Pith Number

pith:QUENB434

pith:2015:QUENB434Q4Z7D5RNEAX76RR6FP

not attested not anchored not stored refs pending

Random walks on the random graph

Allan Sly, Eyal Lubetzky, Nathanael Berestycki, Yuval Peres

arxiv:1504.01999 v3 · 2015-04-08 · 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{QUENB434Q4Z7D5RNEAX76RR6FP}

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	2026-05-18T01:01:49.443045Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8508d0f37c8733f1f62d202fff463e2bf6b47e51ece3a738bb3fddbec9639ff2

Aliases

arxiv: 1504.01999 · arxiv_version: 1504.01999v3 · doi: 10.48550/arxiv.1504.01999 · pith_short_12: QUENB434Q4Z7 · pith_short_16: QUENB434Q4Z7D5RN · pith_short_8: QUENB434

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/QUENB434Q4Z7D5RNEAX76RR6FP \
  | 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: 8508d0f37c8733f1f62d202fff463e2bf6b47e51ece3a738bb3fddbec9639ff2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f1590921e728ea8668381cdb82bd1fc34cafe80d1ed1fad41d092882772a10e",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-04-08T15:02:57Z",
    "title_canon_sha256": "9cf3973d75ed34f0cfae3845448b7f4173496905acf8b0acc49319f0effdd27f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.01999",
    "kind": "arxiv",
    "version": 3
  }
}