Pith Number

pith:HFP47IVA

pith:2013:HFP47IVAJ2UVR3BQM2WGFZC7RV

not attested not anchored not stored refs pending

Operator theoretic differences between Hardy and Dirichlet-type spaces

Fernando P\'erez-Gonz\'alez, Jos\'e \'Angel Pel\'aez, Jouni R\"atty\"a

arxiv:1302.2422 v2 · 2013-02-11 · 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{HFP47IVAJ2UVR3BQM2WGFZC7RV}

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	2026-05-18T03:33:51.401872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

395fcfa2a04ea958ec3066ac62e45f8d503b0919fc81bb2c89ac7f6df11beaeb

Aliases

arxiv: 1302.2422 · arxiv_version: 1302.2422v2 · doi: 10.48550/arxiv.1302.2422 · pith_short_12: HFP47IVAJ2UV · pith_short_16: HFP47IVAJ2UVR3BQ · pith_short_8: HFP47IVA

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/HFP47IVAJ2UVR3BQM2WGFZC7RV \
  | 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: 395fcfa2a04ea958ec3066ac62e45f8d503b0919fc81bb2c89ac7f6df11beaeb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0caa8fc350d6c040751ad75827b64ae6d9935a0f59ac7d3e73800f2a555ef70f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-02-11T09:25:26Z",
    "title_canon_sha256": "f6055ab3a34b131b268a95f9c70cbb359c01fea4af719bfb0b71f31ff951276d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.2422",
    "kind": "arxiv",
    "version": 2
  }
}