Pith Number

pith:VA336DXQ

pith:2025:VA336DXQWMX7DVQ6E3VBRYSXC5

not attested not anchored not stored refs pending

A complete theory of the Clifford commutant

Antonio A. Mele, Jens Eisert, Lennart Bittel, Lorenzo Leone, Salvatore F.E. Oliviero

arxiv:2504.12263 v2 · 2025-04-16 · quant-ph · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VA336DXQWMX7DVQ6E3VBRYSXC5}

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

10 papers in Pith

Stabilizer entropy is trustworthy for mixed states

Non-Clifford Cost of Random Unitaries

Nonstabilizerness and Error Resilience in Noisy Quantum Circuits

Operational interpretation of the Stabilizer Entropy

Demonstrating an unconditional separation between quantum and classical information resources

Receipt and verification

First computed	2026-07-01T01:17:39.605760Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a837bf0ef0b32ff1d61e26ea18e2571755f7d632821ff6320cd7e7c92c546c83

Aliases

arxiv: 2504.12263 · arxiv_version: 2504.12263v2 · doi: 10.48550/arxiv.2504.12263 · pith_short_12: VA336DXQWMX7 · pith_short_16: VA336DXQWMX7DVQ6 · pith_short_8: VA336DXQ

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/VA336DXQWMX7DVQ6E3VBRYSXC5 \
  | 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: a837bf0ef0b32ff1d61e26ea18e2571755f7d632821ff6320cd7e7c92c546c83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7f51cbc113a7b3aa1a0d9bdbd1d4d546231897a628206fa9622175331291ed9",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-04-16T17:21:34Z",
    "title_canon_sha256": "32f93f5b240f3846d67ffdb3466663ef8e8578aa0ce7d0aef51c3976a7336a8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2504.12263",
    "kind": "arxiv",
    "version": 2
  }
}