Pith Number

pith:VVGBBEY4

pith:2014:VVGBBEY46P7NJUFW3TAWMALKTZ

not attested not anchored not stored refs pending

Ranks of Commutators and Generalized Semicommutators of Quasihomogeneous Toeplitz Operators

Xing-Tang Dong, Ze-Hua Zhou

arxiv:1411.0213 v3 · 2014-11-02 · 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{VVGBBEY46P7NJUFW3TAWMALKTZ}

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	2026-05-18T01:20:59.349077Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad4c10931cf3fed4d0b6dcc166016a9e51768542aa5becc0a900bbe222364486

Aliases

arxiv: 1411.0213 · arxiv_version: 1411.0213v3 · doi: 10.48550/arxiv.1411.0213 · pith_short_12: VVGBBEY46P7N · pith_short_16: VVGBBEY46P7NJUFW · pith_short_8: VVGBBEY4

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/VVGBBEY46P7NJUFW3TAWMALKTZ \
  | 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: ad4c10931cf3fed4d0b6dcc166016a9e51768542aa5becc0a900bbe222364486

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c1b2dee78a7a54e4f15fc16138421bd4c9e796b64a2058f1c7c0b0f9ab4fdd6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-11-02T07:25:21Z",
    "title_canon_sha256": "4bcafe7068fe496618433c1619044434cb4b089c3099952407593b1278931704"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.0213",
    "kind": "arxiv",
    "version": 3
  }
}