Pith Number

pith:ZKWYBVST

pith:2013:ZKWYBVST65KM6TGXLKQXVWTOCZ

not attested not anchored not stored refs pending

Proof of two conjectures of Ciucu and Krattenthaler on the enumeration of lozenge tilings of hexagons with cut off corners

Ilse Fischer, Mihai Ciucu

arxiv:1309.4640 v1 · 2013-09-18 · 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{ZKWYBVST65KM6TGXLKQXVWTOCZ}

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	2026-05-18T03:12:58.736024Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

caad80d653f754cf4cd75aa17ada6e164cda9063fcc5c44972568351bfc49ca9

Aliases

arxiv: 1309.4640 · arxiv_version: 1309.4640v1 · doi: 10.48550/arxiv.1309.4640 · pith_short_12: ZKWYBVST65KM · pith_short_16: ZKWYBVST65KM6TGX · pith_short_8: ZKWYBVST

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/ZKWYBVST65KM6TGXLKQXVWTOCZ \
  | 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: caad80d653f754cf4cd75aa17ada6e164cda9063fcc5c44972568351bfc49ca9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "631c7c61656ff1e93ebd7275cd2ee4b5b01ecd57b1fa6489afe8686c84f43dd9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-09-18T13:30:11Z",
    "title_canon_sha256": "955b6cbd095ad81f2baefa7b60d4f46a9a8e3e73daa6df4734cc5a75b734d4d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.4640",
    "kind": "arxiv",
    "version": 1
  }
}