Pith Number

pith:D5WLRMPN

pith:2015:D5WLRMPN5C6FO25H5WNNMA7GPU

not attested not anchored not stored refs pending

Exact minimum codegree threshold for $K^- _4$-factors

Allan Lo, Andrew Treglown, Jie Han, Yi Zhao

arxiv:1509.02577 v1 · 2015-09-08 · 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{D5WLRMPN5C6FO25H5WNNMA7GPU}

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	2026-05-18T01:33:34.699336Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f6cb8b1ede8bc576ba7ed9ad603e67d0aba3a4abab2c34ef93cf6584de7668a

Aliases

arxiv: 1509.02577 · arxiv_version: 1509.02577v1 · doi: 10.48550/arxiv.1509.02577 · pith_short_12: D5WLRMPN5C6F · pith_short_16: D5WLRMPN5C6FO25H · pith_short_8: D5WLRMPN

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/D5WLRMPN5C6FO25H5WNNMA7GPU \
  | 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: 1f6cb8b1ede8bc576ba7ed9ad603e67d0aba3a4abab2c34ef93cf6584de7668a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6378ef607599ef2f580965f63e512411ed194a6d38f8fc5c0b98b38c26668e77",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-09-08T23:16:33Z",
    "title_canon_sha256": "6a0f72b3b5d886da28f0c5db408a6270059fa1b408711413121cbb25ecf6c85f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.02577",
    "kind": "arxiv",
    "version": 1
  }
}