Pith Number

pith:2VCVSVHW

pith:2011:2VCVSVHWSABPKMZXVWSTWEAMA7

not attested not anchored not stored refs pending

Horoball packings and their densities by generalized simplicial density function in the hyperbolic space

Jen\H{o} Szirmai

arxiv:1105.4315 v2 · 2011-05-22 · math.MG · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2VCVSVHWSABPKMZXVWSTWEAMA7}

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	2026-05-18T01:09:25.478014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d5455954f69002f53337ada53b100c07cacc935dc1e8c9e3f2732cae98980ff6

Aliases

arxiv: 1105.4315 · arxiv_version: 1105.4315v2 · doi: 10.48550/arxiv.1105.4315 · pith_short_12: 2VCVSVHWSABP · pith_short_16: 2VCVSVHWSABPKMZX · pith_short_8: 2VCVSVHW

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/2VCVSVHWSABPKMZXVWSTWEAMA7 \
  | 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: d5455954f69002f53337ada53b100c07cacc935dc1e8c9e3f2732cae98980ff6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8ab9d36620a2b9dd17b663ba2fb772f57414872d304f18b20be3206a96c696f",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2011-05-22T08:16:18Z",
    "title_canon_sha256": "1baea5f31c2006bf3ab2adf1c87bfc12d0c0cd4b6668c0d7c2d2d69b4ea6d588"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.4315",
    "kind": "arxiv",
    "version": 2
  }
}