Pith Number

pith:E2JWU3DM

pith:2026:E2JWU3DMOWRXDCV55QC5XRINGO

not attested not anchored not stored refs pending

An Erd\H{o}s-P\'osa theorem for cycles and faces of distinct lengths

Caleb McFarland, J. Pascal Gollin, Kevin Hendrey, Marek Soko{\l}owski, Maximilian Gorsky, Meike Hatzel, Paul Wollan, Sebastian Wiederrecht, Tony Huynh

arxiv:2607.06869 v1 · 2026-07-08 · 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{E2JWU3DMOWRXDCV55QC5XRINGO}

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	2026-07-09T00:19:31.983299Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26936a6c6c75a3718abdec05dbc50d33ae5619c561e1bea1c15b1954654e036c

Aliases

arxiv: 2607.06869 · arxiv_version: 2607.06869v1 · doi: 10.48550/arxiv.2607.06869 · pith_short_12: E2JWU3DMOWRX · pith_short_16: E2JWU3DMOWRXDCV5 · pith_short_8: E2JWU3DM

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/E2JWU3DMOWRXDCV55QC5XRINGO \
  | 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: 26936a6c6c75a3718abdec05dbc50d33ae5619c561e1bea1c15b1954654e036c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80b24e8f6e21c221ec2045ed29e64c740796c3ecb031d671f9fa278e3029194d",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-08T00:01:19Z",
    "title_canon_sha256": "b2b91fc7a4472c2af210cf73364ba738cde069bbefdec83d3dfa54bcd9089cd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.06869",
    "kind": "arxiv",
    "version": 1
  }
}