Pith Number

pith:FXL7A6P6

pith:2013:FXL7A6P6AZH72Y2PYZFJHEGZIA

not attested not anchored not stored refs pending

Cesaro-Hardy operators on bilateral grand Lebesgue spaces

E.Ostrovsky, L.Sirota

arxiv:1307.5481 v1 · 2013-07-20 · 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{FXL7A6P6AZH72Y2PYZFJHEGZIA}

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	2026-05-18T03:17:55.590590Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2dd7f079fe064ffd634fc64a9390d9403bcb48f9ba7bc28f906ff9fe4c7589f8

Aliases

arxiv: 1307.5481 · arxiv_version: 1307.5481v1 · doi: 10.48550/arxiv.1307.5481 · pith_short_12: FXL7A6P6AZH7 · pith_short_16: FXL7A6P6AZH72Y2P · pith_short_8: FXL7A6P6

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/FXL7A6P6AZH72Y2PYZFJHEGZIA \
  | 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: 2dd7f079fe064ffd634fc64a9390d9403bcb48f9ba7bc28f906ff9fe4c7589f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "32838eb543e34c7f8696c3417505b99d3b8d144c7193ab44b7a260c608284af6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-07-20T23:57:57Z",
    "title_canon_sha256": "1e8a49e5136e7e220609d485922a8cfeb60ff5b086bfc5ab0c8fcc29860c111c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.5481",
    "kind": "arxiv",
    "version": 1
  }
}