Pith Number

pith:UTZ5V76Q

pith:2016:UTZ5V76QYFVAQ3WRO64XGNCVVL

not attested not anchored not stored refs pending

Sharp value for the norm of composition and multiplicative operators between two different Grand Lebesgue spaces

E.Ostrovsky, L.Sirota

arxiv:1608.03317 v1 · 2016-08-11 · 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{UTZ5V76QYFVAQ3WRO64XGNCVVL}

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	2026-05-18T01:09:29.201761Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4f3daffd0c16a086ed177b9733455aaf8dff45f8e4f22897bfdaeb50ceb4d91

Aliases

arxiv: 1608.03317 · arxiv_version: 1608.03317v1 · doi: 10.48550/arxiv.1608.03317 · pith_short_12: UTZ5V76QYFVA · pith_short_16: UTZ5V76QYFVAQ3WR · pith_short_8: UTZ5V76Q

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/UTZ5V76QYFVAQ3WRO64XGNCVVL \
  | 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: a4f3daffd0c16a086ed177b9733455aaf8dff45f8e4f22897bfdaeb50ceb4d91

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3c6b4922082a66529a901611a2c715d259a1052809899791d2fbc186ebbd87d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-08-11T00:16:13Z",
    "title_canon_sha256": "c21ff4fd380e2c08eec080b21d4799b993d1eaff061c937d00cc3a0f20a46a62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.03317",
    "kind": "arxiv",
    "version": 1
  }
}