Pith Number

pith:NJD7QEAC

pith:2025:NJD7QEACDOUZWAXKJ7V5GPMUV4

not attested not anchored not stored refs pending

Sharp quantitative integral inequalities for harmonic extensions

Jonas W. Peteranderl, Larry Read, Rupert L. Frank

arxiv:2508.09940 v1 · 2025-08-13 · math.AP · math.CA · 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{NJD7QEACDOUZWAXKJ7V5GPMUV4}

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.

Cited by

1 paper in Pith

Stability for the Affine Sobolev Inequality and its Critical Points for $p\ge 2$

Receipt and verification

First computed	2026-07-05T11:53:24.770967Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a47f810021ba99b02ea4febd33d94af23880f99f555ce3eb7de7fde3f7b29f2

Aliases

arxiv: 2508.09940 · arxiv_version: 2508.09940v1 · doi: 10.48550/arxiv.2508.09940 · pith_short_12: NJD7QEACDOUZ · pith_short_16: NJD7QEACDOUZWAXK · pith_short_8: NJD7QEAC

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/NJD7QEACDOUZWAXKJ7V5GPMUV4 \
  | 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: 6a47f810021ba99b02ea4febd33d94af23880f99f555ce3eb7de7fde3f7b29f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d57bf8125ab8f4a54539ef067a031aa7c9a4ae165268c9a6750fac61c2e2da11",
    "cross_cats_sorted": [
      "math.CA",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-08-13T16:49:40Z",
    "title_canon_sha256": "b8e87e8a5cdc200aca4940133a786968e39deee46daca0eb2c4388d2ad9b3b02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.09940",
    "kind": "arxiv",
    "version": 1
  }
}