Pith Number

pith:62Z4NQZP

pith:2012:62Z4NQZPVGDLOTFKDINDHFQLVX

not attested not anchored not stored refs pending

Tensor Products of Random Unitary Matrices

Karol Zyczkowski, Marek Kus, Marek Smaczynski, Ofer Zeitouni, Tomasz Tkocz

arxiv:1203.3818 v1 · 2012-03-16 · math.PR · 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{62Z4NQZPVGDLOTFKDINDHFQLVX}

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	2026-05-18T03:33:26.189309Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f6b3c6c32fa986b74caa1a1a33960badff9e7119646068d91429aba8ca15482a

Aliases

arxiv: 1203.3818 · arxiv_version: 1203.3818v1 · doi: 10.48550/arxiv.1203.3818 · pith_short_12: 62Z4NQZPVGDL · pith_short_16: 62Z4NQZPVGDLOTFK · pith_short_8: 62Z4NQZP

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/62Z4NQZPVGDLOTFKDINDHFQLVX \
  | 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: f6b3c6c32fa986b74caa1a1a33960badff9e7119646068d91429aba8ca15482a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d302843e7aeca92706da8a94c8f66e24a688e145856d9d27ef11ac6965a54c30",
    "cross_cats_sorted": [
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-03-16T21:03:25Z",
    "title_canon_sha256": "37d0e8167bb8752ca778ed690aa132181d66725efa47faa8b39b1b585e303023"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.3818",
    "kind": "arxiv",
    "version": 1
  }
}