Pith Number

pith:IPWP6AJN

pith:2010:IPWP6AJNQLYI36VWVP4IXHK6ZG

not attested not anchored not stored refs pending

Cover times, blanket times, and majorizing measures

James R. Lee, Jian Ding, Yuval Peres

arxiv:1004.4371 v5 · 2010-04-25 · math.PR · cs.DS · math.MG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IPWP6AJNQLYI36VWVP4IXHK6ZG}

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	2026-05-18T04:11:31.917284Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43ecff012d82f08dfab6abf88b9d5ec98fbc672a59e1299a5a061887f7483fbe

Aliases

arxiv: 1004.4371 · arxiv_version: 1004.4371v5 · doi: 10.48550/arxiv.1004.4371 · pith_short_12: IPWP6AJNQLYI · pith_short_16: IPWP6AJNQLYI36VW · pith_short_8: IPWP6AJN

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/IPWP6AJNQLYI36VWVP4IXHK6ZG \
  | 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: 43ecff012d82f08dfab6abf88b9d5ec98fbc672a59e1299a5a061887f7483fbe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c9821c6cfb56ec078d4909b9bb022adf19f727eb9e0c48a752be332ee03a7fc",
    "cross_cats_sorted": [
      "cs.DS",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-04-25T18:19:47Z",
    "title_canon_sha256": "43d2aac03e986de50b8ed93c81e00d7b0192f377a902643bb251d3cfba69643d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.4371",
    "kind": "arxiv",
    "version": 5
  }
}