Pith Number

pith:L6FS2PAQ

pith:2025:L6FS2PAQCSXTVK4O6TCLXNKRKY

not attested not anchored not stored refs pending

Density Hajnal--Szemer\'{e}di theorem for cliques of size four

Caiyun Hu, Jianfeng Hou, Xizhi Liu, Yixiao Zhang

arxiv:2501.00801 v1 · 2025-01-01 · 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{L6FS2PAQCSXTVK4O6TCLXNKRKY}

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

Tiling $H$ in dense graphs

Receipt and verification

First computed	2026-07-05T09:56:10.447558Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f8b2d3c1014af3aab8ef4c4bbb551563a4cb564bfe3cc21ad0d6518a69f2f5f

Aliases

arxiv: 2501.00801 · arxiv_version: 2501.00801v1 · doi: 10.48550/arxiv.2501.00801 · pith_short_12: L6FS2PAQCSXT · pith_short_16: L6FS2PAQCSXTVK4O · pith_short_8: L6FS2PAQ

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/L6FS2PAQCSXTVK4O6TCLXNKRKY \
  | 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: 5f8b2d3c1014af3aab8ef4c4bbb551563a4cb564bfe3cc21ad0d6518a69f2f5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af4cec6b020d8b2aa02e9889e5288bbaaad4feb13fd06ed3f4333155f0169838",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-01-01T10:53:18Z",
    "title_canon_sha256": "2c4571c305a14d85b60aa0dd59892e3ec189202190fbccaabf4efa231a5b84a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.00801",
    "kind": "arxiv",
    "version": 1
  }
}