Pith Number

pith:ZSYXJCNL

pith:2006:ZSYXJCNLDH7775DW4FD43VYVAZ

not attested not anchored not stored refs pending

Linear dynamical entropy and free-independence for quantized maps on the torus

Monika Pogorzelska, Robert Alicki

arxiv:quant-ph/0611092 v1 · 2006-11-08 · 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{ZSYXJCNLDH7775DW4FD43VYVAZ}

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	2026-05-18T01:37:53.908705Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ccb17489ab19fffff476e147cdd715065de963f0ba56e022b808e3edf45f7585

Aliases

arxiv: quant-ph/0611092 · arxiv_version: quant-ph/0611092v1 · doi: 10.48550/arxiv.quant-ph/0611092 · pith_short_12: ZSYXJCNLDH77 · pith_short_16: ZSYXJCNLDH7775DW · pith_short_8: ZSYXJCNL

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/ZSYXJCNLDH7775DW4FD43VYVAZ \
  | 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: ccb17489ab19fffff476e147cdd715065de963f0ba56e022b808e3edf45f7585

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf4b06646030531269cc7a03b600a29bcc6c7da5b020a5489c8b2516acbb3f24",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2006-11-08T18:04:18Z",
    "title_canon_sha256": "f87c79ccf14b8c71edae0ab9fa32d13d71ba19584d3cc413aaff97d85f7db43c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0611092",
    "kind": "arxiv",
    "version": 1
  }
}