Pith Number

pith:67G2YZ5O

pith:2013:67G2YZ5O7BDXMSQCE7IIN3Z5UG

not attested not anchored not stored refs pending

On extremal graphs with at most $\ell$ internally disjoint Steiner trees connecting any n-1 vertices

Xueliang Li, Yaping Mao

arxiv:1304.3774 v1 · 2013-04-13 · 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{67G2YZ5O7BDXMSQCE7IIN3Z5UG}

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	2026-05-18T03:28:04.392242Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7cdac67aef847764a0227d086ef3da19173dedd59ceb1d196910bb5670404f0

Aliases

arxiv: 1304.3774 · arxiv_version: 1304.3774v1 · doi: 10.48550/arxiv.1304.3774 · pith_short_12: 67G2YZ5O7BDX · pith_short_16: 67G2YZ5O7BDXMSQC · pith_short_8: 67G2YZ5O

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/67G2YZ5O7BDXMSQCE7IIN3Z5UG \
  | 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: f7cdac67aef847764a0227d086ef3da19173dedd59ceb1d196910bb5670404f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08b178d0aa163ffe03eb45ee33186872f548130e81b79e4073b5938ed5a4eb98",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-04-13T04:23:23Z",
    "title_canon_sha256": "d0a5e30cccfd3b60ab44b6a66f64a1b169ad5fb646daa6d3ab58733301befeb0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.3774",
    "kind": "arxiv",
    "version": 1
  }
}