Pith Number

pith:MCIUMG73

pith:2011:MCIUMG73TBNLZSRYRIN2RHU6AE

not attested not anchored not stored refs pending

Solvable rational extensions of the Morse and Kepler-Coulomb potentials

Yves Grandati (FCN)

arxiv:1103.5023 v1 · 2011-03-25 · math-ph · 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{MCIUMG73TBNLZSRYRIN2RHU6AE}

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	2026-05-18T02:02:44.931204Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6091461bfb985abcca388a1ba89e9e0118d57a3a6422c9de126397d0d466aca7

Aliases

arxiv: 1103.5023 · arxiv_version: 1103.5023v1 · doi: 10.48550/arxiv.1103.5023 · pith_short_12: MCIUMG73TBNL · pith_short_16: MCIUMG73TBNLZSRY · pith_short_8: MCIUMG73

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/MCIUMG73TBNLZSRYRIN2RHU6AE \
  | 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: 6091461bfb985abcca388a1ba89e9e0118d57a3a6422c9de126397d0d466aca7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "01134e77abf2a1e53a8d76ff55a2af526746def41269ba960f7aae6850068da7",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-03-25T16:34:18Z",
    "title_canon_sha256": "4913e77c371d89504a0fb10b85b7bba4fbdd182bafd2a7e15a82af128ecee999"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.5023",
    "kind": "arxiv",
    "version": 1
  }
}