Pith Number

pith:Z576T7C7

pith:2014:Z576T7C7T6AXPAP7DOOXM557UI

not attested not anchored not stored refs pending

An example of a quantum statistical model which cannot be mapped to a less informative one by any trace preserving positive map

Keiji Matsumoto

arxiv:1409.5658 v1 · 2014-09-19 · quant-ph · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z576T7C7T6AXPAP7DOOXM557UI}

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

2 papers in Pith

Sufficiency and Petz recovery for positive maps

Receipt and verification

First computed	2026-05-18T02:42:26.673367Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf7fe9fc5f9f817781ff1b9d7677bfa22b2f4ae8934705fe7e4909d3d3f23b9e

Aliases

arxiv: 1409.5658 · arxiv_version: 1409.5658v1 · doi: 10.48550/arxiv.1409.5658 · pith_short_12: Z576T7C7T6AX · pith_short_16: Z576T7C7T6AXPAP7 · pith_short_8: Z576T7C7

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/Z576T7C7T6AXPAP7DOOXM557UI \
  | 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: cf7fe9fc5f9f817781ff1b9d7677bfa22b2f4ae8934705fe7e4909d3d3f23b9e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99d567d6b4eda317207dd7ddf84d6fe67e71567ab5c19f90e1d967fdeeb16ae3",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2014-09-19T13:45:45Z",
    "title_canon_sha256": "e23d8bc4c5953516de69e794345c8457b89891b53b0b74df19de9fce8203e4f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.5658",
    "kind": "arxiv",
    "version": 1
  }
}