Pith Number

pith:VHYE3CGS

pith:2025:VHYE3CGSFG6Z5QQY5JTMINT7OM

not attested not anchored not stored refs pending

On the maximum number of edges of outer k-planar graphs

Maximilian Pfister

arxiv:2505.24490 v1 · 2025-05-30 · 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{VHYE3CGSFG6Z5QQY5JTMINT7OM}

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	2026-07-05T11:12:50.969047Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9f04d88d229bd9ec218ea66c4367f7313119289584ce35d17ec2b37160f0088

Aliases

arxiv: 2505.24490 · arxiv_version: 2505.24490v1 · doi: 10.48550/arxiv.2505.24490 · pith_short_12: VHYE3CGSFG6Z · pith_short_16: VHYE3CGSFG6Z5QQY · pith_short_8: VHYE3CGS

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/VHYE3CGSFG6Z5QQY5JTMINT7OM \
  | 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: a9f04d88d229bd9ec218ea66c4367f7313119289584ce35d17ec2b37160f0088

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f2a9482d0f968576a3f90d987d74fc533b63bf695eb02a1d6d8e265c3e2d388",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-05-30T11:43:14Z",
    "title_canon_sha256": "6e1e33ee2c7ec36609f3ccd6b7634a795be7f779096df7c0cbfa088a39e28d73"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.24490",
    "kind": "arxiv",
    "version": 1
  }
}