Pith Number

pith:O2KFT37Q

pith:2025:O2KFT37QYATLJ7TBNJOBXT263V

not attested not anchored not stored refs pending

Sharp estimates of quantum covering problems via a novel trace inequality

Christoph Hirche, Hao-Chung Cheng, Hao-Wei Huang, Li Gao, Po-Chieh Liu

arxiv:2507.07961 v1 · 2025-07-10 · quant-ph · cs.IT · math.FA · math.IT · 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{O2KFT37QYATLJ7TBNJOBXT263V}

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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

4 papers in Pith

Smoothing Exponents and Decoupling in Semifinite von Neumann Algebras

Quantum Noncommutativity Uniquely Determines Relative Entropy

Optimal Trace Inequalities for Single-Shot Quantum Information

Receipt and verification

First computed	2026-07-05T11:35:07.626165Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

769459eff0c026b4fe616a5c1bcf5edd48116e28eeb58896cb189eea807774f8

Aliases

arxiv: 2507.07961 · arxiv_version: 2507.07961v1 · doi: 10.48550/arxiv.2507.07961 · pith_short_12: O2KFT37QYATL · pith_short_16: O2KFT37QYATLJ7TB · pith_short_8: O2KFT37Q

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/O2KFT37QYATLJ7TBNJOBXT263V \
  | 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: 769459eff0c026b4fe616a5c1bcf5edd48116e28eeb58896cb189eea807774f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f430d5d3c85ebe0472ddd8371bcec831319dd22cff77f67dd0137e27bc983e9",
    "cross_cats_sorted": [
      "cs.IT",
      "math.FA",
      "math.IT",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-07-10T17:41:50Z",
    "title_canon_sha256": "da4940a03a1ed0aed4211ee441cc9118aa26c057de137f4ce94ad64e48837db0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.07961",
    "kind": "arxiv",
    "version": 1
  }
}