Pith Number

pith:GFXBXOMF

pith:2015:GFXBXOMFKLRA4FEZTGLLE3BXDP

not attested not anchored not stored refs pending

Boundedness of commutators generated by m-th Calder\'on-Zygmund type singular integrals and local Campanato functions on generalized local Morrey spaces

Hongyang Xue, Huixia Mo

arxiv:1506.03187 v2 · 2015-06-10 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GFXBXOMFKLRA4FEZTGLLE3BXDP}

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	2026-05-18T01:26:57.581228Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

316e1bb98552e20e14999996b26c371bd947ec0efb99bf583c4d601551a8bd5b

Aliases

arxiv: 1506.03187 · arxiv_version: 1506.03187v2 · doi: 10.48550/arxiv.1506.03187 · pith_short_12: GFXBXOMFKLRA · pith_short_16: GFXBXOMFKLRA4FEZ · pith_short_8: GFXBXOMF

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/GFXBXOMFKLRA4FEZTGLLE3BXDP \
  | 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: 316e1bb98552e20e14999996b26c371bd947ec0efb99bf583c4d601551a8bd5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07d1766493e1a793536e2ea000bad55de3af8356acd45238bc360a951392b4ea",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-06-10T06:58:09Z",
    "title_canon_sha256": "774c12afa1fe7e32fdae6d9763130aed3a14bcc8a514fe9142f8b014265d1df4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.03187",
    "kind": "arxiv",
    "version": 2
  }
}