Pith Number

pith:HYHV7D22

pith:2012:HYHV7D22QQJWYL2XIPP3JGFEOQ

not attested not anchored not stored refs pending

The probability densities of the first hitting times of Bessel processes

Hiroyuki Matsumoto, Yuji Hamana

arxiv:1206.2120 v2 · 2012-06-11 · 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{HYHV7D22QQJWYL2XIPP3JGFEOQ}

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	2026-05-18T03:17:44.717821Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e0f5f8f5a84136c2f5743dfb498a47400e6e55f8bcee8812e7c5ad7daa2b3cc

Aliases

arxiv: 1206.2120 · arxiv_version: 1206.2120v2 · doi: 10.48550/arxiv.1206.2120 · pith_short_12: HYHV7D22QQJW · pith_short_16: HYHV7D22QQJWYL2X · pith_short_8: HYHV7D22

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/HYHV7D22QQJWYL2XIPP3JGFEOQ \
  | 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: 3e0f5f8f5a84136c2f5743dfb498a47400e6e55f8bcee8812e7c5ad7daa2b3cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0d3713618b7721cf4e581c62dd403376cafbf74ee6a1d34a0167ef75579695e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-06-11T07:49:02Z",
    "title_canon_sha256": "079133b8661876d8e2972b0cf4d9543fb6ddbc96168e45998dc54ee12c41ef06"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.2120",
    "kind": "arxiv",
    "version": 2
  }
}