Pith Number

pith:B4BXUQTQ

pith:2009:B4BXUQTQ2W2HDH5D56FZCP3E57

not attested not anchored not stored refs pending

Coherent tangent bundles and Gauss-Bonnet formulas for wave fronts

Kentaro Saji, Kotaro Yamada, Masaaki Umehara

arxiv:0910.3456 v3 · 2009-10-19 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B4BXUQTQ2W2HDH5D56FZCP3E57}

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	2026-05-18T04:36:51.317028Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f037a4270d5b4719fa3ef8b913f64efc4bbe6a96e3f7f3ca800b54932bc79dd

Aliases

arxiv: 0910.3456 · arxiv_version: 0910.3456v3 · doi: 10.48550/arxiv.0910.3456 · pith_short_12: B4BXUQTQ2W2H · pith_short_16: B4BXUQTQ2W2HDH5D · pith_short_8: B4BXUQTQ

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/B4BXUQTQ2W2HDH5D56FZCP3E57 \
  | 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: 0f037a4270d5b4719fa3ef8b913f64efc4bbe6a96e3f7f3ca800b54932bc79dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "30b399071fecba045de095fda430855563737be1061bf2454af5b5fcd3ebaf99",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-10-19T05:01:14Z",
    "title_canon_sha256": "cecde13a8bfb336d36b6eed0d8993e164126b63c41f4b4d8880fe083976a3ded"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.3456",
    "kind": "arxiv",
    "version": 3
  }
}