Pith Number

pith:CFQFOXEK

pith:2011:CFQFOXEKV5OPHQDTF3UHVTXXJR

not attested not anchored not stored refs pending

Geometry of the set of mixed quantum states: An apophatic approach

Ingemar Bengtsson, Karol \.Zyczkowski, Stephan Weis

arxiv:1112.2347 v2 · 2011-12-11 · 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{CFQFOXEKV5OPHQDTF3UHVTXXJR}

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	2026-05-18T01:14:53.672970Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1160575c8aaf5cf3c0732ee87acef74c42c6a5dfad82167fc2199c93ba7eaedd

Aliases

arxiv: 1112.2347 · arxiv_version: 1112.2347v2 · doi: 10.48550/arxiv.1112.2347 · pith_short_12: CFQFOXEKV5OP · pith_short_16: CFQFOXEKV5OPHQDT · pith_short_8: CFQFOXEK

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/CFQFOXEKV5OPHQDTF3UHVTXXJR \
  | 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: 1160575c8aaf5cf3c0732ee87acef74c42c6a5dfad82167fc2199c93ba7eaedd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d426a3e5025b0b6498f66d856a13f5ae7ddc80a2c9e693adbd53fc900f5ba521",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2011-12-11T11:16:15Z",
    "title_canon_sha256": "2ed2359807ac411e2a67d82d37d302e40ed3346547b0bd3a8c9966367f571450"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.2347",
    "kind": "arxiv",
    "version": 2
  }
}