Pith Number

pith:5W7U4LVW

pith:2025:5W7U4LVWSOIMEZFHT3OUUUH7HX

not attested not anchored not stored refs pending

Error Exponents for Quantum Packing Problems via An Operator Layer Cake Theorem

Hao-Chung Cheng, Po-Chieh Liu

arxiv:2507.06232 v4 · 2025-07-08 · quant-ph · cs.IT · math-ph · math.FA · math.IT · 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{5W7U4LVWSOIMEZFHT3OUUUH7HX}

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

4 papers in Pith

Sufficiency and Petz recovery for positive maps

Optimal Trace Inequalities for Single-Shot Quantum Information

Sufficiency and Petz recovery for positive maps

Optimal Trace Inequalities for Single-Shot Quantum Information

Receipt and verification

First computed	2026-06-05T01:15:14.749086Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

edbf4e2eb69390c264a79edd4a50ff3de1b076ad64326e5b4f807fb6739e2755

Aliases

arxiv: 2507.06232 · arxiv_version: 2507.06232v4 · doi: 10.48550/arxiv.2507.06232 · pith_short_12: 5W7U4LVWSOIM · pith_short_16: 5W7U4LVWSOIMEZFH · pith_short_8: 5W7U4LVW

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/5W7U4LVWSOIMEZFHT3OUUUH7HX \
  | 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: edbf4e2eb69390c264a79edd4a50ff3de1b076ad64326e5b4f807fb6739e2755

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2ec011bcb81aa2df72a32c356b6bf223150ca0f7630bd08be8704c8ea9afae0",
    "cross_cats_sorted": [
      "cs.IT",
      "math-ph",
      "math.FA",
      "math.IT",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-07-08T17:59:58Z",
    "title_canon_sha256": "13cee88fc7aad923ee63ff462e99b9d0e9719b732eedfc588fd6fd21755c2ea5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.06232",
    "kind": "arxiv",
    "version": 4
  }
}