Pith Number

pith:AVUPJFW6

pith:2015:AVUPJFW6LXQ6JPYTUOAI5E24XK

not attested not anchored not stored refs pending

On topological graphs with at most four crossings per edge

Eyal Ackerman

arxiv:1509.01932 v2 · 2015-09-07 · 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{AVUPJFW6LXQ6JPYTUOAI5E24XK}

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.

Cited by

1 paper in Pith

Some remarks on the midrange crossing constant

Receipt and verification

First computed	2026-05-17T23:50:39.024802Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0568f496de5de1e4bf13a3808e935cbabf28d75c96bf8f0d22ecc0a76e2d769c

Aliases

arxiv: 1509.01932 · arxiv_version: 1509.01932v2 · doi: 10.48550/arxiv.1509.01932 · pith_short_12: AVUPJFW6LXQ6 · pith_short_16: AVUPJFW6LXQ6JPYT · pith_short_8: AVUPJFW6

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/AVUPJFW6LXQ6JPYTUOAI5E24XK \
  | 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: 0568f496de5de1e4bf13a3808e935cbabf28d75c96bf8f0d22ecc0a76e2d769c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "45c83cb8560a418d45a364d5b03dca47e59395aebb4e4e508cf43dee69bd5c76",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-09-07T07:24:05Z",
    "title_canon_sha256": "6af2b70e5743b764cb118bf47c10370257dd81151292b438d9a092cee4d419dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.01932",
    "kind": "arxiv",
    "version": 2
  }
}