Pith Number

pith:Z24W7EKO

pith:2012:Z24W7EKOQPXZTMUIPGES4IRMVZ

not attested not anchored not stored refs pending

A multiplicative property characterizes quasinormal composition operators in $L^2$-spaces

Il Bong Jung, Jan Stochel, Piotr Budzynski, Zenon Jan Jablonski

arxiv:1207.2638 v1 · 2012-07-11 · 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{Z24W7EKOQPXZTMUIPGES4IRMVZ}

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	2026-05-18T03:10:37.319041Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ceb96f914e83ef99b28879892e222cae45856fbcd5159e7af1e880435aa83db0

Aliases

arxiv: 1207.2638 · arxiv_version: 1207.2638v1 · doi: 10.48550/arxiv.1207.2638 · pith_short_12: Z24W7EKOQPXZ · pith_short_16: Z24W7EKOQPXZTMUI · pith_short_8: Z24W7EKO

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/Z24W7EKOQPXZTMUIPGES4IRMVZ \
  | 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: ceb96f914e83ef99b28879892e222cae45856fbcd5159e7af1e880435aa83db0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14c6f87010e55ff1c0583f2e14900462e55424d7540f83ec9865aa61d15f0f7c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-07-11T13:40:02Z",
    "title_canon_sha256": "0bfeaab8ec919b66819099e332c6d0e5befbc4f0eea09fd159196e66134786e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.2638",
    "kind": "arxiv",
    "version": 1
  }
}