Pith Number

pith:QBTDLUND

pith:2018:QBTDLUND6E4QOB4QJC65HW3YYN

not attested not anchored not stored refs pending

On Hardy and Caffarelli-Kohn-Nirenberg inequalities

Hoai-Minh Nguyen, Marco Squassina

arxiv:1801.06329 v1 · 2018-01-19 · math.CA · 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{QBTDLUND6E4QOB4QJC65HW3YYN}

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	2026-05-18T00:25:30.484172Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

806635d1a3f13907079048bdd3db78c37008b5f94476a012096df4a5e5ffe2a4

Aliases

arxiv: 1801.06329 · arxiv_version: 1801.06329v1 · doi: 10.48550/arxiv.1801.06329 · pith_short_12: QBTDLUND6E4Q · pith_short_16: QBTDLUND6E4QOB4Q · pith_short_8: QBTDLUND

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/QBTDLUND6E4QOB4QJC65HW3YYN \
  | 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: 806635d1a3f13907079048bdd3db78c37008b5f94476a012096df4a5e5ffe2a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fcfdf95c84eb1a11cb1379095a69d8ed17f107b1624132bcdcb509e177243c9f",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-01-19T08:14:22Z",
    "title_canon_sha256": "822f41b220042001725090170e42624e5ac54dea33473d3164d3bd86e619c3c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.06329",
    "kind": "arxiv",
    "version": 1
  }
}