Pith Number

pith:AKVB4YFT

pith:2002:AKVB4YFTXJU57ZUDCDOOQFSQRZ

not attested not anchored not stored refs pending

The polynomial invariants of four qubits

J.-G. Luque, J.-Y. Thibon

arxiv:quant-ph/0212069 v6 · 2002-12-11 · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AKVB4YFTXJU57ZUDCDOOQFSQRZ}

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.

Cited by

2 papers in Pith

Separability from Multipartite Measures

Receipt and verification

First computed	2026-05-18T03:34:00.399369Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02aa1e60b3ba69dfe68310dce816508e4cb047e33a62165d2b5b790eba011c6d

Aliases

arxiv: quant-ph/0212069 · arxiv_version: quant-ph/0212069v6 · doi: 10.48550/arxiv.quant-ph/0212069 · pith_short_12: AKVB4YFTXJU5 · pith_short_16: AKVB4YFTXJU57ZUD · pith_short_8: AKVB4YFT

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/AKVB4YFTXJU57ZUDCDOOQFSQRZ \
  | 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: 02aa1e60b3ba69dfe68310dce816508e4cb047e33a62165d2b5b790eba011c6d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af7f00d7e44c94431abc1405acff3a3aab58b88e092a9bde0140e3c9b90a7ed9",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2002-12-11T15:17:11Z",
    "title_canon_sha256": "5fabd9ef81d467239f88de92265a43bf4c6f9c438f8f8a9416d1f6557c66a3c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0212069",
    "kind": "arxiv",
    "version": 6
  }
}