Pith Number

pith:3DGTDKE6

pith:2015:3DGTDKE65S7HRVVVWID5VSVIOI

not attested not anchored not stored refs pending

Generalized Kronecker formula for Bernoulli numbers and self-intersections of curves on a surface

Nariya Kawazumi, Shinji Fukuhara, Yusuke Kuno

arxiv:1505.04840 v1 · 2015-05-19 · math.NT · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3DGTDKE65S7HRVVVWID5VSVIOI}

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	2026-05-18T02:05:23.027941Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8cd31a89eecbe78d6b5b207dacaa8723493ad0604fa119e5f64ef56eb99f7c5

Aliases

arxiv: 1505.04840 · arxiv_version: 1505.04840v1 · doi: 10.48550/arxiv.1505.04840 · pith_short_12: 3DGTDKE65S7H · pith_short_16: 3DGTDKE65S7HRVVV · pith_short_8: 3DGTDKE6

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/3DGTDKE65S7HRVVVWID5VSVIOI \
  | 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: d8cd31a89eecbe78d6b5b207dacaa8723493ad0604fa119e5f64ef56eb99f7c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bfed542be73783b49962b6bd0433f1769b8525dd8cbe8137323430d20405367b",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-05-19T00:01:30Z",
    "title_canon_sha256": "e2868525721264d4d3264f0208b2f74ce67e81f604d740414a8ee338b64a243d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.04840",
    "kind": "arxiv",
    "version": 1
  }
}