Pith Number

pith:WESSAVEK

pith:2015:WESSAVEKXU4IAA7D3EVRXUWQBD

not attested not anchored not stored refs pending

Exponential Decay of Matrix $\Phi$-Entropies on Markov Semigroups with Applications to Dynamical Evolutions of Quantum Ensembles

Hao-Chung Cheng, Marco Tomamichel, Min-Hsiu Hsieh

arxiv:1511.02627 v1 · 2015-11-09 · quant-ph · cs.IT · math-ph · math.IT · math.MP · math.OA · 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{WESSAVEKXU4IAA7D3EVRXUWQBD}

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	2026-05-17T23:47:08.885685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b12520548abd388003e3d92b1bd2d008c283c4ea55b37a532bb97399ff02aab8

Aliases

arxiv: 1511.02627 · arxiv_version: 1511.02627v1 · doi: 10.48550/arxiv.1511.02627 · pith_short_12: WESSAVEKXU4I · pith_short_16: WESSAVEKXU4IAA7D · pith_short_8: WESSAVEK

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/WESSAVEKXU4IAA7D3EVRXUWQBD \
  | 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: b12520548abd388003e3d92b1bd2d008c283c4ea55b37a532bb97399ff02aab8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13300f290d54c468975adde682416997c53acaef407fb4d3a08b3200375a727b",
    "cross_cats_sorted": [
      "cs.IT",
      "math-ph",
      "math.IT",
      "math.MP",
      "math.OA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2015-11-09T10:47:02Z",
    "title_canon_sha256": "f2d2e07f83334b05bf8133cca21d23f54e66612adb46cce9c058678cf7bb14e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.02627",
    "kind": "arxiv",
    "version": 1
  }
}