Pith Number

pith:FM5LK3HH

pith:2017:FM5LK3HH42LVQCWIN7E6P2GACQ

not attested not anchored not stored refs pending

On density of subgraphs of Cartesian products

Arnaud Labourel, S\'ebastien Ratel, Victor Chepoi

arxiv:1711.11485 v3 · 2017-11-30 · cs.DM · 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{FM5LK3HH42LVQCWIN7E6P2GACQ}

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	2026-05-17T23:39:42.015551Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b3ab56ce7e697580ac86fc9e7e8c0140f09b411edeccdd112209b90af84c636

Aliases

arxiv: 1711.11485 · arxiv_version: 1711.11485v3 · doi: 10.48550/arxiv.1711.11485 · pith_short_12: FM5LK3HH42LV · pith_short_16: FM5LK3HH42LVQCWI · pith_short_8: FM5LK3HH

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/FM5LK3HH42LVQCWIN7E6P2GACQ \
  | 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: 2b3ab56ce7e697580ac86fc9e7e8c0140f09b411edeccdd112209b90af84c636

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7158d5c71597816fe7516a1764763bc1fd8b67b608750f6be20e4592f392620a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2017-11-30T16:08:56Z",
    "title_canon_sha256": "b7f70635be5dbd44c700b56606d08349e2516d08c8dec050da38e94f5f021609"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.11485",
    "kind": "arxiv",
    "version": 3
  }
}