Pith Number

pith:LV2QFF3Y

pith:2010:LV2QFF3YZ5LAZYMUJ5YW4MCMVD

not attested not anchored not stored refs pending

On Graph Crossing Number and Edge Planarization

Anastasios Sidiropoulos, Julia Chuzhoy, Yury Makarychev

arxiv:1010.3976 v1 · 2010-10-19 · cs.DS · 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{LV2QFF3YZ5LAZYMUJ5YW4MCMVD}

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	2026-05-18T04:39:07.135153Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5d75029778cf560ce1944f716e304ca8cf6772cbea248e81294401da5ec1a13b

Aliases

arxiv: 1010.3976 · arxiv_version: 1010.3976v1 · doi: 10.48550/arxiv.1010.3976 · pith_short_12: LV2QFF3YZ5LA · pith_short_16: LV2QFF3YZ5LAZYMU · pith_short_8: LV2QFF3Y

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/LV2QFF3YZ5LAZYMUJ5YW4MCMVD \
  | 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: 5d75029778cf560ce1944f716e304ca8cf6772cbea248e81294401da5ec1a13b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "283c1a2cb9fb68cf2a01087fdfe0a2e0dd9555206187397b73bc03b4e6200c64",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2010-10-19T16:52:33Z",
    "title_canon_sha256": "d24620a4efaa290211b81010cb6583517c47ef8678caab1e78f03f6a4998c0a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.3976",
    "kind": "arxiv",
    "version": 1
  }
}