Pith Number

pith:P2NU6TZT

pith:2012:P2NU6TZTOXWSUHZHJ2EPQIJ7HA

not attested not anchored not stored refs pending

The Bochner-Riesz means for Fourier-Bessel expansions: norm inequalities for the maximal operator and almost everywhere convergence

L. Roncal, \'O. Ciaurri

arxiv:1207.5749 v1 · 2012-07-24 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P2NU6TZTOXWSUHZHJ2EPQIJ7HA}

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.

Receipt and verification

First computed	2026-05-18T03:50:11.424746Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e9b4f4f3375ed2a1f274e88f8213f383e628b7e93647a9f32d784acf5eea967

Aliases

arxiv: 1207.5749 · arxiv_version: 1207.5749v1 · doi: 10.48550/arxiv.1207.5749 · pith_short_12: P2NU6TZTOXWS · pith_short_16: P2NU6TZTOXWSUHZH · pith_short_8: P2NU6TZT

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/P2NU6TZTOXWSUHZHJ2EPQIJ7HA \
  | 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: 7e9b4f4f3375ed2a1f274e88f8213f383e628b7e93647a9f32d784acf5eea967

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f1150934b28a37f3ef12b3f49f07574cdd911d23b1941cc533b2af62760c4b0b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-07-24T17:09:12Z",
    "title_canon_sha256": "700be7c95e7923482763ae826058117ad7f0cace7cafd7f233aa6678573e558f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.5749",
    "kind": "arxiv",
    "version": 1
  }
}