Pith Number

pith:5HX4K7WK

pith:2015:5HX4K7WKFSP7FHIU5Y7LX7B3NR

not attested not anchored not stored refs pending

A class of permutation-invariant measurements and their relation to quantum relative entropies

Janis N\"otzel

arxiv:1507.04609 v3 · 2015-07-16 · quant-ph · math-ph · math.MP · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5HX4K7WKFSP7FHIU5Y7LX7B3NR}

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

A Quantum Method of Types

Receipt and verification

First computed	2026-05-18T00:57:04.916341Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9efc57eca2c9ff29d14ee3ebbfc3b6c647d1d03c045e837f1b49cf1d9933ddd

Aliases

arxiv: 1507.04609 · arxiv_version: 1507.04609v3 · doi: 10.48550/arxiv.1507.04609 · pith_short_12: 5HX4K7WKFSP7 · pith_short_16: 5HX4K7WKFSP7FHIU · pith_short_8: 5HX4K7WK

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/5HX4K7WKFSP7FHIU5Y7LX7B3NR \
  | 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: e9efc57eca2c9ff29d14ee3ebbfc3b6c647d1d03c045e837f1b49cf1d9933ddd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6946411146e3fd95f0f45c7490d6225cd7bed8002bc0d411fb7ac2284a44311",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2015-07-16T15:03:40Z",
    "title_canon_sha256": "39084a3f7513519b58cfe69dd6dd754507a54cde3404bdfa6f0fa14727f60812"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.04609",
    "kind": "arxiv",
    "version": 3
  }
}