{"paper":{"title":"Derivative hierarchy as the origin of kernel-dependent trends in Gaussian process reconstructions of the hubble parameter","arxiv_id":"2608.26774","primary_cat":"astro-ph.CO","submitted_at":"2026-08-27T08:05:37+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":0.95,"id":"s0","own":true,"role":"contribution","text":"We perform a model independent reconstruction of the cosmic expansion history using Gaussian Process regression, investigating how the smoothness properties of covariance kernels influence the inferred Hubble parameter.","hedge":{"p":0.83,"label":"asserted"},"own_p":0.95,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.05,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.95,"interpretation":0.0}},{"i":1,"p":0.99,"id":"s1","own":true,"role":"method","text":"Using 32 cosmic chronometer measurements, we reconstruct $H(z)$ with the Mat\\'ern $3/2$, $5/2$, $7/2$, $9/2$, and Squared Exponential kernels, which form a well-defined hierarchy of differentiability.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.04,"quantitative":true,"quantitative_p":0.94,"role_probabilities":{"gap":0.0,"method":0.99,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.0}},{"i":2,"p":1.0,"id":"s2","own":true,"role":"result","text":"Across this hierarchy, we observe a systematic and monotonic trend in which increasing kernel smoothness is associated with progressively lower reconstructed values of the present-day Hubble constant $H_0$, accompanied by reduced statistical uncertainties.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.59,"quantitative":true,"quantitative_p":0.95,"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":1.0,"id":"s3","own":true,"role":"interpretation","text":"Rather than indicating a statistical preference for a specific kernel, this behaviour reflects the sensitivity of non-parametric reconstructions to the assumed smoothness prior encoded in the covariance function.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.52,"main_claim_p":0.44,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":1.0}},{"i":4,"p":0.97,"id":"s4","own":true,"role":"result","text":"The same ordering is reflected in descriptive goodness-of-fit statistics and remains stable when incorporating recent DESI DR2 BAO measurements and performing jackknife resampling tests, demonstrating robustness against individual data points and dataset variations.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.1,"quantitative":false,"quantitative_p":0.4,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.97,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.01}},{"i":5,"p":0.73,"id":"s5","own":true,"role":"interpretation","text":"Additional analysis of derivative reconstructions shows that differences in kernel differentiability propagate into the local slope of the expansion history, providing a consistent interpretation of the observed ordering in $H_0$.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.94,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.11,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.24,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.73}},{"i":6,"p":0.95,"id":"s6","own":true,"role":"interpretation","text":"Our results highlight that kernel smoothness plays an important role in Gaussian Process reconstructions and should be carefully accounted for when interpreting non-parametric cosmological inferences.","hedge":{"p":0.94,"label":"asserted"},"own_p":0.62,"main_claim_p":0.79,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.05,"contribution":0.0,"interpretation":0.95}}]},"compiled":{"main_claim":{"p":0.86,"text":"Our results highlight that kernel smoothness plays an important role in Gaussian Process reconstructions and should be carefully accounted for when interpreting non-parametric cosmological inferences.","location":"abstract s6","hedge_strength":{"p":0.94,"label":"asserted"}},"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":5883,"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":0.03,"states_limitation":0.8,"human_participants":0.01,"controlled_comparison":0.07,"randomized_assignment":0.01,"states_quantitative_result":0.37,"compares_with_prior_results":0.14,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":0.94,"value":"analysis of existing data","probabilities":{"argument":0.0,"literature":0.0,"proof_or_derivation":0.0,"analysis_of_existing_data":0.94,"observation_or_experiment":0.0,"simulation_or_computation":0.06}},"contribution_type":{"p":0.52,"value":"simulation study","probabilities":{"review":0.0,"method_or_tool":0.01,"empirical_study":0.41,"simulation_study":0.52,"theoretical_result":0.04,"dataset_or_benchmark":0.0,"position_or_commentary":0.02}},"contribution_statement":{"p":0.51,"text":"We perform a model independent reconstruction of the cosmic expansion history using Gaussian Process regression, investigating how the smoothness properties of covariance kernels influence the inferred Hubble parameter.","location":"abstract s0"}},"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":7,"sentences_in_abstract":7},"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}}