Pith Number

pith:NT4YVVBD

pith:2011:NT4YVVBDBAJGSNAUCI3ECGORF7

not attested not anchored not stored refs pending

Caffarelli-Kohn-Nirenberg type inequalities for the weighted biharmonic operator: existence of extremal functions, breaking positivity and breaking symmetry

Paolo Caldiroli, Roberta Musina

arxiv:1106.3934 v1 · 2011-06-20 · 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{NT4YVVBDBAJGSNAUCI3ECGORF7}

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	2026-05-18T04:19:41.839614Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6cf98ad423081269341412364119d12fd2aa2403c199025ce6ae58feacc1f6ff

Aliases

arxiv: 1106.3934 · arxiv_version: 1106.3934v1 · doi: 10.48550/arxiv.1106.3934 · pith_short_12: NT4YVVBDBAJG · pith_short_16: NT4YVVBDBAJGSNAU · pith_short_8: NT4YVVBD

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/NT4YVVBDBAJGSNAUCI3ECGORF7 \
  | 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: 6cf98ad423081269341412364119d12fd2aa2403c199025ce6ae58feacc1f6ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5a84431d0debdf9282db6a1d72b2c60d47aa19f45b3a67129d1fea9a9f83a2f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-06-20T15:11:58Z",
    "title_canon_sha256": "618311df6d5bb7f3794c0f9341305cfc7f7aa00255ae1d10afd221dd807d4962"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.3934",
    "kind": "arxiv",
    "version": 1
  }
}