Pith Number

pith:BTTAUCLX

pith:2015:BTTAUCLXOPT3ZWNNRGSFMKPDHL

not attested not anchored not stored refs pending

Effective equidistribution and property tau

Akshay Venkatesh, Amir Mohammadi, Gregory Margulis, Manfred Einsiedler

arxiv:1503.05884 v3 · 2015-03-19 · math.NT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BTTAUCLXOPT3ZWNNRGSFMKPDHL}

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	2026-05-17T23:42:15.589084Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ce60a097773e7bcd9ad89a45629e33ad9cdfd42d70c5e13d3a4cc7b649d52f9

Aliases

arxiv: 1503.05884 · arxiv_version: 1503.05884v3 · doi: 10.48550/arxiv.1503.05884 · pith_short_12: BTTAUCLXOPT3 · pith_short_16: BTTAUCLXOPT3ZWNN · pith_short_8: BTTAUCLX

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/BTTAUCLXOPT3ZWNNRGSFMKPDHL \
  | 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: 0ce60a097773e7bcd9ad89a45629e33ad9cdfd42d70c5e13d3a4cc7b649d52f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e532ebf3a75f91ae79511647054d8427b3ee95b0c304f4c33e72a50beb12d094",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-03-19T18:58:29Z",
    "title_canon_sha256": "74e254559287f955ce1ed0fc3ba7e4f848f920e24579563905c9334778c24d9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.05884",
    "kind": "arxiv",
    "version": 3
  }
}