Pith Number

pith:WGBF5OMQ

pith:2018:WGBF5OMQQKUMPO5PTKN5BPDNBA

not attested not anchored not stored refs pending

Spanning trees with at most 4 leaves in $K_{1,5}-$free graphs

Dang Dinh Hanh, Pham Hoang Ha, Yuan Chen

arxiv:1804.09332 v2 · 2018-04-25 · 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{WGBF5OMQQKUMPO5PTKN5BPDNBA}

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	2026-05-18T00:02:49.450245Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1825eb99082a8c7bbaf9a9bd0bc6d080ae7d48a64d21b7eee8692c7ce2e4000

Aliases

arxiv: 1804.09332 · arxiv_version: 1804.09332v2 · doi: 10.48550/arxiv.1804.09332 · pith_short_12: WGBF5OMQQKUM · pith_short_16: WGBF5OMQQKUMPO5P · pith_short_8: WGBF5OMQ

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/WGBF5OMQQKUMPO5PTKN5BPDNBA \
  | 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: b1825eb99082a8c7bbaf9a9bd0bc6d080ae7d48a64d21b7eee8692c7ce2e4000

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f8c2abb56825b9dc7be34e1e0c0673359b347b94834434b6bcbd7ee6d981417",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-04-25T03:15:44Z",
    "title_canon_sha256": "a62248a5effc84e40ff466a326fed95d5ccc215ff6dc832f861a5b6fd45329a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.09332",
    "kind": "arxiv",
    "version": 2
  }
}