Pith Number

pith:Z6DC4JTZ

pith:2013:Z6DC4JTZLA455UKIQUZZ4VTVJL

not attested not anchored not stored refs pending

Weak Hardy Spaces $WH_L^p({\mathbb R}^n)$ Associated to Operators Satisfying $k$-Davies-Gaffney Estimates

Dachun Yang, Der-Chen Chang, Huoxiong Wu, Jun Cao

arxiv:1308.5385 v2 · 2013-08-25 · math.CA · 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{Z6DC4JTZLA455UKIQUZZ4VTVJL}

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	2026-05-18T02:32:31.092868Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf862e26795839ded14885339e56754afa1cb0d613f74cdd27ecf05b4c357491

Aliases

arxiv: 1308.5385 · arxiv_version: 1308.5385v2 · doi: 10.48550/arxiv.1308.5385 · pith_short_12: Z6DC4JTZLA45 · pith_short_16: Z6DC4JTZLA455UKI · pith_short_8: Z6DC4JTZ

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/Z6DC4JTZLA455UKIQUZZ4VTVJL \
  | 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: cf862e26795839ded14885339e56754afa1cb0d613f74cdd27ecf05b4c357491

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6cf34a61b4a667b241a4c402fb8ba3cd078580f1b52812d066e30cc21982be5",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-08-25T08:01:48Z",
    "title_canon_sha256": "9ac3b19a9744b9f25643979be0658bd0490b0608491549fb03374bd1e0e6723f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.5385",
    "kind": "arxiv",
    "version": 2
  }
}