Pith Number

pith:BKX3TOLK

pith:2012:BKX3TOLKIKQUU3LUDJH6IH3RCL

not attested not anchored not stored refs pending

Low entropy output states for products of random unitary channels

Benoit Collins, Ion Nechita, Motohisa Fukuda

arxiv:1208.1449 v1 · 2012-08-07 · math-ph · math.MP · 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{BKX3TOLKIKQUU3LUDJH6IH3RCL}

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	2026-05-17T23:52:44.920518Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0aafb9b96a42a14a6d741a4fe41f7112c33b8f7d71d6d8038b2285504524d0d2

Aliases

arxiv: 1208.1449 · arxiv_version: 1208.1449v1 · doi: 10.48550/arxiv.1208.1449 · pith_short_12: BKX3TOLKIKQU · pith_short_16: BKX3TOLKIKQUU3LU · pith_short_8: BKX3TOLK

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/BKX3TOLKIKQUU3LUDJH6IH3RCL \
  | 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: 0aafb9b96a42a14a6d741a4fe41f7112c33b8f7d71d6d8038b2285504524d0d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b02d17bda0bcabf8c33b3e7c8a52785836f84de8c711e75067a3de677256d0bb",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-08-07T15:46:16Z",
    "title_canon_sha256": "268236757d5c6e18bd6ea612cd7d4e846fb3cff00042621b6f9f56b65e01235a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.1449",
    "kind": "arxiv",
    "version": 1
  }
}