Pith Number

pith:WMQMTPJQ

pith:2010:WMQMTPJQOVTNI3AYKPR4NKET4Y

not attested not anchored not stored refs pending

Smoothness of Extremizers of a Convolution Inequality

Michael Christ, Qingying Xue

arxiv:1012.5458 v1 · 2010-12-25 · 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{WMQMTPJQOVTNI3AYKPR4NKET4Y}

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	2026-05-18T04:32:23.433128Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b320c9bd307566d46c1853e3c6a893e6375aa75393240659ecb23c5852a71dbc

Aliases

arxiv: 1012.5458 · arxiv_version: 1012.5458v1 · doi: 10.48550/arxiv.1012.5458 · pith_short_12: WMQMTPJQOVTN · pith_short_16: WMQMTPJQOVTNI3AY · pith_short_8: WMQMTPJQ

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/WMQMTPJQOVTNI3AYKPR4NKET4Y \
  | 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: b320c9bd307566d46c1853e3c6a893e6375aa75393240659ecb23c5852a71dbc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "827a22bfd1bf48074391a758d4214cb4d145ce52b6e80a2f5434832b15e50aa6",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-12-25T07:35:38Z",
    "title_canon_sha256": "57963b6cbdd8b95ff561e7266c617dd273819a43d1a2627b5645562741244bdd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5458",
    "kind": "arxiv",
    "version": 1
  }
}