Pith Number

pith:P3OP4NX6

pith:2016:P3OP4NX6PLNEWK5JOO7RPCFVCN

not attested not anchored not stored refs pending

Spectral characterizations of two families of nearly complete bipartite graphs

Chia-an Liu, Chih-wen Weng

arxiv:1601.07012 v1 · 2016-01-26 · 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{P3OP4NX6PLNEWK5JOO7RPCFVCN}

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	2026-05-18T01:21:59.292867Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7edcfe36fe7ada4b2ba973bf1788b51362030d08db72b86223afa7fa6768e292

Aliases

arxiv: 1601.07012 · arxiv_version: 1601.07012v1 · doi: 10.48550/arxiv.1601.07012 · pith_short_12: P3OP4NX6PLNE · pith_short_16: P3OP4NX6PLNEWK5J · pith_short_8: P3OP4NX6

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/P3OP4NX6PLNEWK5JOO7RPCFVCN \
  | 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: 7edcfe36fe7ada4b2ba973bf1788b51362030d08db72b86223afa7fa6768e292

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "013d9c7dc6c4a59fa3713bf0091af11a20c892261dee4c0edeed459d61b39d0a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-01-26T13:23:40Z",
    "title_canon_sha256": "d916e1899b5a083b6e38a9dc19e037a4031d4a531c08ac0ee97a49085c6c148d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.07012",
    "kind": "arxiv",
    "version": 1
  }
}