Pith Number

pith:WVQEG7ET

pith:2025:WVQEG7ET4WACI6DLU6ECSI6AAV

not attested not anchored not stored refs pending

Integrable systems from Poisson reductions of generalized Hamiltonian torus actions

L. Feher, M. Fairon

Sufficient conditions let an integrable system with symmetry K descend to an integrable system on the dense open set of the quotient Poisson space M/K.

arxiv:2507.12051 v2 · 2025-07-16 · math-ph · hep-th · math.MP · math.SG · nlin.SI

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\pithnumber{WVQEG7ET4WACI6DLU6ECSI6AAV}

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Record completeness

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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

We develop a set of sufficient conditions for guaranteeing that an integrable system with a symmetry group K on a manifold M descends to an integrable system on a dense open subset of the quotient Poisson space M/K.

C2weakest assumption

The unreduced system on M is supposed to possess action variables that generate a proper, effective action of a group of the form U(1)^ℓ1 × R^ℓ2 and descend to action variables of the reduced system (abstract, paragraph on generalized Hamiltonian torus actions).

C3one line summary

Develops sufficient conditions for Poisson reduction of generalized Hamiltonian torus actions to preserve integrability and applies them to open problems on Lie group doubles and flat-connection moduli spaces.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-21T01:04:15.294495Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b560437c93e58024786ba7882923c0055a9d9f63c24d590f3ee02781a49d5703

Aliases

arxiv: 2507.12051 · arxiv_version: 2507.12051v2 · doi: 10.48550/arxiv.2507.12051 · pith_short_12: WVQEG7ET4WAC · pith_short_16: WVQEG7ET4WACI6DL · pith_short_8: WVQEG7ET

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WVQEG7ET4WACI6DLU6ECSI6AAV \
  | 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: b560437c93e58024786ba7882923c0055a9d9f63c24d590f3ee02781a49d5703

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c3b5b14e7f1aa868bbe1b89273d870e54fd220b0206e49ee923d9044f7dfd36",
    "cross_cats_sorted": [
      "hep-th",
      "math.MP",
      "math.SG",
      "nlin.SI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2025-07-16T09:11:05Z",
    "title_canon_sha256": "739303d1aaad2166fae9891cbb7d3f9204cfa9704d51523b87ae17279eca8b18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.12051",
    "kind": "arxiv",
    "version": 2
  }
}