Pith Number

pith:G25R7SQY

pith:2012:G25R7SQYEJ5Y7WKHXQ2YGYY4CU

not attested not anchored not stored refs pending

On the growth of $L^2$-invariants for sequences of lattices in Lie groups

Ian Biringer, Iddo Samet, Jean Raimbault, Miklos Abert, Nicolas Bergeron, Nikolay Nikolov, Tsachik Gelander

arxiv:1210.2961 v4 · 2012-10-10 · math.RT · math.DG · math.GR · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{G25R7SQYEJ5Y7WKHXQ2YGYY4CU}

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	2026-05-18T00:53:40.986475Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

36bb1fca18227b8fd947bc3583631c151946428be1df0ad35d7068e83bfd9c76

Aliases

arxiv: 1210.2961 · arxiv_version: 1210.2961v4 · doi: 10.48550/arxiv.1210.2961 · pith_short_12: G25R7SQYEJ5Y · pith_short_16: G25R7SQYEJ5Y7WKH · pith_short_8: G25R7SQY

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/G25R7SQYEJ5Y7WKHXQ2YGYY4CU \
  | 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: 36bb1fca18227b8fd947bc3583631c151946428be1df0ad35d7068e83bfd9c76

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b74a552db6cb2dbe13b4f1733523f6be53afded5e2f0e2d22a999313796b9e4",
    "cross_cats_sorted": [
      "math.DG",
      "math.GR",
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2012-10-10T15:59:24Z",
    "title_canon_sha256": "92b79eb3aa09a053a207304dce6950ca0551fa11859c08a7abbaf736eaa88ce1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.2961",
    "kind": "arxiv",
    "version": 4
  }
}