Pith Number

pith:W2Q4XFBL

pith:2012:W2Q4XFBLJM3ZPACOBPOESZIWXT

not attested not anchored not stored refs pending

On extremal graphs with at most two internally disjoint Steiner trees connecting any three vertices

Hengzhe Li, Xueliang Li, Yaping Mao

arxiv:1210.8021 v2 · 2012-10-30 · 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{W2Q4XFBLJM3ZPACOBPOESZIWXT}

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	2026-05-18T03:35:25.302045Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6a1cb942b4b3797804e0bdc496516bcfb8c9d76566b5dc2483121a37b5b5ecc

Aliases

arxiv: 1210.8021 · arxiv_version: 1210.8021v2 · doi: 10.48550/arxiv.1210.8021 · pith_short_12: W2Q4XFBLJM3Z · pith_short_16: W2Q4XFBLJM3ZPACO · pith_short_8: W2Q4XFBL

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/W2Q4XFBLJM3ZPACOBPOESZIWXT \
  | 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: b6a1cb942b4b3797804e0bdc496516bcfb8c9d76566b5dc2483121a37b5b5ecc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1948d3ee5ea4e716b5250f4c293a8bc82c5b1d5d8011be5a2ec71ad110e1d6f4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-10-30T14:24:49Z",
    "title_canon_sha256": "cb2c62ddee8b0491fe09943a7a5e4c3d72271942f7ca733bfa92090eedecb13c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.8021",
    "kind": "arxiv",
    "version": 2
  }
}