Pith Number

pith:NO5RHD5O

pith:2026:NO5RHD5OR2B4X44IUPJVMIXGNI

not attested not anchored not stored refs pending

Fractional Gagliardo--Nirenberg Inequalities: Pointwise Estimates,Sharp Asymptotics, and Optimal Target Spaces

Dachun Yang, Pingxu Hu, Wen Yuan, Yinqin Li

arxiv:2608.06813 v1 · 2026-08-07 · math.CA · 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{NO5RHD5OR2B4X44IUPJVMIXGNI}

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	2026-08-10T01:12:10.260529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6bbb138fae8e83cbf388a3d35622e66a39de2c27bafcc46e90c862c1f65d9294

Aliases

arxiv: 2608.06813 · arxiv_version: 2608.06813v1 · doi: 10.48550/arxiv.2608.06813 · pith_short_12: NO5RHD5OR2B4 · pith_short_16: NO5RHD5OR2B4X44I · pith_short_8: NO5RHD5O

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/NO5RHD5OR2B4X44IUPJVMIXGNI \
  | 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: 6bbb138fae8e83cbf388a3d35622e66a39de2c27bafcc46e90c862c1f65d9294

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ad27ca09c31dc913034832ff40b52170594be04a5aedb83bbf4a3070ddb5249",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-08-07T05:08:21Z",
    "title_canon_sha256": "b039a5c41f4c62d002715e7c430b4803e49b37023b79527ee0213e9c1a530257"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.06813",
    "kind": "arxiv",
    "version": 1
  }
}