Pith Number

pith:ZTCHRUIP

pith:2015:ZTCHRUIPDIFLURP4DYVLDWFF7I

not attested not anchored not stored refs pending

Lieb's concavity theorem, matrix geometric means, and semidefinite optimization

Hamza Fawzi, James Saunderson

arxiv:1512.03401 v3 · 2015-12-10 · math.OC · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZTCHRUIPDIFLURP4DYVLDWFF7I}

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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

Semidefinite optimization of the quantum relative entropy of channels

Receipt and verification

First computed	2026-07-05T00:54:26.207715Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ccc478d10f1a0aba45fc1e2ab1d8a5fa3e5e488afee2346b48414d3d2313c0b4

Aliases

arxiv: 1512.03401 · arxiv_version: 1512.03401v3 · doi: 10.48550/arxiv.1512.03401 · pith_short_12: ZTCHRUIPDIFL · pith_short_16: ZTCHRUIPDIFLURP4 · pith_short_8: ZTCHRUIP

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/ZTCHRUIPDIFLURP4DYVLDWFF7I \
  | 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: ccc478d10f1a0aba45fc1e2ab1d8a5fa3e5e488afee2346b48414d3d2313c0b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1539ee1116ad01a5cb2f82d33b5d0558dc80f6a654b808ce102bcf73f716fea3",
    "cross_cats_sorted": [
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2015-12-10T20:27:51Z",
    "title_canon_sha256": "1bf907930ca2ad07898b491e4183b34dc2c0bb9dcb7e48ee1efbd50ea6eebabe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.03401",
    "kind": "arxiv",
    "version": 3
  }
}