Pith Number

pith:4UDY52K5

pith:2026:4UDY52K5FBI7R4CQTLQWXR7TFE

not attested not anchored not stored refs pending

Counter-examples for Tensorization Property of Strong Data Processing Inequality for Quantum Divergences

Yu Cao

arxiv:2608.13204 v1 · 2026-08-13 · 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{4UDY52K5FBI7R4CQTLQWXR7TFE}

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	2026-08-14T01:00:39.457269Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5078ee95d2851f8f0509ae16bc7f3291a063dd9e64b8c0879ab488cd269bd9b

Aliases

arxiv: 2608.13204 · arxiv_version: 2608.13204v1 · doi: 10.48550/arxiv.2608.13204 · pith_short_12: 4UDY52K5FBI7 · pith_short_16: 4UDY52K5FBI7R4CQ · pith_short_8: 4UDY52K5

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/4UDY52K5FBI7R4CQTLQWXR7TFE \
  | 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: e5078ee95d2851f8f0509ae16bc7f3291a063dd9e64b8c0879ab488cd269bd9b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "70f101950d9ed6fb68f283685f8614940f462b27a77fb1c85973e73c94520cfc",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-08-13T13:07:36Z",
    "title_canon_sha256": "88cff95f2f2402694c2eab650cad6b0f70e0ba910b28033e0924b89bec915299"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.13204",
    "kind": "arxiv",
    "version": 1
  }
}