Pith Number

pith:CH2LM4UO

pith:2011:CH2LM4UOOFUYK5RVCEPZOQ3JMX

not attested not anchored not stored refs pending

Which random walks are cyclic?

Carla Valente, Davide Gabrielli

arxiv:1107.5336 v2 · 2011-07-26 · 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{CH2LM4UOOFUYK5RVCEPZOQ3JMX}

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	2026-05-18T03:57:37.191662Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11f4b6728e7169857635111f97436965e0992a4e1de7c6690da416ffae785a3f

Aliases

arxiv: 1107.5336 · arxiv_version: 1107.5336v2 · doi: 10.48550/arxiv.1107.5336 · pith_short_12: CH2LM4UOOFUY · pith_short_16: CH2LM4UOOFUYK5RV · pith_short_8: CH2LM4UO

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/CH2LM4UOOFUYK5RVCEPZOQ3JMX \
  | 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: 11f4b6728e7169857635111f97436965e0992a4e1de7c6690da416ffae785a3f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4716375158c6d1aa4072797ed629683d55809381a970605fda13e47cc82dfd0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-07-26T21:12:38Z",
    "title_canon_sha256": "b6dd7bf665db895a0d42980e7697ce647903837889ad2dd0c263164d04f9a67b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.5336",
    "kind": "arxiv",
    "version": 2
  }
}