Pith Number

pith:2KHPZ7EA

pith:2019:2KHPZ7EABSKYL6VQSTNMPAKRLM

not attested not anchored not stored refs pending

Resistance distance-based graph invariants and the number of spanning trees of linear crossed octagonal graphs

Jia-Bao Liu, Jing Zhao, Sakander Hayat

arxiv:1905.09424 v1 · 2019-05-23 · 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{2KHPZ7EABSKYL6VQSTNMPAKRLM}

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	2026-05-17T23:45:17.087326Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d28efcfc800c9585fab094dac781515b129eb430b5065004220fd110a23f3586

Aliases

arxiv: 1905.09424 · arxiv_version: 1905.09424v1 · doi: 10.48550/arxiv.1905.09424 · pith_short_12: 2KHPZ7EABSKY · pith_short_16: 2KHPZ7EABSKYL6VQ · pith_short_8: 2KHPZ7EA

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/2KHPZ7EABSKYL6VQSTNMPAKRLM \
  | 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: d28efcfc800c9585fab094dac781515b129eb430b5065004220fd110a23f3586

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6df423eed6c7e32ac03aadcb66ba37947a6e4eb66eb5d25e87aa28efd1c49f2",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2019-05-23T01:37:43Z",
    "title_canon_sha256": "1f0cbfc3ccdb03ded9a4802cace020b4a5f5d1f34f6661b5e81c3059403c3d89"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.09424",
    "kind": "arxiv",
    "version": 1
  }
}