Pith Number

pith:PJZDPA2R

pith:2015:PJZDPA2RFRNVOEGOYB3OYVFYVD

not attested not anchored not stored refs pending

Weighted Endpoint Estimates for Commutators of Calder\'on-Zygmund Operators

Dachun Yang, Luong Dang Ky, Yiyu Liang

arxiv:1510.05855 v1 · 2015-10-20 · math.CA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PJZDPA2RFRNVOEGOYB3OYVFYVD}

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	2026-05-18T01:29:39.524845Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a723783512c5b5710cec076ec54b8a8e0564298f075a0ba453e84871b287ee7

Aliases

arxiv: 1510.05855 · arxiv_version: 1510.05855v1 · doi: 10.48550/arxiv.1510.05855 · pith_short_12: PJZDPA2RFRNV · pith_short_16: PJZDPA2RFRNVOEGO · pith_short_8: PJZDPA2R

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/PJZDPA2RFRNVOEGOYB3OYVFYVD \
  | 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: 7a723783512c5b5710cec076ec54b8a8e0564298f075a0ba453e84871b287ee7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64e8613c7bbe1216d4a7e4da82e6c836530b83e8e89959e749f9c3c38c2c9c88",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-10-20T12:18:20Z",
    "title_canon_sha256": "8bf01c9f96ee64522bd3e76e2a0d79509d1012e38c6a4cbe7c39547452edb1a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.05855",
    "kind": "arxiv",
    "version": 1
  }
}