Pith Number

pith:7UVWZJBB

pith:2025:7UVWZJBBFGMCHO3T2IY4BEGZ3D

not attested not anchored not stored refs pending

Spectral conditions for graphs to contain $k$-factors

Wenqian Zhang, Xinying Tang

arxiv:2508.05678 v1 · 2025-08-05 · 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{7UVWZJBBFGMCHO3T2IY4BEGZ3D}

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

A note on the spectral radius and $[a,b]$-factor of graphs

Receipt and verification

First computed	2026-07-05T11:50:41.411089Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd2b6ca421299823bb73d231c090d9d8dabe7656520a6ea0fb8d9f693e8db639

Aliases

arxiv: 2508.05678 · arxiv_version: 2508.05678v1 · doi: 10.48550/arxiv.2508.05678 · pith_short_12: 7UVWZJBBFGMC · pith_short_16: 7UVWZJBBFGMCHO3T · pith_short_8: 7UVWZJBB

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/7UVWZJBBFGMCHO3T2IY4BEGZ3D \
  | 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: fd2b6ca421299823bb73d231c090d9d8dabe7656520a6ea0fb8d9f693e8db639

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "949fe734c1744d4846c6cd73a5a86993344f0220bc2dfba391e76f3d8c174076",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-08-05T12:54:36Z",
    "title_canon_sha256": "a07924d735dad684377e67f203fa5a3537e42961d91469a1ca88acdb1af0c9fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.05678",
    "kind": "arxiv",
    "version": 1
  }
}