Pith Number

pith:HFOIDZ4F

pith:2000:HFOIDZ4FUPMPKAXBXBG4QLNDBC

not attested not anchored not stored refs pending

Toward the Rectilinear Crossing Number of $K_n$: New Drawings, Upper Bounds, and Asymptotics

Alex Brodsky, Ellen Gethner, Stephane Durocher

arxiv:cs/0009028 v1 · 2000-09-28 · cs.DM · cs.CG · 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{HFOIDZ4FUPMPKAXBXBG4QLNDBC}

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	2026-05-18T04:11:49.824055Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

395c81e785a3d8f502e1b84dc82da308afeb61c9c4540994b19251c5cdfd096e

Aliases

arxiv: cs/0009028 · arxiv_version: cs/0009028v1 · doi: 10.48550/arxiv.cs/0009028 · pith_short_12: HFOIDZ4FUPMP · pith_short_16: HFOIDZ4FUPMPKAXB · pith_short_8: HFOIDZ4F

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/HFOIDZ4FUPMPKAXBXBG4QLNDBC \
  | 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: 395c81e785a3d8f502e1b84dc82da308afeb61c9c4540994b19251c5cdfd096e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4af3a19b468bd1cdb12de7bd64bf53f5093ae52c64a6d886ea0ea304d22b7656",
    "cross_cats_sorted": [
      "cs.CG",
      "math.CO"
    ],
    "license": "",
    "primary_cat": "cs.DM",
    "submitted_at": "2000-09-28T16:33:06Z",
    "title_canon_sha256": "925efa9ec30c25181892eb99a9b400065ae4cfbe1670e892af6ea2067e68cd19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "cs/0009028",
    "kind": "arxiv",
    "version": 1
  }
}