Pith Number

pith:LUAQACGJ

pith:2016:LUAQACGJ4FIS7BTZTHDNCPZZ55

not attested not anchored not stored refs pending

Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups

Durvudkhan Suragan, Michael Ruzhansky

arxiv:1603.06239 v2 · 2016-03-20 · math.CA · math.AP · 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{LUAQACGJ4FIS7BTZTHDNCPZZ55}

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	2026-05-18T00:38:12.873125Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5d010008c9e1512f867999c6d13f39ef4875add5b5f0b10da0ce153a62851b12

Aliases

arxiv: 1603.06239 · arxiv_version: 1603.06239v2 · doi: 10.48550/arxiv.1603.06239 · pith_short_12: LUAQACGJ4FIS · pith_short_16: LUAQACGJ4FIS7BTZ · pith_short_8: LUAQACGJ

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/LUAQACGJ4FIS7BTZTHDNCPZZ55 \
  | 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: 5d010008c9e1512f867999c6d13f39ef4875add5b5f0b10da0ce153a62851b12

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6eee3c286b205932c72dd212edae1d5cd432bda638b796ad46c20a32ec57bc1",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-03-20T17:01:57Z",
    "title_canon_sha256": "0cf9bf78f867e1061c326e5978e59e44b28495b8bc7ca50883a56f7ebb962950"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.06239",
    "kind": "arxiv",
    "version": 2
  }
}