Pith Number

pith:DG5G3JD7

pith:2010:DG5G3JD72U7LOVWDHRJIIF5AQZ

not attested not anchored not stored refs pending

A discrete Gauss-Bonnet type theorem

Oliver Knill

arxiv:1009.2292 v1 · 2010-09-13 · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DG5G3JD72U7LOVWDHRJIIF5AQZ}

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	2026-05-18T04:41:04.481422Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19ba6da47fd53eb756c33c528417a08671c96636d87ed3d5ab69c3ac9768c721

Aliases

arxiv: 1009.2292 · arxiv_version: 1009.2292v1 · doi: 10.48550/arxiv.1009.2292 · pith_short_12: DG5G3JD72U7L · pith_short_16: DG5G3JD72U7LOVWD · pith_short_8: DG5G3JD7

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/DG5G3JD72U7LOVWDHRJIIF5AQZ \
  | 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: 19ba6da47fd53eb756c33c528417a08671c96636d87ed3d5ab69c3ac9768c721

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9248fc8adbe13c3fe54e8b76140c78a1f4612500b468b052e0df683fecb0255",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2010-09-13T03:44:10Z",
    "title_canon_sha256": "6ba33edc780eb15c59ad3c66565e3522e0375f3843439f31331787ff788e6223"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.2292",
    "kind": "arxiv",
    "version": 1
  }
}