Pith Number

pith:B4IPLIFP

pith:2013:B4IPLIFPYYZ2T2VFHJAMOWFV6S

not attested not anchored not stored refs pending

Sobolev and Hardy-Littlewood-Sobolev inequalities

Gaspard Jankowiak (CEREMADE), Jean Dolbeault (CEREMADE)

arxiv:1312.2568 v3 · 2013-12-09 · 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{B4IPLIFPYYZ2T2VFHJAMOWFV6S}

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	2026-05-18T02:52:49.398452Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f10f5a0afc633a9eaa53a40c758b5f49054842e2276912473963edeb87b05cd

Aliases

arxiv: 1312.2568 · arxiv_version: 1312.2568v3 · doi: 10.48550/arxiv.1312.2568 · pith_short_12: B4IPLIFPYYZ2 · pith_short_16: B4IPLIFPYYZ2T2VF · pith_short_8: B4IPLIFP

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/B4IPLIFPYYZ2T2VFHJAMOWFV6S \
  | 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: 0f10f5a0afc633a9eaa53a40c758b5f49054842e2276912473963edeb87b05cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73bb7d8ecf5b38bd327351c240c8109c2e0299d8b8789100d125182915ca0197",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-12-09T20:31:25Z",
    "title_canon_sha256": "3335b7d8ac26359cd8ae4e71ae24164ab6a084922432d1c6da501cedc305e9d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.2568",
    "kind": "arxiv",
    "version": 3
  }
}