Pith Number

pith:WXFP3M4J

pith:2019:WXFP3M4J3Y43YJF7T6TXVLWHAL

not attested not anchored not stored refs pending

Cop number of graphs without long holes

Vaidy Sivaraman

arxiv:2001.00477 v1 · 2019-12-30 · math.CO · cs.DM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WXFP3M4J3Y43YJF7T6TXVLWHAL}

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

$4K_1$-free graph with the cop number $3$

Receipt and verification

First computed	2026-07-05T00:29:24.690531Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5cafdb389de39bc24bf9fa77aaec702d1308fd86436107d421525d9a7eb1c64

Aliases

arxiv: 2001.00477 · arxiv_version: 2001.00477v1 · doi: 10.48550/arxiv.2001.00477 · pith_short_12: WXFP3M4J3Y43 · pith_short_16: WXFP3M4J3Y43YJF7 · pith_short_8: WXFP3M4J

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/WXFP3M4J3Y43YJF7T6TXVLWHAL \
  | 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: b5cafdb389de39bc24bf9fa77aaec702d1308fd86436107d421525d9a7eb1c64

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0241a11adaddf9509c25a20e5d21dc8c557b2c42427c545492ba20688a431110",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-12-30T02:01:04Z",
    "title_canon_sha256": "615bfcdac712d95f3c6ebd235d4fc1eaae3981c5229dd7cc0cabbb48fca7f734"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2001.00477",
    "kind": "arxiv",
    "version": 1
  }
}