Pith Number

pith:VBSEMKO2

pith:2026:VBSEMKO2N5UDUKBGXJGSDRFHW5

not attested not anchored not stored refs pending

Caffarelli-Kohn-Nirenberg and Weighted Gaussian Poincar\'e Inequalities: a complete characterization of sharp $L^2$ stability and $L^p$ extensions

Anh Xuan Do, Guozhen Lu, Nguyen Lam, Van Hoang Nguyen

arxiv:2606.08939 v1 · 2026-06-08 · 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{VBSEMKO2N5UDUKBGXJGSDRFHW5}

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	2026-06-09T02:07:48.791894Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8644629da6f683a2826ba4d21c4a7b74bbd66b8924cea0b15090510ff536bae

Aliases

arxiv: 2606.08939 · arxiv_version: 2606.08939v1 · doi: 10.48550/arxiv.2606.08939 · pith_short_12: VBSEMKO2N5UD · pith_short_16: VBSEMKO2N5UDUKBG · pith_short_8: VBSEMKO2

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/VBSEMKO2N5UDUKBGXJGSDRFHW5 \
  | 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: a8644629da6f683a2826ba4d21c4a7b74bbd66b8924cea0b15090510ff536bae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7dbd1dcd2b0a8f6a423d61f157a5eee85c27de7ed756283e55911061917742f2",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-08T02:36:03Z",
    "title_canon_sha256": "e58bff7397710a47a5f293d50566c8ce602b7c73dab1eeea5d119f42f4cddbd1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.08939",
    "kind": "arxiv",
    "version": 1
  }
}