Pith Number

pith:IA6C4M6V

pith:2025:IA6C4M6VSAOVWBR5UNOFELESOA

not attested not anchored not stored refs pending

Sharp weak bounds for the Hardy-Littlewood-P\'{o}lya operator and the weak bounds for the multilinear integral operator

Tianyang He

arxiv:2505.17707 v2 · 2025-05-23 · 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{IA6C4M6VSAOVWBR5UNOFELESOA}

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	2026-06-02T02:04:06.239874Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

403c2e33d5901d5b063da35c522c92703b807e5672c7fb87fe33a9126c58d9bc

Aliases

arxiv: 2505.17707 · arxiv_version: 2505.17707v2 · doi: 10.48550/arxiv.2505.17707 · pith_short_12: IA6C4M6VSAOV · pith_short_16: IA6C4M6VSAOVWBR5 · pith_short_8: IA6C4M6V

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/IA6C4M6VSAOVWBR5UNOFELESOA \
  | 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: 403c2e33d5901d5b063da35c522c92703b807e5672c7fb87fe33a9126c58d9bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "429d26064f794ee4ca91c110c77bb0d7b89aeb2e3c4ab1cdfa338046f5fb266b",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2025-05-23T10:21:41Z",
    "title_canon_sha256": "4057184bfa78d1c743c6b285a6caa4785539e9cc638b7361ca9d336a6bcb6d3a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.17707",
    "kind": "arxiv",
    "version": 2
  }
}