Pith Number

pith:YD3HKRRO

pith:2012:YD3HKRROEE5L2MGYTGTIWVXK47

not attested not anchored not stored refs pending

Random walks on random horospheric products

Florian Sobieczky, Vadim A. Kaimanovich

arxiv:1201.0329 v1 · 2012-01-01 · 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{YD3HKRROEE5L2MGYTGTIWVXK47}

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	2026-05-18T04:05:25.494625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c0f675462e213abd30d899a68b56eae7ece048778ec79c4907844661a15e5099

Aliases

arxiv: 1201.0329 · arxiv_version: 1201.0329v1 · doi: 10.48550/arxiv.1201.0329 · pith_short_12: YD3HKRROEE5L · pith_short_16: YD3HKRROEE5L2MGY · pith_short_8: YD3HKRRO

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/YD3HKRROEE5L2MGYTGTIWVXK47 \
  | 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: c0f675462e213abd30d899a68b56eae7ece048778ec79c4907844661a15e5099

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d6763f5f7da24258b4fd73f4a270c6d80dd544dee66bfc015c3097fa3f86e80",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-01-01T04:35:13Z",
    "title_canon_sha256": "430b37764dae45d70db8926f46bd078a55c8a6b24c0066156f4294df4b168b98"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.0329",
    "kind": "arxiv",
    "version": 1
  }
}