Pith Number

pith:P75OSPLH

pith:2013:P75OSPLHUMKUEHDXGQYDRZHOB2

not attested not anchored not stored refs pending

Hardy-Littlewood-Sobolev Type Inequality and Stein-Wiess Type Inequality on Carnot Groups

Pengcheng Niu, Tingxi Hu

arxiv:1303.5185 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{P75OSPLHUMKUEHDXGQYDRZHOB2}

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	2026-05-18T03:30:14.232634Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ffae93d67a315421c77343038e4ee0e99db4c59cac3f0043511d0c9b3f7b491

Aliases

arxiv: 1303.5185 · arxiv_version: 1303.5185v1 · doi: 10.48550/arxiv.1303.5185 · pith_short_12: P75OSPLHUMKU · pith_short_16: P75OSPLHUMKUEHDX · pith_short_8: P75OSPLH

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/P75OSPLHUMKUEHDXGQYDRZHOB2 \
  | 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: 7ffae93d67a315421c77343038e4ee0e99db4c59cac3f0043511d0c9b3f7b491

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5ce2d00743cff060bdbf4e7fa0190c884528fc0eb251355a07f13a3f6cfca93",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-03-21T07:56:02Z",
    "title_canon_sha256": "3d8c971fc6f63f01d5bd5da6b7f1d9ca85f71879c6b66542e9d5b4282bc4cfb6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.5185",
    "kind": "arxiv",
    "version": 1
  }
}