Pith Number

pith:AITPL5ET

pith:2014:AITPL5ETS3JQVXEAC7D2RWZKCJ

not attested not anchored not stored refs pending

The Laplacian polynomial of graphs derived from regular graphs and applications

Fu-Tao Hu, Jia-Bao Liu, Xiang-Feng Pan

arxiv:1411.5509 v1 · 2014-11-20 · 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{AITPL5ETS3JQVXEAC7D2RWZKCJ}

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	2026-05-18T02:33:24.459897Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0226f5f49396d30adc8017c7a8db2a126563aa3dac8feff98f9a31e491c81056

Aliases

arxiv: 1411.5509 · arxiv_version: 1411.5509v1 · doi: 10.48550/arxiv.1411.5509 · pith_short_12: AITPL5ETS3JQ · pith_short_16: AITPL5ETS3JQVXEA · pith_short_8: AITPL5ET

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/AITPL5ETS3JQVXEAC7D2RWZKCJ \
  | 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: 0226f5f49396d30adc8017c7a8db2a126563aa3dac8feff98f9a31e491c81056

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e51004d1efb7cfb4a32d83be05a9f775e709da35275d72354b4216e72dba62d4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-11-20T11:43:19Z",
    "title_canon_sha256": "d9c4e3ecf614250a2e6a8274f7567e1f6d7da13a4829eb2580bc04b2613fb800"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.5509",
    "kind": "arxiv",
    "version": 1
  }
}