Pith Number

pith:DQENWDCI

pith:2013:DQENWDCI6YMOWHXD56STA5OGAJ

not attested not anchored not stored refs pending

Moore-Penrose Invertibility of Differences and Products of Projections in Rings with Involution

Jianlong Chen, Long Wang, Shuangshuang Zhang, Xiaoxiang Zhang

arxiv:1307.4142 v1 · 2013-07-16 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DQENWDCI6YMOWHXD56STA5OGAJ}

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	2026-05-18T03:18:19.529542Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c08db0c48f618eb1ee3efa53075c6025bb67adaa51b8769ec47ce73ed287793

Aliases

arxiv: 1307.4142 · arxiv_version: 1307.4142v1 · doi: 10.48550/arxiv.1307.4142 · pith_short_12: DQENWDCI6YMO · pith_short_16: DQENWDCI6YMOWHXD · pith_short_8: DQENWDCI

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/DQENWDCI6YMOWHXD56STA5OGAJ \
  | 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: 1c08db0c48f618eb1ee3efa53075c6025bb67adaa51b8769ec47ce73ed287793

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4555db628ac16ac3cd966337eabde1e6ef377a154b854bf6bcb9ade88a1fe6b5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2013-07-16T01:36:37Z",
    "title_canon_sha256": "6301884f76f2386f534f30ef4eba8519fc033bf375a3af3d7e95bd1e1e2cfa15"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.4142",
    "kind": "arxiv",
    "version": 1
  }
}