Pith Number

pith:KKQZCQYH

pith:2019:KKQZCQYHVTHEOZJPOCMVEKWVVJ

not attested not anchored not stored refs pending

On the minimum number of minimal codewords

Alfred Wassermann, Michael Kiermaier, Romar dela Cruz, Sascha Kurz

arxiv:1912.09804 v1 · 2019-12-20 · 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{KKQZCQYHVTHEOZJPOCMVEKWVVJ}

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	2026-07-05T05:33:57.487002Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

52a1914307acce47652f7099522ad5aa54d212ea92e0a451575a397969adeaf3

Aliases

arxiv: 1912.09804 · arxiv_version: 1912.09804v1 · doi: 10.48550/arxiv.1912.09804 · pith_short_12: KKQZCQYHVTHE · pith_short_16: KKQZCQYHVTHEOZJP · pith_short_8: KKQZCQYH

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/KKQZCQYHVTHEOZJPOCMVEKWVVJ \
  | 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: 52a1914307acce47652f7099522ad5aa54d212ea92e0a451575a397969adeaf3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8956bb9641ab6d30b69e4ddc9f8bbb530b0c8c36cfc7d22f3697f84bd19d2a26",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-12-20T13:15:18Z",
    "title_canon_sha256": "bedfcfaee1fe4df1921701fc97d8b2b5d1dc6ce69d066c18a036f7ccca4f2270"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1912.09804",
    "kind": "arxiv",
    "version": 1
  }
}