Pith Number

pith:GZ2ZNOA4

pith:2012:GZ2ZNOA4FROUD6NVEVX5TQEX43

not attested not anchored not stored refs pending

Spectra of the neighbourhood corona of two graphs

Sanming Zhou, Xiaogang Liu

arxiv:1209.5906 v3 · 2012-09-26 · 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{GZ2ZNOA4FROUD6NVEVX5TQEX43}

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	2026-05-18T02:41:17.313450Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

367596b81c2c5d41f9b5256fd9c097e6e261d8bf83f945200804b8dccc5e8431

Aliases

arxiv: 1209.5906 · arxiv_version: 1209.5906v3 · doi: 10.48550/arxiv.1209.5906 · pith_short_12: GZ2ZNOA4FROU · pith_short_16: GZ2ZNOA4FROUD6NV · pith_short_8: GZ2ZNOA4

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/GZ2ZNOA4FROUD6NVEVX5TQEX43 \
  | 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: 367596b81c2c5d41f9b5256fd9c097e6e261d8bf83f945200804b8dccc5e8431

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f4d3e44bcf06dc474491e956db89c1d792422842e3e541d80530d8c3f08fdab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-09-26T11:48:23Z",
    "title_canon_sha256": "098f5bb3e811b7b822c45ab422b699d1bec815cd5a9ae2e68382975312f106db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5906",
    "kind": "arxiv",
    "version": 3
  }
}