Pith Number

pith:JL4PPD36

pith:2015:JL4PPD362GQ7SI7D74KU3ZKKG7

not attested not anchored not stored refs pending

Anisotropic Hardy-Lorentz Spaces and Their Applications

Dachun Yang, Jun Liu, Wen Yuan

arxiv:1512.05081 v1 · 2015-12-16 · 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{JL4PPD362GQ7SI7D74KU3ZKKG7}

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	2026-05-18T01:08:12.434566Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4af8f78f7ed1a1f923e3ff154de54a37cafcbc6420f4f41e84d3bd0e1e3c2434

Aliases

arxiv: 1512.05081 · arxiv_version: 1512.05081v1 · doi: 10.48550/arxiv.1512.05081 · pith_short_12: JL4PPD362GQ7 · pith_short_16: JL4PPD362GQ7SI7D · pith_short_8: JL4PPD36

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/JL4PPD362GQ7SI7D74KU3ZKKG7 \
  | 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: 4af8f78f7ed1a1f923e3ff154de54a37cafcbc6420f4f41e84d3bd0e1e3c2434

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "553f6379b437c171b32ef624708dd9d48eba153a9d981b4b9427a5918518252b",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-12-16T08:02:34Z",
    "title_canon_sha256": "bcdce98d4b43e4c370833132bfeeccd23ffd08efeebb46375ed08b982a31eec6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.05081",
    "kind": "arxiv",
    "version": 1
  }
}