{"paper":{"title":"Constraining $f(R)$ gravity and evolving dark energy via large-scale structure and phase-space trajectories","arxiv_id":"2609.10651","primary_cat":"physics.gen-ph","submitted_at":"2026-09-09T14:27:11+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-1.13.0 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":1.0,"id":"s0","own":true,"role":"contribution","text":"We present a joint observational analysis confronting viable $f(R)$ modified gravity theories, specifically the Hu \\& Sawicki and Starobinsky models, with background and large-scale structure (LSS) data.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.93,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.08,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":1.0,"interpretation":0.0}},{"i":1,"p":1.0,"id":"s1","own":true,"role":"method","text":"Utilizing Monte-Carlo Markov chain (MCMC) sampling across datasets including baryon acoustic oscillations (BAO), type Ia supernovae (SNeIa), cosmic microwave background (CMB) distance priors, and linear growth measurements ($f\\sigma_8$, $f$, $\\sigma_8$), we place tight constraints on the model parameters governing deviations from General Relativity.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.1,"role_probabilities":{"gap":0.0,"method":1.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":1.0,"id":"s2","own":true,"role":"result","text":"For the full dataset combination, we obtain $\\log_{10} b_\\mathrm{HS} = -6.325_{-1.138}^{+1.216}$ for the Hu \\& Sawicki model and $b_\\mathrm{S} = (0.8\\pm61.0)\\times10^{-4}$ for the Starobinsky model.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.12,"quantitative":true,"quantitative_p":0.99,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":3,"p":0.91,"id":"s3","own":true,"role":"result","text":"Model comparison based on the Akaike Information Criterion indicates that these $f(R)$ extensions are statistically favored over flat $\\Lambda\\text{CDM}$ ($|\\Delta\\text{AIC}| \\ge 3.99$) for the combined data.","hedge":{"p":0.51,"label":"hedged_possibility"},"own_p":0.94,"main_claim_p":0.33,"quantitative":true,"quantitative_p":0.99,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.91,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.09}},{"i":4,"p":0.53,"id":"s4","own":true,"role":"result","text":"However, when considering the Bayesian Information Criterion, the evidence for support is significantly reduced.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.84,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.16,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.53,"background":0.0,"limitation":0.2,"future_work":0.0,"contribution":0.0,"interpretation":0.27}},{"i":5,"p":0.88,"id":"s5","own":true,"role":"contribution","text":"Furthermore, we construct two-dimensional phase-space diagrams in the $(\\mu, \\gamma)$ and $(\\mu, \\Sigma)$ planes across several redshifts, establishing a novel diagnostic null-test allowing us to probe for deviations from $\\Lambda\\text{CDM}$, corresponding to the fixed point $(1,1)$ in both planes, using LSS 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$\\Lambda\\text{CDM}$ ($|\\Delta\\text{AIC}| \\ge 3.99$) for the combined data.","location":"abstract s3","hedge_strength":{"p":0.51,"label":"hedged possibility"}},"provenance":{"route":{"via":"TypeSafe API","model":"classifier-1.13.0","endpoint":"https://api.typesafe.ai/v1/systemone","provider":"TypeSafe"},"packing":"one request per paper","requests":1,"input_tokens":6140,"cost_usd_reported":0.0},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13.0","abstract_states":{"claims_first":0.15,"states_limitation":0.85,"human_participants":0.01,"controlled_comparison":0.72,"randomized_assignment":0.01,"states_quantitative_result":0.99,"compares_with_prior_results":0.9,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":1.0,"value":"analysis of existing 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