Pith Number

pith:3DVZD7L7

pith:2004:3DVZD7L7A6JSFT67QF3MTO5FOZ

not attested not anchored not stored refs pending

Discrete analogues in harmonic analysis: Spherical averages

A. Magyar, E. M. Stein, S. Wainger

arxiv:math/0409365 v1 · 2004-09-20 · 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{3DVZD7L7A6JSFT67QF3MTO5FOZ}

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

Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages

Receipt and verification

First computed	2026-07-04T14:39:05.184127Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8eb91fd7f079322cfdf8176c9bba57650588f24351efaac419b985cad4664e1

Aliases

arxiv: math/0409365 · arxiv_version: math/0409365v1 · doi: 10.48550/arxiv.math/0409365 · pith_short_12: 3DVZD7L7A6JS · pith_short_16: 3DVZD7L7A6JSFT67 · pith_short_8: 3DVZD7L7

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/3DVZD7L7A6JSFT67QF3MTO5FOZ \
  | 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: d8eb91fd7f079322cfdf8176c9bba57650588f24351efaac419b985cad4664e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4515e518c8e195ab70163868b8551a2a6434991af0da9aff1276b7d86f3023d3",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "2004-09-20T17:39:49Z",
    "title_canon_sha256": "9d03df7caaab6f184ba3c6516c1ba282802207fc23f901168cfd46349a81fe47"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0409365",
    "kind": "arxiv",
    "version": 1
  }
}