Pith Number

pith:B4ERTZ6T

pith:2009:B4ERTZ6TC2XGODMPBFZWZVVQOX

not attested not anchored not stored refs pending

An infinite family of solvable and integrable quantum systems on a plane

Alexander V. Turbiner, Fr\'ed\'erick Tremblay, Pavel Winternitz

arxiv:0904.0738 v3 · 2009-04-04 · math-ph · hep-th · math.DS · math.MP · nlin.SI · physics.class-ph · 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{B4ERTZ6TC2XGODMPBFZWZVVQOX}

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

1 paper in Pith

Quantum two-dimensional superintegrable systems in flat space: exact-solvability, hidden algebra, polynomial algebra of integrals

Receipt and verification

First computed	2026-05-18T02:14:07.469274Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f0919e7d316ae670d8f09736cd6b075ccf15e81918827c49497a0b9086fe1c6

Aliases

arxiv: 0904.0738 · arxiv_version: 0904.0738v3 · doi: 10.48550/arxiv.0904.0738 · pith_short_12: B4ERTZ6TC2XG · pith_short_16: B4ERTZ6TC2XGODMP · pith_short_8: B4ERTZ6T

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/B4ERTZ6TC2XGODMPBFZWZVVQOX \
  | 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: 0f0919e7d316ae670d8f09736cd6b075ccf15e81918827c49497a0b9086fe1c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a7d4ff68bcf5a05fb9aaa0b6ec77ec3f71e795f8fabadece432a884c60ded20",
    "cross_cats_sorted": [
      "hep-th",
      "math.DS",
      "math.MP",
      "nlin.SI",
      "physics.class-ph",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2009-04-04T20:08:13Z",
    "title_canon_sha256": "3ddad861cfdaab6dcecfcec7b3fd7839691a33131cd411b516ea5b72ff3038af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.0738",
    "kind": "arxiv",
    "version": 3
  }
}