Pith Number

pith:JAKQKREC

pith:2024:JAKQKRECMWMUDVXGSKZ3OHGCIJ

not attested not anchored not stored refs pending

An almost sharp quantitative version of the Duffin-Schaeffer conjecture

Daodao Yang, Dimitris Koukoulopoulos, James Maynard

arxiv:2404.14628 v2 · 2024-04-22 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JAKQKRECMWMUDVXGSKZ3OHGCIJ}

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 century of metric Diophantine approximation and half a decade since Koukoulopoulos-Maynard

Receipt and verification

First computed	2026-07-05T09:09:21.892564Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4815054482659941d6e692b3b71cc242451addcb6a7e9eb78e39371cf3d401f0

Aliases

arxiv: 2404.14628 · arxiv_version: 2404.14628v2 · doi: 10.48550/arxiv.2404.14628 · pith_short_12: JAKQKRECMWMU · pith_short_16: JAKQKRECMWMUDVXG · pith_short_8: JAKQKREC

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/JAKQKRECMWMUDVXGSKZ3OHGCIJ \
  | 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: 4815054482659941d6e692b3b71cc242451addcb6a7e9eb78e39371cf3d401f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c84224ce6254119ccc2dae02681685f2b8dc69ac8c0d05ce7e2f9880369c368",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-04-22T23:54:58Z",
    "title_canon_sha256": "5469190d2de83bded704a4e76556c790873ebfa85f56c9b4976c1fff4a8c38a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2404.14628",
    "kind": "arxiv",
    "version": 2
  }
}