Pith Number

pith:52QEE4KL

pith:2016:52QEE4KLMLNIDDHIGWW5RRSDRG

not attested not anchored not stored refs pending

Characterisations of Matrix and Operator-Valued $\Phi$-Entropies, and Operator Efron-Stein Inequalities

Hao-Chung Cheng, Min-Hsiu Hsieh

arxiv:1602.00233 v1 · 2016-01-31 · math-ph · cs.IT · math.IT · math.MP · math.PR · 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{52QEE4KLMLNIDDHIGWW5RRSDRG}

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	2026-05-18T01:07:58.316820Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eea042714b62da818ce835add8c64389890a5fae244c3848069b888f26b6eb73

Aliases

arxiv: 1602.00233 · arxiv_version: 1602.00233v1 · doi: 10.48550/arxiv.1602.00233 · pith_short_12: 52QEE4KLMLNI · pith_short_16: 52QEE4KLMLNIDDHI · pith_short_8: 52QEE4KL

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/52QEE4KLMLNIDDHIGWW5RRSDRG \
  | 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: eea042714b62da818ce835add8c64389890a5fae244c3848069b888f26b6eb73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7ec3249d2ff89d6d8dff2bb8b1f8ca07c3d7059535272770bac3037fa66230f",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "math.MP",
      "math.PR",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-01-31T11:51:34Z",
    "title_canon_sha256": "7650abe706b7b88d0b7918ca5e4cc3b7908ebf110f4f3305dc941f6c447d70ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.00233",
    "kind": "arxiv",
    "version": 1
  }
}