Pith Number

pith:JNDNTRB4

pith:2011:JNDNTRB4PQIP2EOVPPUAMGRVBZ

not attested not anchored not stored refs pending

Symplectic Covariance Properties for Shubin and Born-Jordan Pseudo-Differential Operators

Maurice A. de Gosson

arxiv:1104.5198 v1 · 2011-04-27 · math-ph · math.CA · math.MP · math.SG · 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{JNDNTRB4PQIP2EOVPPUAMGRVBZ}

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	2026-05-18T04:23:22.444142Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b46d9c43c7c10fd11d57be8061a350e53395287ba83963125fa3f02a6ecd10a

Aliases

arxiv: 1104.5198 · arxiv_version: 1104.5198v1 · doi: 10.48550/arxiv.1104.5198 · pith_short_12: JNDNTRB4PQIP · pith_short_16: JNDNTRB4PQIP2EOV · pith_short_8: JNDNTRB4

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/JNDNTRB4PQIP2EOVPPUAMGRVBZ \
  | 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: 4b46d9c43c7c10fd11d57be8061a350e53395287ba83963125fa3f02a6ecd10a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb6f2568fc44e926872fb2d611372b6dd93e3cb65f9571524f1a224ec151c968",
    "cross_cats_sorted": [
      "math.CA",
      "math.MP",
      "math.SG",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-04-27T17:41:43Z",
    "title_canon_sha256": "3ea9f65a084bbbbd3ab0e21a53e9ed6c13ba1a03a1f2eadc3303e6c0cca8887a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.5198",
    "kind": "arxiv",
    "version": 1
  }
}