Pith Number

pith:TCGKDEPC

pith:2017:TCGKDEPCNJFAPNBOXMUVMW4RXF

not attested not anchored not stored refs pending

Weighted Composition Operators Acting on Harmonic Hardy Spaces

Congwen Liu, Lifang Zhou, Pengyan Hu, Taishun Liu

arxiv:1708.05225 v1 · 2017-08-17 · math.CV · 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{TCGKDEPCNJFAPNBOXMUVMW4RXF}

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	2026-05-18T00:37:53.538123Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

988ca191e26a4a07b42ebb29565b91b97cc877c031bb403ff486b7fda41a48e3

Aliases

arxiv: 1708.05225 · arxiv_version: 1708.05225v1 · doi: 10.48550/arxiv.1708.05225 · pith_short_12: TCGKDEPCNJFA · pith_short_16: TCGKDEPCNJFAPNBO · pith_short_8: TCGKDEPC

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/TCGKDEPCNJFAPNBOXMUVMW4RXF \
  | 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: 988ca191e26a4a07b42ebb29565b91b97cc877c031bb403ff486b7fda41a48e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87569c4222969cf2c6dd5e8322035cf97ba36a041c9eddf6cf34665e90cef2be",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2017-08-17T12:16:51Z",
    "title_canon_sha256": "cec7a24ed617ac3ee508f1b3c763ae77128f38d5da7332565d73957db161bd2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.05225",
    "kind": "arxiv",
    "version": 1
  }
}