Pith Number

pith:LC232NKX

pith:2012:LC232NKXOT7KCPAFU37V2G257M

not attested not anchored not stored refs pending

Improvement on the decay of crossing numbers

G\'eza T\'oth, Jakub \v{C}ern\'y, Jan Kyn\v{c}l

arxiv:1201.5421 v1 · 2012-01-26 · 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{LC232NKXOT7KCPAFU37V2G257M}

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	2026-05-18T03:16:40.602244Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

58b5bd355774fea13c05a6ff5d1b5dfb3ec75a1cf7bfbe985697c66e4251436a

Aliases

arxiv: 1201.5421 · arxiv_version: 1201.5421v1 · doi: 10.48550/arxiv.1201.5421 · pith_short_12: LC232NKXOT7K · pith_short_16: LC232NKXOT7KCPAF · pith_short_8: LC232NKX

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/LC232NKXOT7KCPAFU37V2G257M \
  | 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: 58b5bd355774fea13c05a6ff5d1b5dfb3ec75a1cf7bfbe985697c66e4251436a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c727d2069f999cc83dd840c323ce4094d93fdcb688b30327c268c443d7496ae",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-01-26T01:15:44Z",
    "title_canon_sha256": "0447c1d8bebd62aa869bcf5d7ca27546468646c79899e8c4f19883119e0f6a40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.5421",
    "kind": "arxiv",
    "version": 1
  }
}