Pith Number

pith:7MHR25SV

pith:2013:7MHR25SVGCKKKOGA3AEBEOREWD

not attested not anchored not stored refs pending

p-Summing Multiplication Operators, dyadic Hardy Spaces and atomic Decomposition

Johanna Penteker, Paul F.X. M\"uller

arxiv:1310.4312 v4 · 2013-10-16 · 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{7MHR25SVGCKKKOGA3AEBEOREWD}

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	2026-05-18T01:30:15.714167Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb0f1d76553094a538c0d808123a24b0f66c3f6bd1657462ae744e072ce27800

Aliases

arxiv: 1310.4312 · arxiv_version: 1310.4312v4 · doi: 10.48550/arxiv.1310.4312 · pith_short_12: 7MHR25SVGCKK · pith_short_16: 7MHR25SVGCKKKOGA · pith_short_8: 7MHR25SV

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/7MHR25SVGCKKKOGA3AEBEOREWD \
  | 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: fb0f1d76553094a538c0d808123a24b0f66c3f6bd1657462ae744e072ce27800

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0de3f7ec2abfba0aad69d2eba2db71800cbb0a6c4f4dc5495da1e296cc9e9a60",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-10-16T09:56:28Z",
    "title_canon_sha256": "d8c0e46bf99ec2380afcf4988dea2d44014863fec466ae2075b889d113ebd1d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.4312",
    "kind": "arxiv",
    "version": 4
  }
}