Pith Number

pith:IQS2QM6Q

pith:2024:IQS2QM6QZMMTB5WUJBXZNP24EQ

not attested not anchored not stored refs pending

Phase Space Representation of the Density Operator: Bopp Pseudodifferential Calculus and Moyal Product

Maurice de Gosson

arxiv:2411.14391 v2 · 2024-11-21 · math-ph · math.MP · math.OA · 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{IQS2QM6QZMMTB5WUJBXZNP24EQ}

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	2026-07-05T09:41:46.117367Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4425a833d0cb1930f6d4486f96bf5c2417c2b764df98a062e120d91cf8d34dc3

Aliases

arxiv: 2411.14391 · arxiv_version: 2411.14391v2 · doi: 10.48550/arxiv.2411.14391 · pith_short_12: IQS2QM6QZMMT · pith_short_16: IQS2QM6QZMMTB5WU · pith_short_8: IQS2QM6Q

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/IQS2QM6QZMMTB5WUJBXZNP24EQ \
  | 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: 4425a833d0cb1930f6d4486f96bf5c2417c2b764df98a062e120d91cf8d34dc3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42734ca0b450f19a19e32d8c8b976d550d06903b216b569dff4e0e124f373cff",
    "cross_cats_sorted": [
      "math.MP",
      "math.OA",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2024-11-21T18:24:11Z",
    "title_canon_sha256": "a6056d6d646f006c38bea48c0ab52243358b10b7aa35f26a35a13e9bc1b2dda8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.14391",
    "kind": "arxiv",
    "version": 2
  }
}