Pith Number

pith:4DUDRAMA

pith:2019:4DUDRAMABTCDL2HDBSS747VCX4

not attested not anchored not stored refs pending

Lyapunov exponents for Quantum Channels: an entropy formula and generic properties

Artur O. Lopes, Jader E. Brasil, Josue Knorst

arxiv:1908.08942 v3 · 2019-08-22 · math.DS · 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{4DUDRAMABTCDL2HDBSS747VCX4}

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	2026-07-05T03:14:31.525841Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0e83881800cc435e8e30ca5fe7ea2bf2f98bba0d43e697fb2b050f19c1b9497

Aliases

arxiv: 1908.08942 · arxiv_version: 1908.08942v3 · doi: 10.48550/arxiv.1908.08942 · pith_short_12: 4DUDRAMABTCD · pith_short_16: 4DUDRAMABTCDL2HD · pith_short_8: 4DUDRAMA

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/4DUDRAMABTCDL2HDBSS747VCX4 \
  | 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: e0e83881800cc435e8e30ca5fe7ea2bf2f98bba0d43e697fb2b050f19c1b9497

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13246d76d83dc6bc23ea24a114dcd960a1f9374d8a638fd7405e351fec335766",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2019-08-22T23:14:50Z",
    "title_canon_sha256": "9547182a6bd695338fdb7d36aaa7ad1417147039ed15bdb89e634b2ab9c9651b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.08942",
    "kind": "arxiv",
    "version": 3
  }
}