Pith Number

pith:HJXCMKQ6

pith:2013:HJXCMKQ6JCS7WJGQ4YKDVCG7UM

not attested not anchored not stored refs pending

Unicyclic Graphs with equal Laplacian Energy

Carlos Hoppen, Eliseu Fritscher, Vilmar Trevisan

arxiv:1304.1221 v1 · 2013-04-04 · math.CO · cs.DM · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HJXCMKQ6JCS7WJGQ4YKDVCG7UM}

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	2026-05-18T03:29:04.211894Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a6e262a1e48a5fb24d0e6143a88dfa33618014a6abc23b62fed91119c909085

Aliases

arxiv: 1304.1221 · arxiv_version: 1304.1221v1 · doi: 10.48550/arxiv.1304.1221 · pith_short_12: HJXCMKQ6JCS7 · pith_short_16: HJXCMKQ6JCS7WJGQ · pith_short_8: HJXCMKQ6

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/HJXCMKQ6JCS7WJGQ4YKDVCG7UM \
  | 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: 3a6e262a1e48a5fb24d0e6143a88dfa33618014a6abc23b62fed91119c909085

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5fbd9268de56ae8609ce9aea4a0dc3b34daea156de40ed032b83201888703a56",
    "cross_cats_sorted": [
      "cs.DM",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-04-04T01:21:46Z",
    "title_canon_sha256": "81ec10b0b4b8d37899cd402a1959807729858835ffc9ab4bbd158d1e5cc73899"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.1221",
    "kind": "arxiv",
    "version": 1
  }
}