Pith Number

pith:EPCWKCMF

pith:2025:EPCWKCMFR2TTCAOQR7Q72RKBNU

not attested not anchored not stored refs pending

Lacunary Spherical Maximal Operators on Hyperbolic Spaces

Hong-Wei Zhang, Yunxiang Wang

arxiv:2502.20739 v2 · 2025-02-28 · 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{EPCWKCMFR2TTCAOQR7Q72RKBNU}

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	2026-06-09T01:05:05.768528Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

23c56509858ea73101d08fe1fd45416d2c226b9c375ffff310b6e9a2f6bf2fd5

Aliases

arxiv: 2502.20739 · arxiv_version: 2502.20739v2 · doi: 10.48550/arxiv.2502.20739 · pith_short_12: EPCWKCMFR2TT · pith_short_16: EPCWKCMFR2TTCAOQ · pith_short_8: EPCWKCMF

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/EPCWKCMFR2TTCAOQR7Q72RKBNU \
  | 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: 23c56509858ea73101d08fe1fd45416d2c226b9c375ffff310b6e9a2f6bf2fd5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e0308cc6bad1facd00c84932f189f2998ab684227ad29bbeb493db00e3fd8ea4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2025-02-28T05:40:26Z",
    "title_canon_sha256": "bf06952c01d5dfc1cb31e65aaeab58da65378b314dadba933b71ed28b300f6ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.20739",
    "kind": "arxiv",
    "version": 2
  }
}