Pith Number

pith:PLWENA4A

pith:2013:PLWENA4AY4N7CSE7A6333G3XUB

not attested not anchored not stored refs pending

Quantum discord for two-qubit X states: Analytical formula with very small worst-case error

Yichen Huang

arxiv:1306.0228 v2 · 2013-06-02 · 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{PLWENA4AY4N7CSE7A6333G3XUB}

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	2026-05-18T03:17:00.939215Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7aec468380c71bf1489f07b7bd9b77a04b0ab379ab4d2db0b574d4fcc92261fc

Aliases

arxiv: 1306.0228 · arxiv_version: 1306.0228v2 · doi: 10.48550/arxiv.1306.0228 · pith_short_12: PLWENA4AY4N7 · pith_short_16: PLWENA4AY4N7CSE7 · pith_short_8: PLWENA4A

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/PLWENA4AY4N7CSE7A6333G3XUB \
  | 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: 7aec468380c71bf1489f07b7bd9b77a04b0ab379ab4d2db0b574d4fcc92261fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "67210232ed743a236aba1a8a20d4d7ee6e9310fdfe75e9f9dbf18597be38dfe1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2013-06-02T16:57:23Z",
    "title_canon_sha256": "9070139c50062b245b4408653023b1a918ce33438da52e307527eec71107cda9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0228",
    "kind": "arxiv",
    "version": 2
  }
}