Pith Number

pith:JXKR43UT

pith:2015:JXKR43UTEBMW3SKP722FSFB6G7

not attested not anchored not stored refs pending

The Helmholtz equation with $L^p$ data and Bochner-Riesz multipliers

Michael Goldberg

arxiv:1502.02066 v1 · 2015-02-06 · math.CA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JXKR43UTEBMW3SKP722FSFB6G7}

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	2026-05-18T00:05:56.944956Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4dd51e6e9320596dc94ffeb459143e37fcea5a3e9890575cc2575a21eebdd4f1

Aliases

arxiv: 1502.02066 · arxiv_version: 1502.02066v1 · doi: 10.48550/arxiv.1502.02066 · pith_short_12: JXKR43UTEBMW · pith_short_16: JXKR43UTEBMW3SKP · pith_short_8: JXKR43UT

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/JXKR43UTEBMW3SKP722FSFB6G7 \
  | 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: 4dd51e6e9320596dc94ffeb459143e37fcea5a3e9890575cc2575a21eebdd4f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7621c8c5d2b78509ad12700e1ebbf472003a3c0e17083de56e80312768a6b19c",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-02-06T22:16:38Z",
    "title_canon_sha256": "1a06ce1413030f7f142654c7d9e6c6a0b0f7c92898fb59e13a986b8fc5e29a84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.02066",
    "kind": "arxiv",
    "version": 1
  }
}