Pith Number

pith:KWUQYWUP

pith:2016:KWUQYWUPA4MI3PHNIG2N4Y2RIC

not attested not anchored not stored refs pending

Note on k-planar crossing numbers

Csaba D. T\'oth, G\'eza T\'oth, J\'anos Pach, L\'aszl\'o A. Sz\'ekely

arxiv:1611.05746 v1 · 2016-11-17 · 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{KWUQYWUPA4MI3PHNIG2N4Y2RIC}

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	2026-05-17T23:57:33.090259Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

55a90c5a8f07188dbced41b4de635140bc48b9a34a88045f8c206d0c16d891be

Aliases

arxiv: 1611.05746 · arxiv_version: 1611.05746v1 · doi: 10.48550/arxiv.1611.05746 · pith_short_12: KWUQYWUPA4MI · pith_short_16: KWUQYWUPA4MI3PHN · pith_short_8: KWUQYWUP

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/KWUQYWUPA4MI3PHNIG2N4Y2RIC \
  | 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: 55a90c5a8f07188dbced41b4de635140bc48b9a34a88045f8c206d0c16d891be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3f0df8367758082f86fd7aea34bfe39e326ac59e85467a6d50e75ded0af597c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-11-17T15:56:33Z",
    "title_canon_sha256": "69eb3bfd64654f0ed55e6b6573c711856eb78ae59290c8907cc7955d0b53c99b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.05746",
    "kind": "arxiv",
    "version": 1
  }
}