Pith Number

pith:A4S2GLZJ

pith:2010:A4S2GLZJM6ZU4ZRUSNV2OIPR5F

not attested not anchored not stored refs pending

Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels

Benoit Collins, Ion Nechita

arxiv:1006.3247 v1 · 2010-06-16 · quant-ph · 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{A4S2GLZJM6ZU4ZRUSNV2OIPR5F}

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	2026-05-18T04:02:13.753962Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0725a32f2967b34e6634936ba721f1e969ae3030772c437f44243425369ff077

Aliases

arxiv: 1006.3247 · arxiv_version: 1006.3247v1 · doi: 10.48550/arxiv.1006.3247 · pith_short_12: A4S2GLZJM6ZU · pith_short_16: A4S2GLZJM6ZU4ZRU · pith_short_8: A4S2GLZJ

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/A4S2GLZJM6ZU4ZRUSNV2OIPR5F \
  | 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: 0725a32f2967b34e6634936ba721f1e969ae3030772c437f44243425369ff077

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5e4208c783667f65769b2c9e151eae804502982915086f5cae79149c43fad30",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2010-06-16T15:29:03Z",
    "title_canon_sha256": "6d65e03f84c874cca1b22778b68211880a2adc09be1f05afd0997e58925d3fec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.3247",
    "kind": "arxiv",
    "version": 1
  }
}