Pith Number

pith:62CGOEPJ

pith:2012:62CGOEPJOEQKGNZX6XBKMBBNQV

not attested not anchored not stored refs pending

Concavity of certain matrix trace and norm functions

Fumio Hiai

arxiv:1210.7524 v2 · 2012-10-28 · math.FA · math-ph · math.MP · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{62CGOEPJOEQKGNZX6XBKMBBNQV}

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.

Cited by

2 papers in Pith

Conditions for Large-Sample Majorization of Pairs of Flat States in Terms of $\alpha$-z Relative Entropies

Finite-size quantum key distribution rates from R\'enyi entropies using conic optimization

Receipt and verification

First computed	2026-05-18T03:31:29.295526Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f6846711e97120a33737f5c2a6042d854346ac7c1c395ee89da9b3b48f42e508

Aliases

arxiv: 1210.7524 · arxiv_version: 1210.7524v2 · doi: 10.48550/arxiv.1210.7524 · pith_short_12: 62CGOEPJOEQK · pith_short_16: 62CGOEPJOEQKGNZX · pith_short_8: 62CGOEPJ

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/62CGOEPJOEQKGNZX6XBKMBBNQV \
  | 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: f6846711e97120a33737f5c2a6042d854346ac7c1c395ee89da9b3b48f42e508

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d320d61ae8ea1824f47fe96da453cdc1cd586f714adfd3b3dbc9fd23d31a5de5",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-10-28T23:46:35Z",
    "title_canon_sha256": "2e423cae52fd4c81a33a55674a61f5f6d651f1e669a8ae7d2bc1228824b1926a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.7524",
    "kind": "arxiv",
    "version": 2
  }
}