Pith Number

pith:GK6MXHSH

pith:2000:GK6MXHSH5DS3F7HM2TPU6Q5OD7

not attested not anchored not stored refs pending

Induced measures in the space of mixed quantum states

Hans-Juergen Sommers (Essen), Karol Zyczkowski (Warsaw)

arxiv:quant-ph/0012101 v3 · 2000-12-19 · 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{GK6MXHSH5DS3F7HM2TPU6Q5OD7}

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

3 papers in Pith

Logarithmic negativity typically equals exact entanglement cost

Generalised Entanglement Entropies from Unit-Invariant Singular Value Decomposition

The Maximal Entanglement Limit in Statistical and High Energy Physics

Receipt and verification

First computed	2026-07-04T16:23:06.084062Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32bccb9e47e8e5b2fcecd4df4f43ae1fd5cbf4eb58173af96dd13b10e9ee6bcf

Aliases

arxiv: quant-ph/0012101 · arxiv_version: quant-ph/0012101v3 · doi: 10.48550/arxiv.quant-ph/0012101 · pith_short_12: GK6MXHSH5DS3 · pith_short_16: GK6MXHSH5DS3F7HM · pith_short_8: GK6MXHSH

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/GK6MXHSH5DS3F7HM2TPU6Q5OD7 \
  | 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: 32bccb9e47e8e5b2fcecd4df4f43ae1fd5cbf4eb58173af96dd13b10e9ee6bcf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "def1e771f4e3d8dcd1a6dbc70e79d7d8a448a17fe46395426c9a643639f64ee2",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2000-12-19T16:39:12Z",
    "title_canon_sha256": "962eaccadee0f87984f901ad233f62bbf66f6111b3918c5b7a0abc83ced1f92c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0012101",
    "kind": "arxiv",
    "version": 3
  }
}