Pith Number

pith:2IZW7WPI

pith:2019:2IZW7WPIOMYJ4VH2UMDTEROMP7

not attested not anchored not stored refs pending

A Linear Upper Bound on the Weisfeiler-Leman Dimension of Graphs of Bounded Genus

Martin Grohe, Sandra Kiefer

arxiv:1904.07216 v1 · 2019-04-15 · cs.DM · cs.CC · cs.LO · 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{2IZW7WPIOMYJ4VH2UMDTEROMP7}

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	2026-05-17T23:48:34.897606Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d2336fd9e873309e54faa3073245cc7ff7e0e2a7ac3408e5118d30fb05c9cb9f

Aliases

arxiv: 1904.07216 · arxiv_version: 1904.07216v1 · doi: 10.48550/arxiv.1904.07216 · pith_short_12: 2IZW7WPIOMYJ · pith_short_16: 2IZW7WPIOMYJ4VH2 · pith_short_8: 2IZW7WPI

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/2IZW7WPIOMYJ4VH2UMDTEROMP7 \
  | 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: d2336fd9e873309e54faa3073245cc7ff7e0e2a7ac3408e5118d30fb05c9cb9f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff780301e70f2f8ef621cc6511541bbc8f826aeed3594196cf9d65fe689e007c",
    "cross_cats_sorted": [
      "cs.CC",
      "cs.LO",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2019-04-15T17:49:07Z",
    "title_canon_sha256": "fca11e830d4ca1f19fa79e9b98a2f40d4d199b9686caa2b86f763c14cda59d20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.07216",
    "kind": "arxiv",
    "version": 1
  }
}