Pith Number

pith:H2CU4MOR

pith:2015:H2CU4MORUV2A4ICLWK6LUQ5QYE

not attested not anchored not stored refs pending

Strengthened Monotonicity of Relative Entropy via Pinched Petz Recovery Map

Aram W. Harrow, David Sutter, Marco Tomamichel

arxiv:1507.00303 v3 · 2015-07-01 · 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{H2CU4MORUV2A4ICLWK6LUQ5QYE}

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	2026-05-18T01:15:58.515735Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e854e31d1a5740e204bb2bcba43b0c1303dec7146f8abb0aed0d74fa6b933e0

Aliases

arxiv: 1507.00303 · arxiv_version: 1507.00303v3 · doi: 10.48550/arxiv.1507.00303 · pith_short_12: H2CU4MORUV2A · pith_short_16: H2CU4MORUV2A4ICL · pith_short_8: H2CU4MOR

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/H2CU4MORUV2A4ICLWK6LUQ5QYE \
  | 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: 3e854e31d1a5740e204bb2bcba43b0c1303dec7146f8abb0aed0d74fa6b933e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3694418476d3a3253d669d1b28f929bdae98d93fcfbce724db4016621934e31c",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2015-07-01T18:05:39Z",
    "title_canon_sha256": "7fe2cf5627194a6aed5abd9b7e2d86a49f4e006cd6e5bad86acdc7e05972acf5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.00303",
    "kind": "arxiv",
    "version": 3
  }
}