Pith Number

pith:XG7FWWR4

pith:2015:XG7FWWR4GFQA23HQWXEAKE45IF

not attested not anchored not stored refs pending

A non-homogeneous local $Tb$ theorem for Littlewood-Paley $g_{\lambda}^{*}$-function with $L^p$-testing condition

Mingming Cao, Qingying Xue

arxiv:1507.05291 v1 · 2015-07-19 · 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{XG7FWWR4GFQA23HQWXEAKE45IF}

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	2026-05-18T01:36:37.285372Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9be5b5a3c31600d6cf0b5c805139d416853fbbacfe690da1c748257f16bbb74

Aliases

arxiv: 1507.05291 · arxiv_version: 1507.05291v1 · doi: 10.48550/arxiv.1507.05291 · pith_short_12: XG7FWWR4GFQA · pith_short_16: XG7FWWR4GFQA23HQ · pith_short_8: XG7FWWR4

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/XG7FWWR4GFQA23HQWXEAKE45IF \
  | 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: b9be5b5a3c31600d6cf0b5c805139d416853fbbacfe690da1c748257f16bbb74

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7881138216b5a9453f358b65a1e5336ef2f0bb58738396eb714b17ab9cb2f85",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-07-19T14:22:42Z",
    "title_canon_sha256": "da816b07a48c538e042fce76c7ea5cd69cccbd2bebaaf766589bc4d3cc5f0d05"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.05291",
    "kind": "arxiv",
    "version": 1
  }
}