Pith Number

pith:ATWAL3CY

pith:2014:ATWAL3CYI4YF6XOCIPRUSYFQ5I

not attested not anchored not stored refs pending

Vertex-reinforced random walk on Z with sub-square-root weights is recurrent

Gady Kozma, Jun Chen

arxiv:1401.1036 v2 · 2014-01-06 · 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{ATWAL3CYI4YF6XOCIPRUSYFQ5I}

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	2026-05-18T01:12:20.138419Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04ec05ec5847305f5dc243e34960b0ea27a3bfa05c0d4abc5f0093fa14d69df8

Aliases

arxiv: 1401.1036 · arxiv_version: 1401.1036v2 · doi: 10.48550/arxiv.1401.1036 · pith_short_12: ATWAL3CYI4YF · pith_short_16: ATWAL3CYI4YF6XOC · pith_short_8: ATWAL3CY

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/ATWAL3CYI4YF6XOCIPRUSYFQ5I \
  | 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: 04ec05ec5847305f5dc243e34960b0ea27a3bfa05c0d4abc5f0093fa14d69df8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "322995bdae33de9a72afc8792b3ea65780e49012f6dbfc10dd56c56a7bf6a5fd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-01-06T10:55:23Z",
    "title_canon_sha256": "7d4050dcf0976d735f0b442c05059a8862551c8f12ece760fcb3b6a97bba9321"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.1036",
    "kind": "arxiv",
    "version": 2
  }
}