Pith Number

pith:X73C7BEP

pith:2010:X73C7BEPYLODAO7UOOWLATMZBU

not attested not anchored not stored refs pending

$H$-product and $H$-threshold graphs

Pavel Skums

arxiv:1011.4726 v2 · 2010-11-22 · 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{X73C7BEPYLODAO7UOOWLATMZBU}

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	2026-05-18T01:11:00.694837Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bff62f848fc2dc303bf473acb04d990d3e71d8117be1039d503003835a04b087

Aliases

arxiv: 1011.4726 · arxiv_version: 1011.4726v2 · doi: 10.48550/arxiv.1011.4726 · pith_short_12: X73C7BEPYLOD · pith_short_16: X73C7BEPYLODAO7U · pith_short_8: X73C7BEP

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/X73C7BEPYLODAO7UOOWLATMZBU \
  | 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: bff62f848fc2dc303bf473acb04d990d3e71d8117be1039d503003835a04b087

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc030b123fcbe71baf4d2842b9dcc0be79d9c391fec77b9cfd926ea1325d0625",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-11-22T04:43:20Z",
    "title_canon_sha256": "bc8c51ed93659db3f214bcb81f2ab364ffa62ebf71dda35da91632bfe1ed968a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.4726",
    "kind": "arxiv",
    "version": 2
  }
}