{"paper":{"title":"Scalar Field Cosmology -- Geometry of Dynamics","arxiv_id":"1308.4069","primary_cat":"gr-qc","submitted_at":"2013-08-19T16:25:13+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13-20260917 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":0.78,"id":"s0","own":true,"role":"contribution","text":"We study the Scalar Field Cosmology (SFC) using the geometric language of the phase space.","hedge":{"p":0.97,"label":"asserted"},"own_p":0.93,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.02,"role_probabilities":{"gap":0.0,"method":0.21,"result":0.0,"background":0.01,"limitation":0.0,"future_work":0.0,"contribution":0.78,"interpretation":0.0}},{"i":1,"p":0.67,"id":"s1","own":true,"role":"method","text":"We define and study an ensemble of dynamical systems as a Banach space with a Sobolev metric.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.67,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.33,"interpretation":0.0}},{"i":2,"p":0.91,"id":"s2","own":true,"role":"method","text":"The metric in the ensemble is used to measure a distance between different models.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.55,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.91,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.09,"interpretation":0.0}},{"i":3,"p":0.36,"id":"s3","own":false,"role":"interpretation","text":"We point out the advantages of visualisation of dynamics in the phase space.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.49,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.23,"result":0.01,"background":0.13,"limitation":0.0,"future_work":0.0,"contribution":0.27,"interpretation":0.36}},{"i":4,"p":0.98,"id":"s4","own":true,"role":"contribution","text":"It is investigated the genericity of some class of models in the context of fine tuning of the form of the potential function in the ensemble of SFC.","hedge":{"p":0.83,"label":"asserted"},"own_p":0.8,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.02,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.98,"interpretation":0.0}},{"i":5,"p":0.87,"id":"s5","own":true,"role":"contribution","text":"We also study the symmetries of dynamical systems of SFC by searching for their exact solutions.","hedge":{"p":0.96,"label":"asserted"},"own_p":0.93,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.13,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.87,"interpretation":0.0}},{"i":6,"p":0.51,"id":"s6","own":true,"role":"interpretation","text":"In this context we stressed the importance of scaling solutions.","hedge":{"p":0.95,"label":"asserted"},"own_p":0.55,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.01,"background":0.11,"limitation":0.0,"future_work":0.0,"contribution":0.35,"interpretation":0.51}},{"i":7,"p":0.99,"id":"s7","own":true,"role":"result","text":"It is demonstrated that scaling solutions in the phase space are represented by unstable separatrices of the saddle points.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.86,"main_claim_p":0.16,"quantitative":false,"quantitative_p":0.1,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.99,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.01}},{"i":8,"p":0.95,"id":"s8","own":true,"role":"result","text":"Only critical point itself located on two dimensional stable submanifold can be identified as scaling solution.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.83,"main_claim_p":0.11,"quantitative":true,"quantitative_p":0.58,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.95,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.05}},{"i":9,"p":0.93,"id":"s9","own":true,"role":"result","text":"We have also found a class of potentials of the scalar fields forced by the symmetry of differential equation describing the evolution of the universe.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.93,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.07,"interpretation":0.0}},{"i":10,"p":0.73,"id":"s10","own":true,"role":"result","text":"A class of potentials forced by scaling (homology) symmetries was given.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.86,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.73,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.27,"interpretation":0.0}},{"i":11,"p":0.45,"id":"s11","own":true,"role":"contribution","text":"We point out the role of the notion of a structural stability in the context of the problem of indetermination of the potential form of the Scalar Field Cosmology.","hedge":{"p":0.97,"label":"asserted"},"own_p":0.67,"main_claim_p":0.11,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.01,"method":0.02,"result":0.01,"background":0.08,"limitation":0.0,"future_work":0.0,"contribution":0.45,"interpretation":0.43}},{"i":12,"p":0.51,"id":"s12","own":true,"role":"result","text":"We characterise also the class of potentials which reproduces the \\Lambda CDM model, which is known to be structurally stable.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.79,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.09,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.51,"background":0.02,"limitation":0.0,"future_work":0.0,"contribution":0.47,"interpretation":0.0}},{"i":13,"p":0.47,"id":"s13","own":true,"role":"interpretation","text":"We show that the structural stability issue can be effectively used is selection of the scalar field potential function.","hedge":{"p":0.95,"label":"asserted"},"own_p":0.89,"main_claim_p":0.22,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.24,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.26,"interpretation":0.47}},{"i":14,"p":0.47,"id":"s14","own":true,"role":"interpretation","text":"This enables us to characterise a structurally stable and therefore a generic class of SFC models.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.87,"main_claim_p":0.34,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.38,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.15,"interpretation":0.47}},{"i":15,"p":0.99,"id":"s15","own":true,"role":"result","text":"We have found a nonempty and dense subset of structurally stable models.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.28,"quantitative":false,"quantitative_p":0.16,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.99,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.0}},{"i":16,"p":0.98,"id":"s16","own":true,"role":"result","text":"We show that these models possess symmetry of homology.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.17,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.98,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.01}}]},"compiled":{"main_claim":{"p":0.71,"text":"This enables us to characterise a structurally stable and therefore a generic class of SFC models.","location":"abstract s14","hedge_strength":{"p":0.98,"label":"asserted"}},"provenance":{"route":{"via":"OpenRouter","model":"classifier-1.13","endpoint":"https://openrouter.ai/api/v1/systemone","provider":"TypeSafe"},"packing":"one request per paper","requests":1,"input_tokens":11812,"cost_usd_reported":0.000496},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13-20260917","abstract_states":{"claims_first":0.03,"states_limitation":0.13,"human_participants":0.01,"controlled_comparison":0.02,"randomized_assignment":0.01,"states_quantitative_result":0.07,"compares_with_prior_results":0.17,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":1.0,"value":"proof or derivation","probabilities":{"argument":0.0,"literature":0.0,"proof_or_derivation":1.0,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.0}},"contribution_type":{"p":0.97,"value":"theoretical result","probabilities":{"review":0.0,"method_or_tool":0.03,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":0.97,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":0.44,"text":"We define and study an ensemble of dynamical systems as a Banach space with a Sobolev metric.","location":"abstract s1"}},"coverage":{"tier":"abstract","levels_run":["P abstract"],"not_examined":["full text","figures and tables","references and citing sentences","relations to other papers"],"sources_read":["arXiv listing abstract v1"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":17,"sentences_in_abstract":17},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; the figure is how often the published label matches their consensus","sentence_role_agreement":0.92,"main_claim_agreement":0.908,"typed_citation_agreement":0.933,"typed_citation_agreement_95_interval":[0.917,0.945],"review_comments_accurate":0.758,"review_comments_accurate_95_interval":[0.684,0.82],"review_caught_admitted_error_found_or_related":0.448}}