Pith Number

pith:4ULKH3F6

pith:2016:4ULKH3F6BD2BJZESSGZXS7XFKA

not attested not anchored not stored refs pending

Endpoint estimates for the commutators of multilinear Calder\'{o}n-Zygmund operators with Dini type kernels

Qingying Xue, Zhengyang Li

arxiv:1601.02173 v1 · 2016-01-10 · 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{4ULKH3F6BD2BJZESSGZXS7XFKA}

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	2026-05-18T01:23:07.089748Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e516a3ecbe08f414e49291b3797ee550004f4274e0a846ea8e054a843774379a

Aliases

arxiv: 1601.02173 · arxiv_version: 1601.02173v1 · doi: 10.48550/arxiv.1601.02173 · pith_short_12: 4ULKH3F6BD2B · pith_short_16: 4ULKH3F6BD2BJZES · pith_short_8: 4ULKH3F6

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/4ULKH3F6BD2BJZESSGZXS7XFKA \
  | 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: e516a3ecbe08f414e49291b3797ee550004f4274e0a846ea8e054a843774379a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9109668f63a0d2e30b939a343966fb615129dbb694ce3bf8050443a2abedad22",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-01-10T02:56:00Z",
    "title_canon_sha256": "097a90676c3a5947ca4c1dfb0a457973c59cd25840eda596426ad738e2935537"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.02173",
    "kind": "arxiv",
    "version": 1
  }
}