Pith Number

pith:3NYN75R7

pith:2013:3NYN75R7N6LL5LGELRXQUV4ULP

not attested not anchored not stored refs pending

The least dense hyperball covering to the regular prism tilings in the hyperbolic $n$-space

Jen\"o Szirmai

arxiv:1312.2328 v1 · 2013-12-09 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3NYN75R7N6LL5LGELRXQUV4ULP}

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	2026-05-18T03:05:10.661534Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db70dff63f6f96beacc45c6f0a57945becf9c665cd64b0c0b49305dc0fdf8b71

Aliases

arxiv: 1312.2328 · arxiv_version: 1312.2328v1 · doi: 10.48550/arxiv.1312.2328 · pith_short_12: 3NYN75R7N6LL · pith_short_16: 3NYN75R7N6LL5LGE · pith_short_8: 3NYN75R7

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/3NYN75R7N6LL5LGELRXQUV4ULP \
  | 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: db70dff63f6f96beacc45c6f0a57945becf9c665cd64b0c0b49305dc0fdf8b71

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56ba9cc7dee0547b9faada67dc7b18a74a88f34f3b06ba84b04ba2050f0d724e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2013-12-09T07:30:06Z",
    "title_canon_sha256": "32bd23cdee248e9b0330aaa35a5a9eabd54542d0cf83dda5c1de3f712ec40056"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.2328",
    "kind": "arxiv",
    "version": 1
  }
}