Pith Number

pith:MTUK3MLI

pith:2013:MTUK3MLIZI32HQAVX5UCDTQA7A

not attested not anchored not stored refs pending

Generalized Shemesh criterion, common invariant subspaces and irreducible completely positive superoperators

Andrzej Jamio{\l}kowski, Grzegorz Pastuszak

arxiv:1306.0083 v1 · 2013-06-01 · math.QA · 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{MTUK3MLIZI32HQAVX5UCDTQA7A}

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	2026-05-18T03:21:56.190172Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

64e8adb168ca37a3c015bf6821ce00f812956cb5b5345bdff54a23bf2b819f5a

Aliases

arxiv: 1306.0083 · arxiv_version: 1306.0083v1 · doi: 10.48550/arxiv.1306.0083 · pith_short_12: MTUK3MLIZI32 · pith_short_16: MTUK3MLIZI32HQAV · pith_short_8: MTUK3MLI

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/MTUK3MLIZI32HQAVX5UCDTQA7A \
  | 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: 64e8adb168ca37a3c015bf6821ce00f812956cb5b5345bdff54a23bf2b819f5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09762a9e4f3884f8c4e349263c4a54670d777f89cfe4b92107b9e87093222f55",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2013-06-01T07:21:30Z",
    "title_canon_sha256": "cecb4d9ebea5e7085f9fdb90b53af519a8f02897974ba6bb43855d66b6f61a1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0083",
    "kind": "arxiv",
    "version": 1
  }
}