Pith Number

pith:AQK2DBOY

pith:2017:AQK2DBOYEWKN3DZW76NHXHNTNN

not attested not anchored not stored refs pending

Sharp exponential integrability for critical Riesz potentials and fractional Laplacians on R^n

Carlo Morpurgo, Luigi Fontana

arxiv:1702.02078 v2 · 2017-02-07 · 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{AQK2DBOYEWKN3DZW76NHXHNTNN}

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	2026-05-18T00:30:05.690825Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0415a185d82594dd8f36ff9a7b9db36b5365490a43c1bd1a70c8f6374a8c27fd

Aliases

arxiv: 1702.02078 · arxiv_version: 1702.02078v2 · doi: 10.48550/arxiv.1702.02078 · pith_short_12: AQK2DBOYEWKN · pith_short_16: AQK2DBOYEWKN3DZW · pith_short_8: AQK2DBOY

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/AQK2DBOYEWKN3DZW76NHXHNTNN \
  | 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: 0415a185d82594dd8f36ff9a7b9db36b5365490a43c1bd1a70c8f6374a8c27fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85dc0edb890d4bfca3f8d5e8728d652bc7317c1bc9cda03181798f08f4a4da60",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-02-07T16:10:40Z",
    "title_canon_sha256": "3c60c15b4f2e4f02c15cfa0bd8a0dad18e9e75e4508b0d1533a7037c21cc933b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.02078",
    "kind": "arxiv",
    "version": 2
  }
}