Pith Number

pith:N3JOTKV3

pith:2025:N3JOTKV3LMUO6LA7LM2UDXY7AU

not attested not anchored not stored refs pending

Existence of Bianchi-Egnell stability extremizer for the Hardy-Sobolev inequality

Debabrata Karmakar, Monideep Ghosh, Souptik Chakraborty

arxiv:2505.07039 v2 · 2025-05-11 · math.AP · math.FA

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N3JOTKV3LMUO6LA7LM2UDXY7AU}

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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

1 paper in Pith

Optimal Stability Bounds, Minimizers, and Critical Points for a Critical Nonlocal Sobolev Inequality on the Heisenberg Group

Receipt and verification

First computed	2026-07-05T11:37:44.770636Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ed2e9aabb5b28ef2c1f5b3541df1f051556448a0caa0fde48d6b9af3e35967f

Aliases

arxiv: 2505.07039 · arxiv_version: 2505.07039v2 · doi: 10.48550/arxiv.2505.07039 · pith_short_12: N3JOTKV3LMUO · pith_short_16: N3JOTKV3LMUO6LA7 · pith_short_8: N3JOTKV3

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/N3JOTKV3LMUO6LA7LM2UDXY7AU \
  | 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: 6ed2e9aabb5b28ef2c1f5b3541df1f051556448a0caa0fde48d6b9af3e35967f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c94ab06d135ca3dac895b1bde3b91f1a59929951ec76253889646832c2058e5a",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-05-11T16:21:29Z",
    "title_canon_sha256": "b53513c1f6a5dd604ef0ec5038b3fb94a9677af5d423f34d6bb531ab04ba61a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.07039",
    "kind": "arxiv",
    "version": 2
  }
}