Pith Number

pith:JQ3I3FRJ

pith:2026:JQ3I3FRJHMGLA25WQVJUYS2AYN

not attested not anchored not stored refs pending

Sparse domination of Calder\'on--Zygmund operators by mean oscillations

Andrei K. Lerner

arxiv:2605.25919 v1 · 2026-05-25 · 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{JQ3I3FRJHMGLA25WQVJUYS2AYN}

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	2026-05-26T02:05:18.358299Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4c368d96293b0cb06bb685534c4b40c372d460f8ec334397585392bce671ce39

Aliases

arxiv: 2605.25919 · arxiv_version: 2605.25919v1 · doi: 10.48550/arxiv.2605.25919 · pith_short_12: JQ3I3FRJHMGL · pith_short_16: JQ3I3FRJHMGLA25W · pith_short_8: JQ3I3FRJ

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/JQ3I3FRJHMGLA25WQVJUYS2AYN \
  | 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: 4c368d96293b0cb06bb685534c4b40c372d460f8ec334397585392bce671ce39

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ded968364a28e9a4b89d4aad4e28caf1cd80a04a55b529a85c2a1ed78cfa8deb",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-05-25T14:56:32Z",
    "title_canon_sha256": "6fd6ac3e8262d392dcba191631175e43f7216b7e939ae68efb5d2a8c090f5f5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.25919",
    "kind": "arxiv",
    "version": 1
  }
}