Pith Number

pith:PW3ENXAV

pith:2009:PW3ENXAVCINZN4MOPWTJRCRUSU

not attested not anchored not stored refs pending

Rational solutions for the Riccati-Schr\"odinger equations associated to translationally shape invariant potentials

Alain B\'erard (FCN), Yves Grandati (FCN)

arxiv:0910.4810 v3 · 2009-10-26 · math-ph · hep-th · math.MP · 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{PW3ENXAVCINZN4MOPWTJRCRUSU}

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	2026-05-18T02:34:12.906893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7db646dc15121b96f18e7da6988a349519bbf17c78427c934eb91d7147abd819

Aliases

arxiv: 0910.4810 · arxiv_version: 0910.4810v3 · doi: 10.48550/arxiv.0910.4810 · pith_short_12: PW3ENXAVCINZ · pith_short_16: PW3ENXAVCINZN4MO · pith_short_8: PW3ENXAV

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/PW3ENXAVCINZN4MOPWTJRCRUSU \
  | 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: 7db646dc15121b96f18e7da6988a349519bbf17c78427c934eb91d7147abd819

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41fda9c17e6d1b02334f231bad4091ceaecfbe921fab0d8137e4762115cee2c3",
    "cross_cats_sorted": [
      "hep-th",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2009-10-26T05:41:23Z",
    "title_canon_sha256": "f08444d89e7fa68e059570a201e1deaa7f1eba65ff62b61bfa63a687e9c5dcc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.4810",
    "kind": "arxiv",
    "version": 3
  }
}