Pith Number

pith:SEBP7Z4R

pith:2023:SEBP7Z4RUR6DH7A3JZNQSHZ3WI

not attested not anchored not stored refs pending

On the stability constant of Caffarelli-Kohn-Nirenberg inequality

Shengbing Deng, Xingliang Tian

arxiv:2308.04111 v4 · 2023-08-08 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SEBP7Z4RUR6DH7A3JZNQSHZ3WI}

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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	2026-07-05T09:54:42.890841Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9102ffe791a47c33fc1b4e5b091f3bb218ea0d76db5f830422bdef5eaf7ad50b

Aliases

arxiv: 2308.04111 · arxiv_version: 2308.04111v4 · doi: 10.48550/arxiv.2308.04111 · pith_short_12: SEBP7Z4RUR6D · pith_short_16: SEBP7Z4RUR6DH7A3 · pith_short_8: SEBP7Z4R

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/SEBP7Z4RUR6DH7A3JZNQSHZ3WI \
  | 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: 9102ffe791a47c33fc1b4e5b091f3bb218ea0d76db5f830422bdef5eaf7ad50b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08e8be8b7699003c79e729014c477296698e6606c85bb60ae2943ed603220ff3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2023-08-08T07:53:21Z",
    "title_canon_sha256": "3686a4550e54c464cefc09b6d13263aeabcca56aec0d066a314adbb979fd9912"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2308.04111",
    "kind": "arxiv",
    "version": 4
  }
}