Pith Number

pith:KCNWAR7A

pith:2011:KCNWAR7AEVPC3K2ATOV7UV6HWV

not attested not anchored not stored refs pending

Minor crossing number is additive over arbitrary cuts

Drago Bokal, Jes\'us Lea\~nos, Markus Chimani

arxiv:1111.6024 v1 · 2011-11-25 · 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{KCNWAR7AEVPC3K2ATOV7UV6HWV}

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	2026-05-18T04:07:41.243151Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

509b6047e0255e2dab409babfa57c7b571a0900207d5fcde131ef00a21d6c73e

Aliases

arxiv: 1111.6024 · arxiv_version: 1111.6024v1 · doi: 10.48550/arxiv.1111.6024 · pith_short_12: KCNWAR7AEVPC · pith_short_16: KCNWAR7AEVPC3K2A · pith_short_8: KCNWAR7A

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/KCNWAR7AEVPC3K2ATOV7UV6HWV \
  | 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: 509b6047e0255e2dab409babfa57c7b571a0900207d5fcde131ef00a21d6c73e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0440fd37c86a31aa73c49349f30d562fead5d2bb44ed149b0eaa978fdf41916e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-11-25T15:33:33Z",
    "title_canon_sha256": "422cbb6d26f9dabd85650dfef40aae0219f7b47cd50e19eb6a676a1c1ee253bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.6024",
    "kind": "arxiv",
    "version": 1
  }
}