Pith Number

pith:HWQJSW7P

pith:2024:HWQJSW7PP6UU4GJOGMBDMAYPDX

not attested not anchored not stored refs pending

Proving the Duffin-Schaeffer conjecture without GCD graphs

Aled Walker, Manuel Hauke, Santiago Vazquez Saez

arxiv:2404.15123 v1 · 2024-04-23 · 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{HWQJSW7PP6UU4GJOGMBDMAYPDX}

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

Erd\H{o}s's integer dilation approximation problem and GCD graphs

Receipt and verification

First computed	2026-07-05T08:11:15.622691Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3da0995bef7fa94e192e330236030f1dfe07ecc3366a786423b499e1d932642f

Aliases

arxiv: 2404.15123 · arxiv_version: 2404.15123v1 · doi: 10.48550/arxiv.2404.15123 · pith_short_12: HWQJSW7PP6UU · pith_short_16: HWQJSW7PP6UU4GJO · pith_short_8: HWQJSW7P

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/HWQJSW7PP6UU4GJOGMBDMAYPDX \
  | 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: 3da0995bef7fa94e192e330236030f1dfe07ecc3366a786423b499e1d932642f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c89c15b9b717764358a00ed8484de1ef05c0e78447c5f378270d653d64ee77e8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-04-23T15:23:50Z",
    "title_canon_sha256": "57a6a60dfac37ea5d3a9475948a9ad302f202a6c14cd8a086b821ae6f348a0d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2404.15123",
    "kind": "arxiv",
    "version": 1
  }
}