Pith Number

pith:VTXZZISU

pith:2016:VTXZZISUXK2BVHCURCJPSJMVJM

not attested not anchored not stored refs pending

Wallach sets and squared Bessel particle systems

Jacek Malecki, Piotr Graczyk

arxiv:1602.01597 v1 · 2016-02-04 · 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{VTXZZISUXK2BVHCURCJPSJMVJM}

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	2026-05-18T01:21:18.580505Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

acef9ca254bab41a9c548892f925954b2708baa991ca844ba4cefe552f5b02b7

Aliases

arxiv: 1602.01597 · arxiv_version: 1602.01597v1 · doi: 10.48550/arxiv.1602.01597 · pith_short_12: VTXZZISUXK2B · pith_short_16: VTXZZISUXK2BVHCU · pith_short_8: VTXZZISU

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/VTXZZISUXK2BVHCURCJPSJMVJM \
  | 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: acef9ca254bab41a9c548892f925954b2708baa991ca844ba4cefe552f5b02b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b58b7632233ad705439b25b3f954382efb8d3c4e6e5c8b240c6e29ea9dab353f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-02-04T08:59:13Z",
    "title_canon_sha256": "5f7b4e1722703eb4b6566e89f52d6ef80d158aaebf61c3864c33b5a5876597de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.01597",
    "kind": "arxiv",
    "version": 1
  }
}