Pith Number

pith:4Q7N3GLA

pith:2020:4Q7N3GLAH54ICGAJM6EZQINJUY

not attested not anchored not stored refs pending

Betti numbers of weighted oriented graphs

Beata Casiday, Selvi Kara

arxiv:2009.10903 v1 · 2020-09-23 · math.AC · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4Q7N3GLAH54ICGAJM6EZQINJUY}

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	2026-07-05T01:37:27.258526Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e43edd99603f7881180967899821a9a628a22f7172938f443436cc155b5a51ed

Aliases

arxiv: 2009.10903 · arxiv_version: 2009.10903v1 · doi: 10.48550/arxiv.2009.10903 · pith_short_12: 4Q7N3GLAH54I · pith_short_16: 4Q7N3GLAH54ICGAJ · pith_short_8: 4Q7N3GLA

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/4Q7N3GLAH54ICGAJM6EZQINJUY \
  | 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: e43edd99603f7881180967899821a9a628a22f7172938f443436cc155b5a51ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7919da522c36fa6673128b39193beddef340209aa5e9bda06097e5deb637814",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2020-09-23T02:15:11Z",
    "title_canon_sha256": "0d22912f6e0b8ca9711a8f69cf99ffab4f1249aa6387b68978c84a06bb072b4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2009.10903",
    "kind": "arxiv",
    "version": 1
  }
}