Pith Number

pith:W72CCI53

pith:2018:W72CCI53VF5D72K6YUMYFM5IVE

not attested not anchored not stored refs pending

Tight Upper Bounds on the Crossing Number in a Minor-Closed Class

Bojan Mohar, David R. Wood, Ken-ichi Kawarabayashi, Vida Dujmovi\'c

arxiv:1807.11617 v1 · 2018-07-31 · math.CO · cs.CG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W72CCI53VF5D72K6YUMYFM5IVE}

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	2026-05-18T00:09:21.597450Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7f42123bba97a3fe95ec51982b3a8a93ebd60b1a4175ea428ab94b89c805bf9

Aliases

arxiv: 1807.11617 · arxiv_version: 1807.11617v1 · doi: 10.48550/arxiv.1807.11617 · pith_short_12: W72CCI53VF5D · pith_short_16: W72CCI53VF5D72K6 · pith_short_8: W72CCI53

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/W72CCI53VF5D72K6YUMYFM5IVE \
  | 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: b7f42123bba97a3fe95ec51982b3a8a93ebd60b1a4175ea428ab94b89c805bf9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "090eb8641a4a9d55c52c5febe362465b2271697f2385b02242072d2b1192901d",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-07-31T00:44:34Z",
    "title_canon_sha256": "3f761b3d5a15dd32a3f90ffacfb7b3639219b5b512fae1337c78417f3c071f5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.11617",
    "kind": "arxiv",
    "version": 1
  }
}