Pith Number

pith:YCECPLR5

pith:2019:YCECPLR5LQKXLLZ4DXBNJH53A5

not attested not anchored not stored refs pending

A parametrized Poincare-Hopf Theorem and Clique Cardinalities of graphs

Oliver Knill

arxiv:1906.06611 v1 · 2019-06-15 · math.CO · 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{YCECPLR5LQKXLLZ4DXBNJH53A5}

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

2 papers in Pith

The energy of a simplicial complex

The counting matrix of a simplicial complex

Receipt and verification

First computed	2026-05-17T23:43:13.195964Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c08827ae3d5c1575af3c1dc2d49fbb0777de4612df5abbb308bc812791282f67

Aliases

arxiv: 1906.06611 · arxiv_version: 1906.06611v1 · doi: 10.48550/arxiv.1906.06611 · pith_short_12: YCECPLR5LQKX · pith_short_16: YCECPLR5LQKXLLZ4 · pith_short_8: YCECPLR5

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/YCECPLR5LQKXLLZ4DXBNJH53A5 \
  | 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: c08827ae3d5c1575af3c1dc2d49fbb0777de4612df5abbb308bc812791282f67

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c13ca9a385acbb4ca743727e2f0a82ede71c231fe8267febfae4c9c9503ab991",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-06-15T20:56:11Z",
    "title_canon_sha256": "50bf7de442af3aeef3814652a567b81425b83f0798c05507778c17ebb0891d6e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.06611",
    "kind": "arxiv",
    "version": 1
  }
}