Pith Number

pith:YV33BFEH

pith:2025:YV33BFEH3A2D5KR4MGLL3UBF4S

not attested not anchored not stored refs pending

Lacunary $\delta$-Discretised Spherical Maximal Operators

Chong-Wei Liang, Chun-Yen Shen, Ji Li, Surjeet Singh Choudhary

arxiv:2507.09962 v1 · 2025-07-14 · 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{YV33BFEH3A2D5KR4MGLL3UBF4S}

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	2026-07-05T11:36:42.893902Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c577b09487d8343eaa3c6196bdd025e492bf6c6730f1a90eba1c39c3dd7d6076

Aliases

arxiv: 2507.09962 · arxiv_version: 2507.09962v1 · doi: 10.48550/arxiv.2507.09962 · pith_short_12: YV33BFEH3A2D · pith_short_16: YV33BFEH3A2D5KR4 · pith_short_8: YV33BFEH

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/YV33BFEH3A2D5KR4MGLL3UBF4S \
  | 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: c577b09487d8343eaa3c6196bdd025e492bf6c6730f1a90eba1c39c3dd7d6076

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87830066eb082d458047fdc88f9099210cd9bde2738ae4588119240a19f28a46",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2025-07-14T06:28:06Z",
    "title_canon_sha256": "8d1d5d10c35a8a8917681acd60514e00fe22bb0ec61a73c7229fdd76a0e4486f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.09962",
    "kind": "arxiv",
    "version": 1
  }
}