Pith Number

pith:MB3TB5FD

pith:2015:MB3TB5FDM5B6GIQT2SUB2TYZEU

not attested not anchored not stored refs pending

Minimum vertex degree thresholds for tiling complete 3-partite 3-graphs

Chuanyun Zang, Jie Han, Yi Zhao

arxiv:1503.08730 v2 · 2015-03-30 · 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{MB3TB5FDM5B6GIQT2SUB2TYZEU}

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	2026-05-18T00:38:11.903523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

607730f4a36743e32213d4a81d4f192501469dfc74ba867929154bde0ed1d5e3

Aliases

arxiv: 1503.08730 · arxiv_version: 1503.08730v2 · doi: 10.48550/arxiv.1503.08730 · pith_short_12: MB3TB5FDM5B6 · pith_short_16: MB3TB5FDM5B6GIQT · pith_short_8: MB3TB5FD

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/MB3TB5FDM5B6GIQT2SUB2TYZEU \
  | 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: 607730f4a36743e32213d4a81d4f192501469dfc74ba867929154bde0ed1d5e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "088a0f58758e918d01152162f2bfdd6cc9f3f5c725dc828e72c5e1803680a112",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-03-30T16:13:44Z",
    "title_canon_sha256": "517b2f7a8b1ba8d6c62c3aafa6248cc0133fa478f5e0024bd8d1371cd3ea5f4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.08730",
    "kind": "arxiv",
    "version": 2
  }
}