86"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.0609",
    "kind": "arxiv",
    "version": 2
  }
}