Pith Number

pith:WHC6SF6Y

pith:2025:WHC6SF6YHIYYCFQNT5ZYEJ45UA

not attested not anchored not stored refs pending

A Local Version of Hardy-type Spaces Associated with Ball Quasi-Banach Spaces and Non-negative Self-adjoint Operators on Spaces of Homogeneous Type and Their Applications

Tiantian Zhao, Wenhua Wang, Xiong Liu

arxiv:2503.03301 v1 · 2025-03-05 · 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{WHC6SF6YHIYYCFQNT5ZYEJ45UA}

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	2026-07-05T10:24:42.944107Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1c5e917d83a3181160d9f7382279da01edbcdf3e637b9b437275290925fe7c7

Aliases

arxiv: 2503.03301 · arxiv_version: 2503.03301v1 · doi: 10.48550/arxiv.2503.03301 · pith_short_12: WHC6SF6YHIYY · pith_short_16: WHC6SF6YHIYYCFQN · pith_short_8: WHC6SF6Y

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/WHC6SF6YHIYYCFQNT5ZYEJ45UA \
  | 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: b1c5e917d83a3181160d9f7382279da01edbcdf3e637b9b437275290925fe7c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75198b38180b31b77cb89de95ffdf894f2146fa5590ce32aa58ee8df7c1e3496",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-03-05T09:34:39Z",
    "title_canon_sha256": "474569ebfc66b96ade73f78c70f7eada129ae7c5f17169445f9aa4239ce83ac0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2503.03301",
    "kind": "arxiv",
    "version": 1
  }
}