Pith Number

pith:CGAIEPVJ

pith:2026:CGAIEPVJF3JXJLETXDDPVUVO4H

not attested not anchored not stored refs pending

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

Anh Tuan Duong, Van Hoang Nguyen

arxiv:2606.25692 v1 · 2026-06-24 · 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{CGAIEPVJF3JXJLETXDDPVUVO4H}

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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.

Receipt and verification

First computed	2026-06-25T01:18:12.953560Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1180823ea92ed374ac93b8c6fad2aee1ff875f155e0cf2db3a6418272110b6fe

Aliases

arxiv: 2606.25692 · arxiv_version: 2606.25692v1 · doi: 10.48550/arxiv.2606.25692 · pith_short_12: CGAIEPVJF3JX · pith_short_16: CGAIEPVJF3JXJLET · pith_short_8: CGAIEPVJ

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/CGAIEPVJF3JXJLETXDDPVUVO4H \
  | 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: 1180823ea92ed374ac93b8c6fad2aee1ff875f155e0cf2db3a6418272110b6fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ffd7151cc4818aa68ab5d5684c325d16324a7b06e64fac832accfe977c8274e",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-24T11:02:40Z",
    "title_canon_sha256": "1c22f513ded703f97022092d42de8cc8b455101f8f13f497f2c452391ab9037b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.25692",
    "kind": "arxiv",
    "version": 1
  }
}