Pith Number

pith:65XGKJWD

pith:2023:65XGKJWDDJEN45NDAX2GR4Z4NQ

not attested not anchored not stored refs pending

On the Fourier decay of multiplicative convolutions

Nicolas de Saxc\'e, Pablo Shmerkin, Tuomas Orponen

arxiv:2309.03068 v2 · 2023-09-06 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{65XGKJWDDJEN45NDAX2GR4Z4NQ}

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

Furstenberg set theorem for transversal families of functions

Receipt and verification

First computed	2026-07-05T07:49:55.532598Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f76e6526c31a48de75a305f468f33c6c2b38fa169ae45ea638ac92eff7606710

Aliases

arxiv: 2309.03068 · arxiv_version: 2309.03068v2 · doi: 10.48550/arxiv.2309.03068 · pith_short_12: 65XGKJWDDJEN · pith_short_16: 65XGKJWDDJEN45ND · pith_short_8: 65XGKJWD

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/65XGKJWDDJEN45NDAX2GR4Z4NQ \
  | 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: f76e6526c31a48de75a305f468f33c6c2b38fa169ae45ea638ac92eff7606710

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4320cdd164a61453b71b4b8547350664ad6aada2c0f5777738ba9727a412462",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2023-09-06T15:14:01Z",
    "title_canon_sha256": "43b2cb19a15084434df814f798413faaa8e67f9e5f0d391ff9284eec6b1f6d37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2309.03068",
    "kind": "arxiv",
    "version": 2
  }
}