Pith Number

pith:NDCQQ5UQ

pith:2009:NDCQQ5UQKJC7FESSLUOYFUY2XN

not attested not anchored not stored refs pending

Pointwise Symmetrization Inequalities for Sobolev functions and applications

Joaquim Martin, Mario Milman

arxiv:0908.1751 v4 · 2009-08-12 · math.FA · 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{NDCQQ5UQKJC7FESSLUOYFUY2XN}

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	2026-05-18T00:43:38.160357Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68c50876905245f292525d1d82d31abb5773f54f7dc541c5bc7fb58499df74d2

Aliases

arxiv: 0908.1751 · arxiv_version: 0908.1751v4 · doi: 10.48550/arxiv.0908.1751 · pith_short_12: NDCQQ5UQKJC7 · pith_short_16: NDCQQ5UQKJC7FESS · pith_short_8: NDCQQ5UQ

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/NDCQQ5UQKJC7FESSLUOYFUY2XN \
  | 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: 68c50876905245f292525d1d82d31abb5773f54f7dc541c5bc7fb58499df74d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6cec0b0aecef719b399a35f2f4f83ba91786dab66297ca4f1d9f6fd563e9e0f",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2009-08-12T16:49:20Z",
    "title_canon_sha256": "411d2466c2b849e9ed6903d4ecb90231aae2fdcdc919f4500a24dd268061c2ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.1751",
    "kind": "arxiv",
    "version": 4
  }
}