Pith Number

pith:BB3GGFZM

pith:2011:BB3GGFZM4BJ5NUVQE5JOCKKMG7

not attested not anchored not stored refs pending

Boundedness of singular integrals and their commutators with BMO functions on Hardy spaces

The Anh Bui, Xuan Thinh Duong

arxiv:1110.1770 v2 · 2011-10-08 · 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{BB3GGFZM4BJ5NUVQE5JOCKKMG7}

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	2026-05-18T03:38:23.847327Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

087663172ce053d6d2b02752e1294c37fa0f08bcc90ee2908c3f892bd93e32e5

Aliases

arxiv: 1110.1770 · arxiv_version: 1110.1770v2 · doi: 10.48550/arxiv.1110.1770 · pith_short_12: BB3GGFZM4BJ5 · pith_short_16: BB3GGFZM4BJ5NUVQ · pith_short_8: BB3GGFZM

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/BB3GGFZM4BJ5NUVQE5JOCKKMG7 \
  | 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: 087663172ce053d6d2b02752e1294c37fa0f08bcc90ee2908c3f892bd93e32e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3ebecc31b53e030dbbcbb57c3066fd6921145dcbb181ad728803938af328c7f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-10-08T21:32:53Z",
    "title_canon_sha256": "985b76139e6dcd6bb31d04e9dbf1f48c6e71c8af794007e5c6797ad5a8c55af9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.1770",
    "kind": "arxiv",
    "version": 2
  }
}