Pith Number

pith:GQDLRHAJ

pith:2026:GQDLRHAJBQIAUKWZUQD34CWBRH

not attested not anchored not stored refs pending

On the sharp constants in curl-Sobolev inequalities on $\mathbb{S}^n$

Guofang Wang, Mingwei Zhang

arxiv:2607.19091 v1 · 2026-07-21 · math.DG · math.AP · math.SP

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GQDLRHAJBQIAUKWZUQD34CWBRH}

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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	2026-07-22T01:24:08.131647Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3406b89c090c100a2ad9a407be0ac189cd8ffed4b940a2d3b7300459a6787225

Aliases

arxiv: 2607.19091 · arxiv_version: 2607.19091v1 · doi: 10.48550/arxiv.2607.19091 · pith_short_12: GQDLRHAJBQIA · pith_short_16: GQDLRHAJBQIAUKWZ · pith_short_8: GQDLRHAJ

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/GQDLRHAJBQIAUKWZUQD34CWBRH \
  | 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: 3406b89c090c100a2ad9a407be0ac189cd8ffed4b940a2d3b7300459a6787225

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "759a1daaffe74b00a462d8de85ca46186b17cc9f4e86893f711918dc018047ac",
    "cross_cats_sorted": [
      "math.AP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-07-21T13:30:26Z",
    "title_canon_sha256": "3a2a17451f0ca5968ae74a69c12fd7cb1bc61b945ee849409f993b3ed94265aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.19091",
    "kind": "arxiv",
    "version": 1
  }
}