Pith Number

pith:BTNWES6V

pith:2019:BTNWES6VPPZPNVJS6CU6H5XMEN

not attested not anchored not stored refs pending

A chain rule for the quantum relative entropy

David Sutter, Kun Fang, Omar Fawzi, Renato Renner

arxiv:1909.05826 v1 · 2019-09-12 · quant-ph · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BTNWES6VPPZPNVJS6CU6H5XMEN}

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	2026-07-05T00:48:44.298194Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0cdb624bd57bf2f6d532f0a9e3f6ec236ba5ab83f9271e7433855890de1f6e55

Aliases

arxiv: 1909.05826 · arxiv_version: 1909.05826v1 · doi: 10.48550/arxiv.1909.05826 · pith_short_12: BTNWES6VPPZP · pith_short_16: BTNWES6VPPZPNVJS · pith_short_8: BTNWES6V

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/BTNWES6VPPZPNVJS6CU6H5XMEN \
  | 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: 0cdb624bd57bf2f6d532f0a9e3f6ec236ba5ab83f9271e7433855890de1f6e55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41d0f696435f5ad7267f5a6e51ad7091b071cb8f1b1ca552396b2b9a600f0521",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2019-09-12T17:32:26Z",
    "title_canon_sha256": "896a28058c35e2345513f3031e496ddfe31025f68e7655a18d79528793e5480c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.05826",
    "kind": "arxiv",
    "version": 1
  }
}