Pith Number

pith:FLTURINN

pith:2022:FLTURINNYOYH3QS5WVCNRMACYL

not attested not anchored not stored refs pending

Stability for the Sobolev inequality: existence of a minimizer

Tobias K\"onig

arxiv:2211.14185 v4 · 2022-11-25 · 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{FLTURINNYOYH3QS5WVCNRMACYL}

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.

Cited by

2 papers in Pith

The weighted $L^2$-Caffarelli-Kohn-Nirenberg inequalities for the curl-free vector fields and second order derivatives: The sharp constants and stability estimates

Log-Sobolev and Beckner inequalities and stability of Poincar\'e inequality with weighted Gaussian measures

Receipt and verification

First computed	2026-07-05T06:57:51.400897Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ae748a1adc3b07dc25db544d8b002c2ef0322054c175b3985e352d67591130f

Aliases

arxiv: 2211.14185 · arxiv_version: 2211.14185v4 · doi: 10.48550/arxiv.2211.14185 · pith_short_12: FLTURINNYOYH · pith_short_16: FLTURINNYOYH3QS5 · pith_short_8: FLTURINN

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/FLTURINNYOYH3QS5WVCNRMACYL \
  | 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: 2ae748a1adc3b07dc25db544d8b002c2ef0322054c175b3985e352d67591130f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec9fcdc314dab6a030bdad869828e7ccc0237d1ae58daac0f0b788c139b2b696",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2022-11-25T15:39:37Z",
    "title_canon_sha256": "dfefe0c6aedc5a57eeaab7cc6c8894f8f1afe8b77790b27b07fc16638239496d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.14185",
    "kind": "arxiv",
    "version": 4
  }
}