Pith Number

pith:EAKLVDQ5

pith:2013:EAKLVDQ5L2XYJOTRHQCX2HZ2B7

not attested not anchored not stored refs pending

The Kato-Ponce Inequality

Loukas Grafakos, Seungly Oh

arxiv:1303.5144 v1 · 2013-03-21 · 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{EAKLVDQ5L2XYJOTRHQCX2HZ2B7}

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	2026-05-18T03:30:14.393835Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2014ba8e1d5eaf84ba713c057d1f3a0ffdc86d601ede6894fa8cae55b2a1d613

Aliases

arxiv: 1303.5144 · arxiv_version: 1303.5144v1 · doi: 10.48550/arxiv.1303.5144 · pith_short_12: EAKLVDQ5L2XY · pith_short_16: EAKLVDQ5L2XYJOTR · pith_short_8: EAKLVDQ5

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/EAKLVDQ5L2XYJOTRHQCX2HZ2B7 \
  | 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: 2014ba8e1d5eaf84ba713c057d1f3a0ffdc86d601ede6894fa8cae55b2a1d613

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35b4d1191aad66465e6339a9e1bb8d3dcb6ef98a2ddfb08fc7a08fe183ff689a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-03-21T02:08:52Z",
    "title_canon_sha256": "b337995754d30180b3966256bd93dadaeeca191e11f5dbe6bf3d488bdc7a6249"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.5144",
    "kind": "arxiv",
    "version": 1
  }
}