Pith Number

pith:43YZLUCF

pith:2018:43YZLUCFPKJOT2BQE2DROFERZM

not attested not anchored not stored refs pending

Coulson Integral Formula for the Vertex Energy of a Graph

Beatriz Carely Luna Olivera, Marcelino Ram\'irez Ib\'a\~nez, Octavio Arizmendi

arxiv:1809.07833 v1 · 2018-09-20 · math.SP · 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{43YZLUCFPKJOT2BQE2DROFERZM}

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	2026-05-18T00:05:11.205164Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6f195d0457a92e9e8302687171491cb0f0872480169c93e539705e573e37dfd

Aliases

arxiv: 1809.07833 · arxiv_version: 1809.07833v1 · doi: 10.48550/arxiv.1809.07833 · pith_short_12: 43YZLUCFPKJO · pith_short_16: 43YZLUCFPKJOT2BQ · pith_short_8: 43YZLUCF

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/43YZLUCFPKJOT2BQE2DROFERZM \
  | 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: e6f195d0457a92e9e8302687171491cb0f0872480169c93e539705e573e37dfd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b02d68fb6e5f0618fab861548f602fc90149a6872a2eb0ec89c60100a7251836",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2018-09-20T20:07:04Z",
    "title_canon_sha256": "bbc523f1601b6a51ef747bd8a5dfb2c59dbaf207cb0777e8102a0393b3871fd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.07833",
    "kind": "arxiv",
    "version": 1
  }
}