Pith Number

pith:PGQXX4UB

pith:2015:PGQXX4UB3MIOPD4MQYZ6YQLT62

not attested not anchored not stored refs pending

Laplacian Coefficient, Matching Polynomial and Incidence Energy of of Trees with Described Maximum Degree

Xiao-Dong Zhang, Ya-Lei Jin, Yeong-Nan Yeh

arxiv:1512.01333 v1 · 2015-12-04 · 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{PGQXX4UB3MIOPD4MQYZ6YQLT62}

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	2026-05-18T01:25:17.248023Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79a17bf281db10e78f8c8633ec4173f69c911779e4233419b9d74f6f1a53833c

Aliases

arxiv: 1512.01333 · arxiv_version: 1512.01333v1 · doi: 10.48550/arxiv.1512.01333 · pith_short_12: PGQXX4UB3MIO · pith_short_16: PGQXX4UB3MIOPD4M · pith_short_8: PGQXX4UB

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/PGQXX4UB3MIOPD4MQYZ6YQLT62 \
  | 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: 79a17bf281db10e78f8c8633ec4173f69c911779e4233419b9d74f6f1a53833c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21d50e2da5df13324d3c30de797e9f3194d3d22bcf9aeeacf97e7ffa74b8dc4b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-04T07:56:39Z",
    "title_canon_sha256": "48d58ff4d979fff764ce66422109bfd72ea888ff22214fbca1b404eadcd4ba38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.01333",
    "kind": "arxiv",
    "version": 1
  }
}