Pith Number

pith:QLEM6TXS

pith:2016:QLEM6TXSP7CU5RUMAPOKXYNJ5M

not attested not anchored not stored refs pending

On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and $p$-sub-Laplacian inequalities on stratified groups

Durvudkhan Suragan, Michael Ruzhansky

arxiv:1605.06389 v1 · 2016-05-20 · 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{QLEM6TXSP7CU5RUMAPOKXYNJ5M}

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	2026-05-18T00:52:25.515094Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82c8cf4ef27fc54ec68c03dcabe1a9eb24f403656ae50460ef4ecfca5cf39c72

Aliases

arxiv: 1605.06389 · arxiv_version: 1605.06389v1 · doi: 10.48550/arxiv.1605.06389 · pith_short_12: QLEM6TXSP7CU · pith_short_16: QLEM6TXSP7CU5RUM · pith_short_8: QLEM6TXS

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/QLEM6TXSP7CU5RUMAPOKXYNJ5M \
  | 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: 82c8cf4ef27fc54ec68c03dcabe1a9eb24f403656ae50460ef4ecfca5cf39c72

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75243d73835d35bad9120575e7864f6877bc894963ae65b1904863aa47bba1ac",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-05-20T14:59:41Z",
    "title_canon_sha256": "de027d4264766f93491c7778e12198fdfb151971195e0afe0d25977f066dcb1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.06389",
    "kind": "arxiv",
    "version": 1
  }
}