Pith Number

pith:3UFNIXDM

pith:2015:3UFNIXDMGU72NVGI5LHZRLBT2Y

not attested not anchored not stored refs pending

Boundedness of Commutators on Hardy Spaces over Metric Measure Spaces of Non-homogeneous Type

Dachun Yang, Haibo Lin, Suqing Wu

arxiv:1509.05820 v1 · 2015-09-18 · 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{3UFNIXDMGU72NVGI5LHZRLBT2Y}

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	2026-05-18T01:32:36.573678Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd0ad45c6c353fa6d4c8eacf98ac33d6104dfe1daf401c7617117c0b76c92afa

Aliases

arxiv: 1509.05820 · arxiv_version: 1509.05820v1 · doi: 10.48550/arxiv.1509.05820 · pith_short_12: 3UFNIXDMGU72 · pith_short_16: 3UFNIXDMGU72NVGI · pith_short_8: 3UFNIXDM

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/3UFNIXDMGU72NVGI5LHZRLBT2Y \
  | 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: dd0ad45c6c353fa6d4c8eacf98ac33d6104dfe1daf401c7617117c0b76c92afa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e27d4ef4292e881aee6df277718d3ff8d4472deb0f4dfbdf59728877dc55b7f",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-09-18T23:41:36Z",
    "title_canon_sha256": "9cd7f8bcb33a612b5c7274470949a504d7b780eb2d6c6346941c6ad71b2f6516"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05820",
    "kind": "arxiv",
    "version": 1
  }
}