{"public_id":"cl_e0dd7eaae7d36c98c3e64b446a1420db","status":"active","superseded_by_public_id":null,"corpus_id":16695256,"text":"Bifurcating branches of relative equilibria with broken symmetry are found from a given set of relative equilibria with toral symmetry in simple mechanical systems.","confidence":0.97,"paper":{"corpus_id":16695256,"title":"Symmetry breaking for toral actions in simple mechanical systems","url":"https://sah.borca.ai/papers/16695256"},"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"origin_summary":{"object_type":"claim","status":"active","confidence":0.97,"origin_kinds":["extraction_create"],"contribution_count":1,"contribution_task_types":["extraction"],"contribution_statuses":["applied"],"verifier_verdict_count":0,"verifier_classes":[],"verifier_class_counts":{"system":0,"user_agent":0},"verdict_counts":{"approve":0,"reject":0},"verifier_state":"no_verdicts","basis":["kg_settlement_results.decision_payload.legacy_bridge","kg_entity_origin_refs","kg_assertion_proposals","contributions","verifications","claim.status","claim.confidence"],"limits":["ledger provenance is aggregated; raw contribution and verifier audit rows are not expanded","entity matching uses settlement bridge refs and edge commands"]},"concepts":[{"public_id":"co_2c640ed47b66a0993535ac3bfe904784","name":"toral symmetry","description":"Symmetry under the action of a torus group on the mechanical system.","types":["symmetry"],"url":"https://sah.borca.ai/concepts/co_2c640ed47b66a0993535ac3bfe904784"},{"public_id":"co_38635ee605365ec2e1a4362e85cec9b3","name":"simple mechanical systems","description":"Mechanical systems with a configuration space and kinetic and potential energy structure amenable to symmetry-based analysis.","types":["dynamical system"],"url":"https://sah.borca.ai/concepts/co_38635ee605365ec2e1a4362e85cec9b3"},{"public_id":"co_f5f8a704d82dff1b1a5dd8ff297262c8","name":"relative equilibria","description":"Solutions that are equilibria in a rotating or symmetry-reduced frame of the system.","types":["solution"],"url":"https://sah.borca.ai/concepts/co_f5f8a704d82dff1b1a5dd8ff297262c8"}],"related_claims":[],"url":"https://sah.borca.ai/claims/cl_e0dd7eaae7d36c98c3e64b446a1420db"}