Pith Number

pith:Q3SWBH2D

pith:2016:Q3SWBH2DD5GXK2PQTEYPKSWBIP

not attested not anchored not stored refs pending

Central limit theorems for simultaneous Diophantine approximations

Bassam Fayad, Dmitry Dolgopyat, Ilya Vinogradov

arxiv:1605.00311 v1 · 2016-05-01 · math.DS · math.NT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q3SWBH2DD5GXK2PQTEYPKSWBIP}

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	2026-05-18T01:15:56.211908Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86e5609f431f4d7569f09930f54ac143e661ae5459eaa866e9defe02bc46c4e6

Aliases

arxiv: 1605.00311 · arxiv_version: 1605.00311v1 · doi: 10.48550/arxiv.1605.00311 · pith_short_12: Q3SWBH2DD5GX · pith_short_16: Q3SWBH2DD5GXK2PQ · pith_short_8: Q3SWBH2D

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/Q3SWBH2DD5GXK2PQTEYPKSWBIP \
  | 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: 86e5609f431f4d7569f09930f54ac143e661ae5459eaa866e9defe02bc46c4e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69e9fac66c3a35e1e230f1b7b6fcb86a8d6d4c80bd934312123b4727591334c6",
    "cross_cats_sorted": [
      "math.NT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-05-01T21:32:50Z",
    "title_canon_sha256": "4999c21a3859f60525dad599edb426f0eff7c53bd176c24517ad12eeda167de4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.00311",
    "kind": "arxiv",
    "version": 1
  }
}