Pith Number

pith:MFID7MFS

pith:2007:MFID7MFSBJ2O2TRNL5F2C62RUM

not attested not anchored not stored refs pending

Essential Norms of Weighted Composition Operators between Hardy Spaces in the unit Ball

Ze-Hua Zhou, Zhong-Shan Fang

arxiv:0709.1431 v1 · 2007-09-10 · math.FA · math.CV

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MFID7MFSBJ2O2TRNL5F2C62RUM}

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	2026-05-18T03:03:55.616304Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61503fb0b20a74ed4e2d5f4ba17b51a3239ee096707df7deee1f11849bf8076d

Aliases

arxiv: 0709.1431 · arxiv_version: 0709.1431v1 · doi: 10.48550/arxiv.0709.1431 · pith_short_12: MFID7MFSBJ2O · pith_short_16: MFID7MFSBJ2O2TRN · pith_short_8: MFID7MFS

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/MFID7MFSBJ2O2TRNL5F2C62RUM \
  | 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: 61503fb0b20a74ed4e2d5f4ba17b51a3239ee096707df7deee1f11849bf8076d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d6e546f58edf6ddbae743f23835871bd0ea3dae7c1ddfb15aee218bdfb77fe0",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2007-09-10T16:13:00Z",
    "title_canon_sha256": "655f55f40543b66cc91e860aef70a0eda33aa8315c9800cfc604393ac684b04a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.1431",
    "kind": "arxiv",
    "version": 1
  }
}