Pith Number

pith:5NKM32PU

pith:2022:5NKM32PUAM6UL4GMOAQIBNNSTD

not attested not anchored not stored refs pending

Some estimates for commutators of the fractional maximal function on stratified Lie groups

J. Wu, W. Zhao

arxiv:2206.08340 v3 · 2022-06-01 · 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{5NKM32PUAM6UL4GMOAQIBNNSTD}

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	2026-07-05T06:51:18.129342Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb54cde9f4033d45f0cc702080b5b298c36e98db33a732de1ffd391b5616386b

Aliases

arxiv: 2206.08340 · arxiv_version: 2206.08340v3 · doi: 10.48550/arxiv.2206.08340 · pith_short_12: 5NKM32PUAM6U · pith_short_16: 5NKM32PUAM6UL4GM · pith_short_8: 5NKM32PU

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/5NKM32PUAM6UL4GMOAQIBNNSTD \
  | 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: eb54cde9f4033d45f0cc702080b5b298c36e98db33a732de1ffd391b5616386b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "814d0b79326e1da29123ab6daca566f38d93ea443e5dadbee01260b9837c320c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2022-06-01T12:57:42Z",
    "title_canon_sha256": "6adcb2dcfac9f1623128cd2cc3a3d096ce42dbf523fb9735dcb76784f74efeb6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2206.08340",
    "kind": "arxiv",
    "version": 3
  }
}