Pith Number

pith:AYAD5MOV

pith:2018:AYAD5MOVSZSHRPISKZ3WS5BZGL

not attested not anchored not stored refs pending

On Degree Properties of Crossing-Critical Families of Graphs

(2) Faculty of Informatics, Brno, Czech Republic), Drago Bokal (1), Marek Der\v{n}\'ar (2), Masaryk University, Mathematics, Mojca Bra\v{c}i\v{c} (1), Petr Hlin\v{e}n\'y (2) ((1) Faculty of Natural Sciences, Slovenia, University of Maribor

arxiv:1803.10509 v2 · 2018-03-28 · 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{AYAD5MOVSZSHRPISKZ3WS5BZGL}

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	2026-05-17T23:51:09.754450Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06003eb1d5966478bd12567769743932c85f8e41296d1eda3bf15fdd462224ab

Aliases

arxiv: 1803.10509 · arxiv_version: 1803.10509v2 · doi: 10.48550/arxiv.1803.10509 · pith_short_12: AYAD5MOVSZSH · pith_short_16: AYAD5MOVSZSHRPIS · pith_short_8: AYAD5MOV

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/AYAD5MOVSZSHRPISKZ3WS5BZGL \
  | 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: 06003eb1d5966478bd12567769743932c85f8e41296d1eda3bf15fdd462224ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "723358caef336f026abd6627693121393069fb299a92a8be60153a69183fd602",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-03-28T10:25:27Z",
    "title_canon_sha256": "2cb15c1e6d8eb84bc7cc76e5738ca3efc67a6c3ec137c40fe726a63bff0174f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.10509",
    "kind": "arxiv",
    "version": 2
  }
}