Pith Number

pith:SU4JMWK2

pith:2016:SU4JMWK2N24OU5BJFXJ7ZB7ECD

not attested not anchored not stored refs pending

Kazhdan sets in groups and equidistribution properties

Catalin Badea, Sophie Grivaux

arxiv:1601.04289 v4 · 2016-01-17 · math.GR · math.DS · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SU4JMWK2N24OU5BJFXJ7ZB7ECD}

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	2026-05-18T00:14:23.193780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

953896595a6eb8ea74292dd3fc87e410f8de5650714f7d19fa5716492b86f1f3

Aliases

arxiv: 1601.04289 · arxiv_version: 1601.04289v4 · doi: 10.48550/arxiv.1601.04289 · pith_short_12: SU4JMWK2N24O · pith_short_16: SU4JMWK2N24OU5BJ · pith_short_8: SU4JMWK2

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/SU4JMWK2N24OU5BJFXJ7ZB7ECD \
  | 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: 953896595a6eb8ea74292dd3fc87e410f8de5650714f7d19fa5716492b86f1f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "489a71e6432b2d3fbe310e064b0bfc4ce9cd16c259db7c686f0b8b2070332dae",
    "cross_cats_sorted": [
      "math.DS",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-01-17T13:05:59Z",
    "title_canon_sha256": "324b7121750aabbaa5c3847899732127183a93e2baca174513c0ff47e6aa5c05"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.04289",
    "kind": "arxiv",
    "version": 4
  }
}