Pith Number

pith:BHGHBU3Q

pith:2025:BHGHBU3QXPPTZWNLYDNPSUHOGR

not attested not anchored not stored refs pending

Minimum degree and sparse connected spanning subgraphs

Ting Huang, Yanbo Zhang, Yaojun Chen

arxiv:2507.03264 v1 · 2025-07-04 · 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{BHGHBU3QXPPTZWNLYDNPSUHOGR}

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.

Cited by

1 paper in Pith

Fan-goodness of sparse graphs

Receipt and verification

First computed	2026-07-05T11:31:55.790647Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09cc70d370bbdf3cd9abc0daf950ee3461ef2b423331a543f4dadc60716d03dc

Aliases

arxiv: 2507.03264 · arxiv_version: 2507.03264v1 · doi: 10.48550/arxiv.2507.03264 · pith_short_12: BHGHBU3QXPPT · pith_short_16: BHGHBU3QXPPTZWNL · pith_short_8: BHGHBU3Q

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/BHGHBU3QXPPTZWNLYDNPSUHOGR \
  | 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: 09cc70d370bbdf3cd9abc0daf950ee3461ef2b423331a543f4dadc60716d03dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce0a06f9f7eea9bf3e39c4d9ff20a93056aa2b9358b920eaef785c82bd2d92e0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-04T02:48:45Z",
    "title_canon_sha256": "004be933ec25fdb86c02096313525019eae29766ea39806d99cfda0fd325930a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.03264",
    "kind": "arxiv",
    "version": 1
  }
}