Pith Number

pith:MMO5OGBJ

pith:2018:MMO5OGBJLZCFWAWGFPFIGZULTG

not attested not anchored not stored refs pending

Mixed weak estimates of Sawyer type for generalized maximal operators

Fabio Berra

arxiv:1808.04333 v2 · 2018-08-13 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MMO5OGBJLZCFWAWGFPFIGZULTG}

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	2026-05-18T00:00:12.947026Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

631dd718295e445b02c62bca83668b998efb972a363ff581586e8d997f7c5043

Aliases

arxiv: 1808.04333 · arxiv_version: 1808.04333v2 · doi: 10.48550/arxiv.1808.04333 · pith_short_12: MMO5OGBJLZCF · pith_short_16: MMO5OGBJLZCFWAWG · pith_short_8: MMO5OGBJ

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/MMO5OGBJLZCFWAWGFPFIGZULTG \
  | 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: 631dd718295e445b02c62bca83668b998efb972a363ff581586e8d997f7c5043

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c02e4ae80227e394cbdce0466db0ee3d2ede3141b69d610e82b2ed591b670fc1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-08-13T17:17:28Z",
    "title_canon_sha256": "6d7c52f40fa752404a2578c37b983259b0b13d45c7ddfca698e7e3af0381c909"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.04333",
    "kind": "arxiv",
    "version": 2
  }
}