Pith Number

pith:FUMKL5F4

pith:2023:FUMKL5F4WVFIMTGG3GBSXUTOXS

not attested not anchored not stored refs pending

Induced subgraph density. VI. Bounded VC-dimension

Alex Scott, Paul Seymour, Tung Nguyen

arxiv:2312.15572 v3 · 2023-12-25 · 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{FUMKL5F4WVFIMTGG3GBSXUTOXS}

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

2 papers in Pith

The Twin-Width of Graphs of Bounded VC-Dimension

Uniform set systems with small VC-dimension

Receipt and verification

First computed	2026-07-05T12:07:52.792183Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d18a5f4bcb54a864cc6d9832bd26ebc8dd7bddd4ec3af148d28d54b79191a99

Aliases

arxiv: 2312.15572 · arxiv_version: 2312.15572v3 · doi: 10.48550/arxiv.2312.15572 · pith_short_12: FUMKL5F4WVFI · pith_short_16: FUMKL5F4WVFIMTGG · pith_short_8: FUMKL5F4

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/FUMKL5F4WVFIMTGG3GBSXUTOXS \
  | 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: 2d18a5f4bcb54a864cc6d9832bd26ebc8dd7bddd4ec3af148d28d54b79191a99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a906720522a16c394cbcc0a31b236850a56a085c27d9a7b9b70bfd9dbd34f09",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-12-25T00:53:40Z",
    "title_canon_sha256": "d444d180f52fd013a12582353d110f72580fa72c62dcb79ab2540e6479c23585"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2312.15572",
    "kind": "arxiv",
    "version": 3
  }
}