Pith Number

pith:RFN5Y6M4

pith:2012:RFN5Y6M43RIY45GGEORXQPS5EN

not attested not anchored not stored refs pending

Hardy's operator and normability of generalized Lorentz-Marcinkiewicz spaces, with sharp or weakly sharp constant estimation

E.Ostrovsky, L.Sirota

arxiv:1211.6415 v1 · 2012-11-27 · 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{RFN5Y6M43RIY45GGEORXQPS5EN}

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	2026-05-18T03:39:51.874712Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

895bdc799cdc518e74c623a3783e5d2352f5cd6b31379e28fd66b5a6cdc7fbeb

Aliases

arxiv: 1211.6415 · arxiv_version: 1211.6415v1 · doi: 10.48550/arxiv.1211.6415 · pith_short_12: RFN5Y6M43RIY · pith_short_16: RFN5Y6M43RIY45GG · pith_short_8: RFN5Y6M4

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/RFN5Y6M43RIY45GGEORXQPS5EN \
  | 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: 895bdc799cdc518e74c623a3783e5d2352f5cd6b31379e28fd66b5a6cdc7fbeb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c9c355e0718947b310e7f75c7474dd43bfbf1ba0f6dcfc592f852d8f6f988321",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-11-27T20:36:57Z",
    "title_canon_sha256": "2284048741f15d3b0fce8b94deecb997c05b66f973933a61f12d2aa082f82a7d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.6415",
    "kind": "arxiv",
    "version": 1
  }
}