Pith Number

pith:N64OKLT5

pith:2021:N64OKLT5MUSKCTZ25652676XA6

not attested not anchored not stored refs pending

Averaging with the Divisor Function: $\ell^p$-improving and Sparse Bounds

Christina Giannitsi

arxiv:2102.01778 v2 · 2021-02-02 · 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{N64OKLT5MUSKCTZ25652676XA6}

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	2026-07-05T04:10:11.723278Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6fb8e52e7d6524a14f3aefbbaf7fd707b35144b86c528ab62f7d0dff94bdeac4

Aliases

arxiv: 2102.01778 · arxiv_version: 2102.01778v2 · doi: 10.48550/arxiv.2102.01778 · pith_short_12: N64OKLT5MUSK · pith_short_16: N64OKLT5MUSKCTZ2 · pith_short_8: N64OKLT5

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/N64OKLT5MUSKCTZ25652676XA6 \
  | 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: 6fb8e52e7d6524a14f3aefbbaf7fd707b35144b86c528ab62f7d0dff94bdeac4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "006bd818986824b32dfbf054d26e5bf83bd0c67f96052eb7a4a789a57d7bf1e3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2021-02-02T22:09:32Z",
    "title_canon_sha256": "50d8c71992b5be46dc779fb049843e320dc853fd5ca58d35954f39fbf8ebe13d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2102.01778",
    "kind": "arxiv",
    "version": 2
  }
}