Pith Number

pith:EM3YYJGN

pith:2015:EM3YYJGNWPAK6DVZSUD72ZVBD7

not attested not anchored not stored refs pending

Monotonicity of the Quantum Relative Entropy Under Positive Maps

Alexander M\"uller-Hermes, David Reeb

arxiv:1512.06117 v3 · 2015-12-18 · quant-ph · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EM3YYJGNWPAK6DVZSUD72ZVBD7}

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.

Cited by

1 paper in Pith

Sufficiency and Petz recovery for positive maps

Receipt and verification

First computed	2026-05-18T00:46:04.569248Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

23378c24cdb3c0af0eb99507fd66a11fd7fe920efa5d7482fe5a3bb3fe04e597

Aliases

arxiv: 1512.06117 · arxiv_version: 1512.06117v3 · doi: 10.48550/arxiv.1512.06117 · pith_short_12: EM3YYJGNWPAK · pith_short_16: EM3YYJGNWPAK6DVZ · pith_short_8: EM3YYJGN

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/EM3YYJGNWPAK6DVZSUD72ZVBD7 \
  | 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: 23378c24cdb3c0af0eb99507fd66a11fd7fe920efa5d7482fe5a3bb3fe04e597

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b01c786c4347d95a268e2366f7d9b081ded4c342b620e0cbe4d67589ebb3620b",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2015-12-18T20:58:27Z",
    "title_canon_sha256": "cbaa11aa2689123d514587171aa5be5401a70c8fd45d976569fec657a37935a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06117",
    "kind": "arxiv",
    "version": 3
  }
}