Pith Number

pith:LH7S6XDX

pith:2015:LH7S6XDXE3M6EG72EAIACTUN6X

not attested not anchored not stored refs pending

Rank, combinatorial cost and homology torsion growth in higher rank lattices

Miklos Abert, Nikolay Nikolov, Tsachik Gelander

arxiv:1509.01711 v2 · 2015-09-05 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LH7S6XDXE3M6EG72EAIACTUN6X}

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	2026-05-18T00:32:44.897372Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59ff2f5c7726d9e21bfa2010014e8df5d73302ec2f969084856af30ac3f82895

Aliases

arxiv: 1509.01711 · arxiv_version: 1509.01711v2 · doi: 10.48550/arxiv.1509.01711 · pith_short_12: LH7S6XDXE3M6 · pith_short_16: LH7S6XDXE3M6EG72 · pith_short_8: LH7S6XDX

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/LH7S6XDXE3M6EG72EAIACTUN6X \
  | 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: 59ff2f5c7726d9e21bfa2010014e8df5d73302ec2f969084856af30ac3f82895

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f109fcf485e5b28ff2f4a998077dd1ec9eadaa0338a4b9283c8f4cea49459cd8",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-09-05T15:52:48Z",
    "title_canon_sha256": "6851bcc432f19e314c91473ab24f574fc4a7df1f9dd136ff706d55440b9b8c26"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.01711",
    "kind": "arxiv",
    "version": 2
  }
}