Pith Number

pith:JNIGYSXM

pith:2025:JNIGYSXMZLNJAMJDOO7BYTYHGM

not attested not anchored not stored refs pending

Uniform boundedness of parametric bilinear fractional integrals

Loukas Grafakos, Nuno J. Alves

arxiv:2508.01657 v2 · 2025-08-03 · 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{JNIGYSXMZLNJAMJDOO7BYTYHGM}

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	2026-06-02T01:03:32.956339Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b506c4aeccada90312373be1c4f07333dbb9a2b7f102573a49047797e0f67fe

Aliases

arxiv: 2508.01657 · arxiv_version: 2508.01657v2 · doi: 10.48550/arxiv.2508.01657 · pith_short_12: JNIGYSXMZLNJ · pith_short_16: JNIGYSXMZLNJAMJD · pith_short_8: JNIGYSXM

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/JNIGYSXMZLNJAMJDOO7BYTYHGM \
  | 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: 4b506c4aeccada90312373be1c4f07333dbb9a2b7f102573a49047797e0f67fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b2646d66628cf5824a7589dd2122117d2bff2d9662ef164ec000c3d1761ac12",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2025-08-03T08:31:13Z",
    "title_canon_sha256": "b9bedf55623e64aafab6bbfd2bdb66994af7928281663ab4e1509c541e25bfd7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.01657",
    "kind": "arxiv",
    "version": 2
  }
}