Pith Number

pith:FSAAK2KZ

pith:2026:FSAAK2KZCWAZTAM5FMITNCHRVC

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Periods of N-body Systems Determined Through Dimensional Analysis

Dan Jonsson

A generalization of dimensional analysis derives the periods of n-body gravitational systems up to a constant.

arxiv:2604.10559 v4 · 2026-04-12 · math-ph · math.MP

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\usepackage{pith}
\pithnumber{FSAAK2KZCWAZTAM5FMITNCHRVC}

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

Here we show how to derive generalizations of Kepler's third law to n-body systems by the same technique. Our results agree with conjectures by Sun on the period of a classical n-body system and by Semay and Sun on the quantum-theoretical counterpart of the period of a classical n-body system.

C2weakest assumption

The generalization of classical dimensional analysis presented in a separate article is valid and can be applied to derive periods for n-body systems.

C3one line summary

Generalized dimensional analysis derives periods for classical and quantum n-body systems that match prior conjectures by Sun and by Semay and Sun.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:05:44.627026Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2c80056959158199819d2b113688f1a8889ca64dff993cb45814dd38cfdeabf6

Aliases

arxiv: 2604.10559 · arxiv_version: 2604.10559v4 · doi: 10.48550/arxiv.2604.10559 · pith_short_12: FSAAK2KZCWAZ · pith_short_16: FSAAK2KZCWAZTAM5 · pith_short_8: FSAAK2KZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FSAAK2KZCWAZTAM5FMITNCHRVC \
  | 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: 2c80056959158199819d2b113688f1a8889ca64dff993cb45814dd38cfdeabf6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7939285eb687e4f315630417f8529aaad73d2bddf4d146137a7a2d2991e9fdc5",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-04-12T10:03:48Z",
    "title_canon_sha256": "fe2ec4cfe09871b0ee108b29e79a921887b7cdfdd92a0ca6bf038047c662e97d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.10559",
    "kind": "arxiv",
    "version": 4
  }
}