Pith Number

pith:T4CZ52QT

pith:2016:T4CZ52QTSJIE3CFD5GHRBX53NH

not attested not anchored not stored refs pending

Codegree conditions for tiling complete $k$-partite $k$-graphs and loose cycles

Jie Han, Wei Gao, Yi Zhao

arxiv:1612.07247 v2 · 2016-12-21 · 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{T4CZ52QTSJIE3CFD5GHRBX53NH}

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	2026-05-17T23:51:21.717569Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f059eea1392504d88a3e98f10dfbb69e71ff741fd183810f5301a9e1bc90bb9

Aliases

arxiv: 1612.07247 · arxiv_version: 1612.07247v2 · doi: 10.48550/arxiv.1612.07247 · pith_short_12: T4CZ52QTSJIE · pith_short_16: T4CZ52QTSJIE3CFD · pith_short_8: T4CZ52QT

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/T4CZ52QTSJIE3CFD5GHRBX53NH \
  | 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: 9f059eea1392504d88a3e98f10dfbb69e71ff741fd183810f5301a9e1bc90bb9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c780203fa5e4ba7138071ab2a8761f37ed6a4bc154ab0bc8e51c51e2cf3e93a5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-12-21T17:31:15Z",
    "title_canon_sha256": "c49c501ce45b3f9509c9c7b06bdeadefafb1d049af0cd1a8fb97154e0ea71b46"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.07247",
    "kind": "arxiv",
    "version": 2
  }
}