Pith Number

pith:4NMVYV6W

pith:2022:4NMVYV6W7CH2ESFXZMRQCWJISD

not attested not anchored not stored refs pending

Domination and independence number of large $2$-crossing-critical graphs

Martin Pra\v{c}ek, Maru\v{s}a Lek\v{s}e, Mihael Pa\v{c}nik, Petra Podlogar, Vesna Ir\v{s}i\v{c}

arxiv:2203.12206 v1 · 2022-03-23 · 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{4NMVYV6W7CH2ESFXZMRQCWJISD}

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	2026-07-05T04:07:56.932853Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3595c57d6f88fa248b7cb2301592890d1cd9df2cba3944800242a90aa2595e1

Aliases

arxiv: 2203.12206 · arxiv_version: 2203.12206v1 · doi: 10.48550/arxiv.2203.12206 · pith_short_12: 4NMVYV6W7CH2 · pith_short_16: 4NMVYV6W7CH2ESFX · pith_short_8: 4NMVYV6W

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/4NMVYV6W7CH2ESFXZMRQCWJISD \
  | 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: e3595c57d6f88fa248b7cb2301592890d1cd9df2cba3944800242a90aa2595e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39f736853351c219316589be1f253f7348dc146baafca7a21c186e6cf27120de",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-03-23T05:49:15Z",
    "title_canon_sha256": "3e6d726f59bfb9208a037ef9ec6ad65e6e78a3eb99345c60b90a91806d5a5962"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2203.12206",
    "kind": "arxiv",
    "version": 1
  }
}