Pith Number

pith:5OZ7KHDX

pith:2019:5OZ7KHDXW5WOVF2PWXDQHFZYIS

not attested not anchored not stored refs pending

Most binary matrices have no small defining set

Anita Liebenau, Carly Bodkin, Ian M. Wanless

arxiv:1908.01267 v2 · 2019-08-04 · 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{5OZ7KHDXW5WOVF2PWXDQHFZYIS}

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	2026-07-05T01:13:23.310193Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebb3f51c77b76cea974fb5c7039738449fba5893a61757e3c1ed9834576bb283

Aliases

arxiv: 1908.01267 · arxiv_version: 1908.01267v2 · doi: 10.48550/arxiv.1908.01267 · pith_short_12: 5OZ7KHDXW5WO · pith_short_16: 5OZ7KHDXW5WOVF2P · pith_short_8: 5OZ7KHDX

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/5OZ7KHDXW5WOVF2PWXDQHFZYIS \
  | 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: ebb3f51c77b76cea974fb5c7039738449fba5893a61757e3c1ed9834576bb283

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7d85c2f7b7051d04243042f2708273d3bfbc242bf04fb44faa1c3bba7d4edc0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-08-04T03:43:07Z",
    "title_canon_sha256": "48b9c7ae998e784bd982422ffc00905f00c8cacf731fd7c20abe1a185022f69c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.01267",
    "kind": "arxiv",
    "version": 2
  }
}