Pith Number

pith:JBE43R36

pith:2012:JBE43R36LUXMHGVE7Z634USWB4

not attested not anchored not stored refs pending

A graph theoretical Poincare-Hopf Theorem

Oliver Knill

arxiv:1201.1162 v1 · 2012-01-05 · math.DG · cs.CG · cs.DM · 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{JBE43R36LUXMHGVE7Z634USWB4}

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.

Cited by

1 paper in Pith

The energy of a simplicial complex

Receipt and verification

First computed	2026-05-18T04:05:05.907916Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4849cdc77e5d2ec39aa4fe7dbe52560f123d66acefb5ffb193491b2190e8cab6

Aliases

arxiv: 1201.1162 · arxiv_version: 1201.1162v1 · doi: 10.48550/arxiv.1201.1162 · pith_short_12: JBE43R36LUXM · pith_short_16: JBE43R36LUXMHGVE · pith_short_8: JBE43R36

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/JBE43R36LUXMHGVE7Z634USWB4 \
  | 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: 4849cdc77e5d2ec39aa4fe7dbe52560f123d66acefb5ffb193491b2190e8cab6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ffd8cdf8d060ae877c40d02a5d68981f509b55e74b44ba9116e77ea3b3493b8",
    "cross_cats_sorted": [
      "cs.CG",
      "cs.DM",
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-01-05T13:10:27Z",
    "title_canon_sha256": "89714dbb496881d22968fc3a0e1b18ed6b9146b9a2c2cabfd2379aa6bea1d69b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.1162",
    "kind": "arxiv",
    "version": 1
  }
}