Pith Number

pith:CK6QYHZ5

pith:2015:CK6QYHZ5DAJD6LFIAO6DWQ4PQG

not attested not anchored not stored refs pending

Invariance of Bipartite Separability and PPT-Probabilities over Casimir Invariants of Reduced States

Paul B. Slater

arxiv:1512.07210 v5 · 2015-12-22 · quant-ph · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CK6QYHZ5DAJD6LFIAO6DWQ4PQG}

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	2026-05-18T01:12:59.651509Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12bd0c1f3d18123f2ca803bc3b438f81ad17140c56f68dd84cef6cb47f14532d

Aliases

arxiv: 1512.07210 · arxiv_version: 1512.07210v5 · doi: 10.48550/arxiv.1512.07210 · pith_short_12: CK6QYHZ5DAJD · pith_short_16: CK6QYHZ5DAJD6LFI · pith_short_8: CK6QYHZ5

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/CK6QYHZ5DAJD6LFIAO6DWQ4PQG \
  | 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: 12bd0c1f3d18123f2ca803bc3b438f81ad17140c56f68dd84cef6cb47f14532d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c78e863f01ece1ab8a647b83c93274221a9b7e1ddcef17976191d9d4feace22d",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2015-12-22T19:31:40Z",
    "title_canon_sha256": "1556e9060587f66faa6e52fd1221a01b20c1c41d644ce85d9f256043356087e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.07210",
    "kind": "arxiv",
    "version": 5
  }
}