Pith Number

pith:WDYWKZ57

pith:2019:WDYWKZ57WDSBGRA26UHYW4SWAP

not attested not anchored not stored refs pending

On well-covered direct products

Douglas F. Rall, Kirsti Kuenzel

arxiv:1901.03218 v1 · 2019-01-10 · 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{WDYWKZ57WDSBGRA26UHYW4SWAP}

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	2026-05-17T23:56:35.198275Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0f16567bfb0e413441af50f8b725603e101e51d9bb0adb518c85757a95671f3

Aliases

arxiv: 1901.03218 · arxiv_version: 1901.03218v1 · doi: 10.48550/arxiv.1901.03218 · pith_short_12: WDYWKZ57WDSB · pith_short_16: WDYWKZ57WDSBGRA2 · pith_short_8: WDYWKZ57

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/WDYWKZ57WDSBGRA26UHYW4SWAP \
  | 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: b0f16567bfb0e413441af50f8b725603e101e51d9bb0adb518c85757a95671f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f9873030aa44f1c6ab0911cf2fca47612a3e7f0e66593ff6e5a5b817f53d95c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-01-10T15:28:37Z",
    "title_canon_sha256": "f08d096d61000f4f62d0a6f97799487f9b1b5d41dbda32aa0140bc19b7373368"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.03218",
    "kind": "arxiv",
    "version": 1
  }
}