Pith Number

pith:ECMFQWMD

pith:2013:ECMFQWMDNEU2DHJLKHGYJZQ5Q2

not attested not anchored not stored refs pending

Estimates of essential norms of weighted composition operator from Bloch type spaces to Zygmund type spaces

Yu-Xia Liang, Ze-Hua Zhou

arxiv:1401.0031 v1 · 2013-12-30 · 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{ECMFQWMDNEU2DHJLKHGYJZQ5Q2}

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	2026-05-18T03:03:31.280850Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

20985859836929a19d2b51cd84e61d8691d110e130516f651094e62f12f8545d

Aliases

arxiv: 1401.0031 · arxiv_version: 1401.0031v1 · doi: 10.48550/arxiv.1401.0031 · pith_short_12: ECMFQWMDNEU2 · pith_short_16: ECMFQWMDNEU2DHJL · pith_short_8: ECMFQWMD

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/ECMFQWMDNEU2DHJLKHGYJZQ5Q2 \
  | 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: 20985859836929a19d2b51cd84e61d8691d110e130516f651094e62f12f8545d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6aae560c65a2d52fcc81f1d86fc7803e8d47c3d981415f1bfb9828754c837024",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-12-30T21:51:44Z",
    "title_canon_sha256": "bdc9db22fabe1b8d1d292fdf1b2cf7eedd42901171cc5205db25b9c8d7f3ce58"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.0031",
    "kind": "arxiv",
    "version": 1
  }
}