Pith Number

pith:BRZD5CEM

pith:2012:BRZD5CEMLEN6UROYZFDRYVMLBP

not attested not anchored not stored refs pending

The theorems of Green-Stokes,Gauss-Bonnet and Poincare-Hopf in Graph Theory

Oliver Knill

arxiv:1201.6049 v1 · 2012-01-29 · math.DG · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BRZD5CEMLEN6UROYZFDRYVMLBP}

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	2026-05-18T04:03:33.835949Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c723e888c591bea45d8c9471c558b0bd20ec5dcd02a0bd4027b314a1d6146ee

Aliases

arxiv: 1201.6049 · arxiv_version: 1201.6049v1 · doi: 10.48550/arxiv.1201.6049 · pith_short_12: BRZD5CEMLEN6 · pith_short_16: BRZD5CEMLEN6UROY · pith_short_8: BRZD5CEM

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/BRZD5CEMLEN6UROYZFDRYVMLBP \
  | 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: 0c723e888c591bea45d8c9471c558b0bd20ec5dcd02a0bd4027b314a1d6146ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a0ff90d8ff2e4931a29256ecfc09696bdc4fbfd697585770558381fca36d30f",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-01-29T16:04:59Z",
    "title_canon_sha256": "89ef1cefdffd507c873cd2d8c7bb551ac35be7db0120603be4635b3a3dd136d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.6049",
    "kind": "arxiv",
    "version": 1
  }
}