Pith Number

pith:OXVKBAFT

pith:2026:OXVKBAFTUEFQGMDOINW4LZWFYA

not attested not anchored not stored refs pending

Bilinear Calder\'{o}n-Zygmund operators on Vilenkin groups

Adil Shafi Wani, Qaiser Jahan, Salman Ashraf

arxiv:2606.31360 v1 · 2026-06-30 · 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{OXVKBAFTUEFQGMDOINW4LZWFYA}

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	2026-07-01T01:18:00.462832Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

75eaa080b3a10b03306e436dc5e6c5c030d0dcca48d7236b641aa058dede5dd2

Aliases

arxiv: 2606.31360 · arxiv_version: 2606.31360v1 · doi: 10.48550/arxiv.2606.31360 · pith_short_12: OXVKBAFTUEFQ · pith_short_16: OXVKBAFTUEFQGMDO · pith_short_8: OXVKBAFT

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/OXVKBAFTUEFQGMDOINW4LZWFYA \
  | 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: 75eaa080b3a10b03306e436dc5e6c5c030d0dcca48d7236b641aa058dede5dd2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f462d1a21666ad01a57c076b02b1a90de1d9e5f39eafb2ed446e1e1e635220d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-06-30T08:55:23Z",
    "title_canon_sha256": "0b5bbcd9b28d3b588cc5e23cedf0749f630eca35239ccb7dff0c5a34b03734f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.31360",
    "kind": "arxiv",
    "version": 1
  }
}