Pith Number

pith:JPZJOLPQ

pith:2018:JPZJOLPQPRO7TWJXLUUSYQMIAF

not attested not anchored not stored refs pending

Hardy-Littlewood maximal operator on the associate space of a Banach function space

Alexei Yu. Karlovich

arxiv:1808.05645 v1 · 2018-08-16 · 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{JPZJOLPQPRO7TWJXLUUSYQMIAF}

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	2026-05-18T00:07:56.067914Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4bf2972df07c5df9d9375d292c418801763b735a783cbc05c16983b976f09ad2

Aliases

arxiv: 1808.05645 · arxiv_version: 1808.05645v1 · doi: 10.48550/arxiv.1808.05645 · pith_short_12: JPZJOLPQPRO7 · pith_short_16: JPZJOLPQPRO7TWJX · pith_short_8: JPZJOLPQ

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/JPZJOLPQPRO7TWJXLUUSYQMIAF \
  | 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: 4bf2972df07c5df9d9375d292c418801763b735a783cbc05c16983b976f09ad2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f8438ca7405ccf8fddb6fb2ccf135790df8e06b50ef7beb755423256aefd180",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-08-16T19:08:36Z",
    "title_canon_sha256": "a6888695c1fc40f3210ecf6aa55d89eb246f6444f1b668b26829dd47e8d937e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.05645",
    "kind": "arxiv",
    "version": 1
  }
}