Pith Number

pith:XJ7ZCMDP

pith:2010:XJ7ZCMDPDZSRNRSJEDN3GQVSBO

not attested not anchored not stored refs pending

Modified Landau levels, damped harmonic oscillator and two-dimensional pseudo-bosons

Fabio Bagarello, Jean-Pierre Gazeau, Syed Twareque Ali

arxiv:1010.4221 v1 · 2010-10-20 · 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{XJ7ZCMDPDZSRNRSJEDN3GQVSBO}

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	2026-05-18T04:38:59.600953Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba7f91306f1e6516c64920dbb342b20b89f2ed2fb8ac18073c159e7e0af338e8

Aliases

arxiv: 1010.4221 · arxiv_version: 1010.4221v1 · doi: 10.48550/arxiv.1010.4221 · pith_short_12: XJ7ZCMDPDZSR · pith_short_16: XJ7ZCMDPDZSRNRSJ · pith_short_8: XJ7ZCMDP

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/XJ7ZCMDPDZSRNRSJEDN3GQVSBO \
  | 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: ba7f91306f1e6516c64920dbb342b20b89f2ed2fb8ac18073c159e7e0af338e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "626fc19b620ccc80301dce4c44d8f320002ed9291b63c5fe1fac6b1c39ac57b3",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-10-20T15:07:34Z",
    "title_canon_sha256": "91f65583be9d69d6d97d929482fd1a961252302dc18fd3c6870d05d89ad1769c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4221",
    "kind": "arxiv",
    "version": 1
  }
}