Pith Number

pith:VDQTJ6XK

pith:2016:VDQTJ6XKQHW2QLOUXOLWUJRGWP

not attested not anchored not stored refs pending

Characterizations of the BMO and Lipschitz spaces via commutators on weak Lebesgue and Morrey spaces

Dinghuai Wang, Jiang Zhou, Wenyi Chen

arxiv:1612.08819 v1 · 2016-12-28 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VDQTJ6XKQHW2QLOUXOLWUJRGWP}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T00:53:47.094123Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8e134faea81eda82dd4bb976a2626b3eccbeebdd2504aa5a32d2052bd111075

Aliases

arxiv: 1612.08819 · arxiv_version: 1612.08819v1 · doi: 10.48550/arxiv.1612.08819 · pith_short_12: VDQTJ6XKQHW2 · pith_short_16: VDQTJ6XKQHW2QLOU · pith_short_8: VDQTJ6XK

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/VDQTJ6XKQHW2QLOUXOLWUJRGWP \
  | 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: a8e134faea81eda82dd4bb976a2626b3eccbeebdd2504aa5a32d2052bd111075

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c3361577275233675cd778808405ac34ed1d94df9c154675d486554acf74515",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-12-28T07:43:54Z",
    "title_canon_sha256": "84cff78c4528d61675207c1854d1d24274daf766942d2e500db07864c51a80ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.08819",
    "kind": "arxiv",
    "version": 1
  }
}