Pith Number

pith:ZKQJ7WUK

pith:2011:ZKQJ7WUKTY75JEWWW46MMM57PM

not attested not anchored not stored refs pending

Necessary and sufficient condition for saturating the upper bound of quantum discord

Xiaoguang Wang, Xiao-Ming Lu, Yongming Li, Zhengjun Xi

arxiv:1111.3837 v4 · 2011-11-16 · quant-ph · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZKQJ7WUKTY75JEWWW46MMM57PM}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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

Entanglement inequalities, black holes and the architecture of typical states

Receipt and verification

First computed	2026-05-18T01:59:32.281801Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

caa09fda8a9e3fd492d6b73cc633bf7b0991d7291c7d56a90840074bee15d31e

Aliases

arxiv: 1111.3837 · arxiv_version: 1111.3837v4 · doi: 10.48550/arxiv.1111.3837 · pith_short_12: ZKQJ7WUKTY75 · pith_short_16: ZKQJ7WUKTY75JEWW · pith_short_8: ZKQJ7WUK

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/ZKQJ7WUKTY75JEWWW46MMM57PM \
  | 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: caa09fda8a9e3fd492d6b73cc633bf7b0991d7291c7d56a90840074bee15d31e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "754b75e0ad20be8f1093b6b227ca0fd0208c1ae77d477b003f47c91775d2057f",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2011-11-16T15:34:00Z",
    "title_canon_sha256": "852bcd4693f68a33a39969c8f74b01f2cf70f4797afac2374ed5d9e1b530f03d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.3837",
    "kind": "arxiv",
    "version": 4
  }
}