Pith Number

pith:QE6KSW7S

pith:2012:QE6KSW7SA2MDXFEA56S43EMQ3W

not attested not anchored not stored refs pending

Quasi-isometric co-Hopficity of non-uniform lattices in rank-one semi-simple Lie groups

Anton Lukyanenko, Ilya Kapovich

arxiv:1204.4193 v3 · 2012-04-18 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QE6KSW7SA2MDXFEA56S43EMQ3W}

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	2026-05-18T03:39:28.708068Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

813ca95bf206983b9480efa5cd9190dd999a6b4265da388ab24af0261e3c86a2

Aliases

arxiv: 1204.4193 · arxiv_version: 1204.4193v3 · doi: 10.48550/arxiv.1204.4193 · pith_short_12: QE6KSW7SA2MD · pith_short_16: QE6KSW7SA2MDXFEA · pith_short_8: QE6KSW7S

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/QE6KSW7SA2MDXFEA56S43EMQ3W \
  | 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: 813ca95bf206983b9480efa5cd9190dd999a6b4265da388ab24af0261e3c86a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdb70b35ab406400fb9bae7829f67797c227e09302edcf566739e4cd78b2ca91",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-04-18T20:05:13Z",
    "title_canon_sha256": "0db3879667ca8ffb8fb7dbe43db52231f3e7ab02e0fc1d8a9ce7ea0e07d07305"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.4193",
    "kind": "arxiv",
    "version": 3
  }
}