Pith Number

pith:WGZTG4EU

pith:2025:WGZTG4EUGIMSQ5SNG2JFIGIE7E

not attested not anchored not stored refs pending

Characterization of Vanishing Campanato Spaces via Ball Banach Function Spaces and Its Applications

Dachun Yang, Jin Tao, Xing Fu, Yoshihiro Sawano

arxiv:2508.08536 v1 · 2025-08-12 · math.FA · math.AP · 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{WGZTG4EUGIMSQ5SNG2JFIGIE7E}

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	2026-07-05T11:52:30.141443Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1b3337094321928764d3692541904f922fb92b5f71133370141333a18c5ca4b

Aliases

arxiv: 2508.08536 · arxiv_version: 2508.08536v1 · doi: 10.48550/arxiv.2508.08536 · pith_short_12: WGZTG4EUGIMS · pith_short_16: WGZTG4EUGIMSQ5SN · pith_short_8: WGZTG4EU

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/WGZTG4EUGIMSQ5SNG2JFIGIE7E \
  | 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: b1b3337094321928764d3692541904f922fb92b5f71133370141333a18c5ca4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4122d0bdcd4e3a0ba7eeead028ddf27ffd136c576c6c82cb86f5a002629fdfa6",
    "cross_cats_sorted": [
      "math.AP",
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-08-12T00:58:14Z",
    "title_canon_sha256": "223cd157b02474b8ef43e5a80c539710c08ce4f8cc00d11d58b7428e0420b5f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.08536",
    "kind": "arxiv",
    "version": 1
  }
}