Pith Number

pith:POU4GLHI

pith:2026:POU4GLHINS33NPZ6LLAGUTPFML

not attested not anchored not stored refs pending

Generalization of Selberg's $3/16$ theorem for geometrically finite thin subgroups of $\operatorname{SO}(n, 1)$

Pratyush Sarkar

arxiv:2606.18674 v1 · 2026-06-17 · math.DS · math.NT · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{POU4GLHINS33NPZ6LLAGUTPFML}

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	2026-06-19T16:11:44.254934Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ba9c32ce86cb7b6bf3e5ac06a4de562dabc11674fbb127428339c39526eef21

Aliases

arxiv: 2606.18674 · arxiv_version: 2606.18674v1 · doi: 10.48550/arxiv.2606.18674 · pith_short_12: POU4GLHINS33 · pith_short_16: POU4GLHINS33NPZ6 · pith_short_8: POU4GLHI

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/POU4GLHINS33NPZ6LLAGUTPFML \
  | 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: 7ba9c32ce86cb7b6bf3e5ac06a4de562dabc11674fbb127428339c39526eef21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42492369569b8066ef266df87d75d4c842149566323c54fad0123ca324f031b6",
    "cross_cats_sorted": [
      "math.NT",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-06-17T04:20:23Z",
    "title_canon_sha256": "eadba220c3e2c41c915e7e7b5a4c583eb687dedf883670f59c017dba59287445"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.18674",
    "kind": "arxiv",
    "version": 1
  }
}