Pith Number

pith:QF5SS5HK

pith:2015:QF5SS5HKKMRFSIUJFEW7MSC4BO

not attested not anchored not stored refs pending

Factorization for Hardy spaces and characterization for BMO spaces via commutators in the Bessel setting

Brett D. Wick, Dongyong Yang, Ji Li, Xuan Thinh Duong

arxiv:1509.00079 v2 · 2015-08-31 · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QF5SS5HKKMRFSIUJFEW7MSC4BO}

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	2026-05-18T01:34:05.012324Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

817b2974ea5322592289292df6485c0b88129f1efc34414aff84e580f73ab7bb

Aliases

arxiv: 1509.00079 · arxiv_version: 1509.00079v2 · doi: 10.48550/arxiv.1509.00079 · pith_short_12: QF5SS5HKKMRF · pith_short_16: QF5SS5HKKMRFSIUJ · pith_short_8: QF5SS5HK

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/QF5SS5HKKMRFSIUJFEW7MSC4BO \
  | 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: 817b2974ea5322592289292df6485c0b88129f1efc34414aff84e580f73ab7bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dea389b5dd1d0d7f6cb5da594ad0dcdf6d5a055a027b02017402b6921809615e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-08-31T21:24:14Z",
    "title_canon_sha256": "87bba3ce5e6c3d6bb63aa0fe90dbf2fd3f72b4ec5aa4628abc536409b3b337a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.00079",
    "kind": "arxiv",
    "version": 2
  }
}