Pith Number

pith:RV6FZM73

pith:2015:RV6FZM73QIQSWFFHAAI5MUYK5F

not attested not anchored not stored refs pending

An Upper bound on the growth of Dirichlet tilings of hyperbolic spaces

Itai Benjamini, Tsachik Gelander

arxiv:1504.05873 v2 · 2015-04-22 · math.GR · 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{RV6FZM73QIQSWFFHAAI5MUYK5F}

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	2026-05-18T01:59:34.732456Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8d7c5cb3fb82212b14a70011d6530ae96947718ab94339d6bf6f2306d1c29529

Aliases

arxiv: 1504.05873 · arxiv_version: 1504.05873v2 · doi: 10.48550/arxiv.1504.05873 · pith_short_12: RV6FZM73QIQS · pith_short_16: RV6FZM73QIQSWFFH · pith_short_8: RV6FZM73

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/RV6FZM73QIQSWFFHAAI5MUYK5F \
  | 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: 8d7c5cb3fb82212b14a70011d6530ae96947718ab94339d6bf6f2306d1c29529

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8593574df687f3b8b6ca05c1b1d1705b5cfbc8b663ed38259f3a49a0dfa3b5e",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-04-22T16:42:34Z",
    "title_canon_sha256": "d3ddab9af10af9e06167c27ecc17bfb23812df673af2fcb5b9401ce1988f0381"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.05873",
    "kind": "arxiv",
    "version": 2
  }
}