Pith Number

pith:HKDEM2R6

pith:2025:HKDEM2R6VEST3GQXOWVLV5FM5Y

not attested not anchored not stored refs pending

Additivity and chain rules for quantum entropies via multi-index Schatten norms

Cambyse Rouz\'e, Jan Kochanowski, Omar Fawzi, Thomas Van Himbeeck

arxiv:2502.01611 v3 · 2025-02-03 · quant-ph · math-ph · math.FA · math.MP · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HKDEM2R6VEST3GQXOWVLV5FM5Y}

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

Rigorous Security Proofs for Practical Quantum Key Distribution

Receipt and verification

First computed	2026-06-11T01:09:11.220691Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a86466a3ea9253d9a1775aabaf4acee0a80f501cadc81f3cca6bd78bc96d33a

Aliases

arxiv: 2502.01611 · arxiv_version: 2502.01611v3 · doi: 10.48550/arxiv.2502.01611 · pith_short_12: HKDEM2R6VEST · pith_short_16: HKDEM2R6VEST3GQX · pith_short_8: HKDEM2R6

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/HKDEM2R6VEST3GQXOWVLV5FM5Y \
  | 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: 3a86466a3ea9253d9a1775aabaf4acee0a80f501cadc81f3cca6bd78bc96d33a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b11e97edfe51b0418656e278aea9aec1d8959d99699161b7fbc1eab348a1cd9c",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP",
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-02-03T18:44:59Z",
    "title_canon_sha256": "f2e0887651d76f7b9f4802545bf4a3442fd429086d6b7c914d08a7f3180fc3f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.01611",
    "kind": "arxiv",
    "version": 3
  }
}