Pith Number

pith:44J57QQR

pith:2023:44J57QQR2QFYSWWILZFXXML6SV

not attested not anchored not stored refs pending

The number of tiles of $\mathbb{Z}^d$

Elad Tzalik, Gady Kozma, Itai Benjamini

arxiv:2303.07956 v1 · 2023-03-14 · math.CO · math.DS · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{44J57QQR2QFYSWWILZFXXML6SV}

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	2026-07-05T05:51:13.422634Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e713dfc211d40b895ac85e4b7bb17e9542cbd9e80a8a53da9a821edb1a4d5fb4

Aliases

arxiv: 2303.07956 · arxiv_version: 2303.07956v1 · doi: 10.48550/arxiv.2303.07956 · pith_short_12: 44J57QQR2QFY · pith_short_16: 44J57QQR2QFYSWWI · pith_short_8: 44J57QQR

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/44J57QQR2QFYSWWILZFXXML6SV \
  | 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: e713dfc211d40b895ac85e4b7bb17e9542cbd9e80a8a53da9a821edb1a4d5fb4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ff58f29ab7e09eb0c89471cb23d3cfa1ff6ce6f2444b24e43925bb98e72cf1d",
    "cross_cats_sorted": [
      "math.DS",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-03-14T14:58:41Z",
    "title_canon_sha256": "ce51ef22fc3ef4151c0ee330190aaf1bcb67b7aaa4f8007e442ee2acbe1499cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2303.07956",
    "kind": "arxiv",
    "version": 1
  }
}