Pith Number

pith:JB25FL2P

pith:2015:JB25FL2PQVV73XBXNT7ASWTVMF

not attested not anchored not stored refs pending

Weak-type estimates in Morrey spaces for maximal commutator and commutator of maximal function

Amiran Gogatishvili, M\"ujdat A\u{g}cayaz{\i}, Rza Mustafayev

arxiv:1504.04509 v2 · 2015-04-17 · 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{JB25FL2PQVV73XBXNT7ASWTVMF}

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	2026-05-18T00:09:04.407185Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4875d2af4f856bfddc376cfe095a75614d5153ba4b8078fce9d537e52c13fc6b

Aliases

arxiv: 1504.04509 · arxiv_version: 1504.04509v2 · doi: 10.48550/arxiv.1504.04509 · pith_short_12: JB25FL2PQVV7 · pith_short_16: JB25FL2PQVV73XBX · pith_short_8: JB25FL2P

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/JB25FL2PQVV73XBXNT7ASWTVMF \
  | 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: 4875d2af4f856bfddc376cfe095a75614d5153ba4b8078fce9d537e52c13fc6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a4da0a3d558fb99728d45124c40d9718d4ccffb2762d8a4082c8168ef3cd23d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-04-17T14:23:14Z",
    "title_canon_sha256": "0184755111baa1dc85265beef29cc5fafe772c68dbe0e356ceb7392197dfaede"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.04509",
    "kind": "arxiv",
    "version": 2
  }
}