Pith Number

pith:2EHF76FK

pith:2013:2EHF76FKPURLM2Z5C42GERA47Q

not attested not anchored not stored refs pending

Hardy and uncertainty inequalities on stratified Lie groups

Fulvio Ricci, Michael G. Cowling, Paolo Ciatti

arxiv:1308.2373 v1 · 2013-08-11 · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2EHF76FKPURLM2Z5C42GERA47Q}

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	2026-05-18T03:16:07.619395Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d10e5ff8aa7d22b66b3d173462441cfc263ec41f5f93b5e9da2f01ae42f6d1c9

Aliases

arxiv: 1308.2373 · arxiv_version: 1308.2373v1 · doi: 10.48550/arxiv.1308.2373 · pith_short_12: 2EHF76FKPURL · pith_short_16: 2EHF76FKPURLM2Z5 · pith_short_8: 2EHF76FK

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/2EHF76FKPURLM2Z5C42GERA47Q \
  | 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: d10e5ff8aa7d22b66b3d173462441cfc263ec41f5f93b5e9da2f01ae42f6d1c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "934906142a3ae509bb5cb966951af27c7ac19586e630876775b6b9ab5a4dc37d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-08-11T08:11:39Z",
    "title_canon_sha256": "8e50b318f5d7aed57316ee3ccf74d64bca5b6d22ca34f6025fcf47b51b5d8bb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.2373",
    "kind": "arxiv",
    "version": 1
  }
}