Pith Number

pith:AC5BP6PE

pith:2018:AC5BP6PEVMSE4UKM47UL5Z5RUZ

not attested not anchored not stored refs pending

Boundary of the Range of a random walk and the F\"olner property

George Deligiannidis, Sebastien Gouezel, Zemer Kosloff

arxiv:1810.10454 v2 · 2018-10-24 · math.PR · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AC5BP6PEVMSE4UKM47UL5Z5RUZ}

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	2026-05-17T23:58:01.858592Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00ba17f9e4ab244e514ce7e8bee7b1a674eb582f751b910a32477a55d0aa359b

Aliases

arxiv: 1810.10454 · arxiv_version: 1810.10454v2 · doi: 10.48550/arxiv.1810.10454 · pith_short_12: AC5BP6PEVMSE · pith_short_16: AC5BP6PEVMSE4UKM · pith_short_8: AC5BP6PE

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/AC5BP6PEVMSE4UKM47UL5Z5RUZ \
  | 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: 00ba17f9e4ab244e514ce7e8bee7b1a674eb582f751b910a32477a55d0aa359b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c65a1dda1bbd30e651546f9291115b9dd89f20b955d3ea0d389e4105f34bd0ac",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-10-24T15:32:20Z",
    "title_canon_sha256": "1f6a47024dc68ccfe3f5b2af3463dcbe37edf77d79ebb06d195138e4cc68944c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.10454",
    "kind": "arxiv",
    "version": 2
  }
}