Pith Number

pith:WHRQNCPJ

pith:2020:WHRQNCPJZ6ULCHFY7VY7MX5REX

not attested not anchored not stored refs pending

On Sarnak's Density Conjecture and its Applications

Amitay Kamber, Konstantin Golubev

arxiv:2004.00373 v2 · 2020-04-01 · math.NT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WHRQNCPJZ6ULCHFY7VY7MX5REX}

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.

Cited by

1 paper in Pith

A density theorem for Borel-Type Congruence subgroups and arithmetic applications

Receipt and verification

First computed	2026-07-05T03:50:46.006740Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1e30689e9cfa8b11cb8fd71f65fb125eb004729ed698f2efce9f4fb3ef87c63

Aliases

arxiv: 2004.00373 · arxiv_version: 2004.00373v2 · doi: 10.48550/arxiv.2004.00373 · pith_short_12: WHRQNCPJZ6UL · pith_short_16: WHRQNCPJZ6ULCHFY · pith_short_8: WHRQNCPJ

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/WHRQNCPJZ6ULCHFY7VY7MX5REX \
  | 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: b1e30689e9cfa8b11cb8fd71f65fb125eb004729ed698f2efce9f4fb3ef87c63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3df0c9274b4e03e174fcdb6a691ef2ab3b5f248848ff393743048ef707ce3b6",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2020-04-01T12:19:53Z",
    "title_canon_sha256": "48aefd56ddad98885f8e5466520a5a9704c2b008b55285c1b9b569aaa7afb4c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2004.00373",
    "kind": "arxiv",
    "version": 2
  }
}