Pith Number

pith:ZRZMGJ72

pith:2019:ZRZMGJ72AA3H2PQNH6OFAGJXWY

not attested not anchored not stored refs pending

Integrating by Spheres: Summary of Blaschke-Petkantschin Formulas

Anton Nikitenko

arxiv:1904.10750 v1 · 2019-04-24 · math.MG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZRZMGJ72AA3H2PQNH6OFAGJXWY}

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	2026-05-17T23:47:50.066293Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc72c327fa00367d3e0d3f9c501937b62f2ebd56a47f3a43445639355e4c1b82

Aliases

arxiv: 1904.10750 · arxiv_version: 1904.10750v1 · doi: 10.48550/arxiv.1904.10750 · pith_short_12: ZRZMGJ72AA3H · pith_short_16: ZRZMGJ72AA3H2PQN · pith_short_8: ZRZMGJ72

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/ZRZMGJ72AA3H2PQNH6OFAGJXWY \
  | 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: cc72c327fa00367d3e0d3f9c501937b62f2ebd56a47f3a43445639355e4c1b82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d6eec1c22f84b7129ec2ed78befe6aa020909a19a41800f49b1445e1326407c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2019-04-24T11:25:45Z",
    "title_canon_sha256": "4c3b4b315a2503cfc17f1c40f1942fd5d9ad3939cbeae6d5cf718232130ef1bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.10750",
    "kind": "arxiv",
    "version": 1
  }
}