Pith Number

pith:4XGQJ72Y

pith:2011:4XGQJ72YAEE5KZZVX3Z4LRMVU4

not attested not anchored not stored refs pending

Further development of positive semidefinite solutions of the operator equation $\sum_{j=1}^{n}A^{n-j}XA^{j-1}=B$

Jian Shi, Zongsheng Gao

arxiv:1109.0450 v1 · 2011-09-02 · 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{4XGQJ72YAEE5KZZVX3Z4LRMVU4}

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	2026-05-18T04:14:15.636220Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5cd04ff580109d56735bef3c5c595a73a920a726270e2b07c10d68215f083bb

Aliases

arxiv: 1109.0450 · arxiv_version: 1109.0450v1 · doi: 10.48550/arxiv.1109.0450 · pith_short_12: 4XGQJ72YAEE5 · pith_short_16: 4XGQJ72YAEE5KZZV · pith_short_8: 4XGQJ72Y

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/4XGQJ72YAEE5KZZVX3Z4LRMVU4 \
  | 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: e5cd04ff580109d56735bef3c5c595a73a920a726270e2b07c10d68215f083bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "863a15a715d70fdf3c5ee82100a1a7e40df80d84fab7562e16228f8304c32836",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-09-02T14:13:08Z",
    "title_canon_sha256": "5677b50cce0dcac820239588c64abef25db728ea0465c4d0d51be51f137bd0fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.0450",
    "kind": "arxiv",
    "version": 1
  }
}