Pith Number

pith:H7AS6Q4D

pith:2024:H7AS6Q4DCVPLOIH5O3EAFSOXJJ

not attested not anchored not stored refs pending

Clique covers and decompositions of cliques of graphs

Jialin He, J\'ozsef Balogh, Michael C. Wigal, Robert A. Krueger, The Nguyen

arxiv:2412.05522 v2 · 2024-12-07 · 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{H7AS6Q4DCVPLOIH5O3EAFSOXJJ}

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 Proof of Nash-Williams' Conjecture

Receipt and verification

First computed	2026-07-05T09:53:08.324004Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3fc12f4383155eb720fd76c802c9d74a5965466442b605adc67874f28fc1ab85

Aliases

arxiv: 2412.05522 · arxiv_version: 2412.05522v2 · doi: 10.48550/arxiv.2412.05522 · pith_short_12: H7AS6Q4DCVPL · pith_short_16: H7AS6Q4DCVPLOIH5 · pith_short_8: H7AS6Q4D

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/H7AS6Q4DCVPLOIH5O3EAFSOXJJ \
  | 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: 3fc12f4383155eb720fd76c802c9d74a5965466442b605adc67874f28fc1ab85

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8a0ea16c9fd51f50ef5d42d15add6cc308a9f209b337ad559b6d00c878cd75e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-12-07T03:37:42Z",
    "title_canon_sha256": "5976e28f6c8ffff8024b47b4088a2bdf6d7217509fd4885a272aeea0c7d9a089"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.05522",
    "kind": "arxiv",
    "version": 2
  }
}