Pith Number

pith:43FHU6G4

pith:2013:43FHU6G4SAHWMQ33K2LJ3K4BIG

not attested not anchored not stored refs pending

Shellable drawings and the cylindrical crossing number of $K_n$

Bernardo M. \'Abrego, Gelasio Salazar, Oswin Aichholzer, Pedro Ramos, Silvia Fern\'andez-Merchant

arxiv:1309.3665 v2 · 2013-09-14 · 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{43FHU6G4SAHWMQ33K2LJ3K4BIG}

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	2026-05-18T03:10:45.519406Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6ca7a78dc900f66437b56969dab8141ade6bf76f2465c6be87466d0296bb876

Aliases

arxiv: 1309.3665 · arxiv_version: 1309.3665v2 · doi: 10.48550/arxiv.1309.3665 · pith_short_12: 43FHU6G4SAHW · pith_short_16: 43FHU6G4SAHWMQ33 · pith_short_8: 43FHU6G4

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/43FHU6G4SAHWMQ33K2LJ3K4BIG \
  | 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: e6ca7a78dc900f66437b56969dab8141ade6bf76f2465c6be87466d0296bb876

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6d00104517e6f9ec845f0894fe5029bc48513c75e047bfe1786b34057cde182",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-09-14T13:24:20Z",
    "title_canon_sha256": "66ee686b7323d4afc633589af1bc46f374615b7c6a3fb3acebb5a8cfa3aa044b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.3665",
    "kind": "arxiv",
    "version": 2
  }
}