{"paper":{"title":"Multiplicative and Additive Extractors for Low Entropy Samplable Sources Under Reduced Assumptions","arxiv_id":"2611.07829","primary_cat":"cs.CC","submitted_at":"2026-11-05T11:09:42+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":false,"role":"background","text":"Trevisan and Vadhan [TV, FOCS'00] constructed (seedless) extractors for distributions samplable by poly-size circuits that have very high min-entropy, under the very strong complexity theoretic hardness assumption that $\\mathsf{E}=\\mathsf{DTIME}(2^{O(n)})$ requires size $2^{\\Omega(n)}$ circuits that have oracle access to $\\Sigma_6^{\\text{P}}$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.03,"main_claim_p":0.03,"quantitative":true,"quantitative_p":0.95,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":1.0,"id":"s1","own":true,"role":"contribution","text":"In this paper we give three new explicit constructions of extractors for samplable distributions.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.4,"quantitative":true,"quantitative_p":0.56,"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":2,"p":0.64,"id":"s2","own":true,"role":"result","text":"First, we construct an extractor that extracts one bit, with constant error, for min-entropy $k=O(\\log n)$, which matches the non-constructive probabilistic argument.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.17,"quantitative":true,"quantitative_p":0.97,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.64,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.36,"interpretation":0.0}},{"i":3,"p":0.39,"id":"s3","own":true,"role":"result","text":"This result uses hardness for nondeterministic circuits, and achieves the same parameters as the recent extractor of Oh and Shaltiel [OS, STOC'26] under an incomparable hardness assumption.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.76,"main_claim_p":0.08,"quantitative":true,"quantitative_p":0.74,"role_probabilities":{"gap":0.0,"method":0.05,"result":0.39,"background":0.01,"limitation":0.0,"future_work":0.0,"contribution":0.22,"interpretation":0.33}},{"i":4,"p":0.6,"id":"s4","own":true,"role":"contribution","text":"In contrast to the extractor of [OS26], our extractor (and, similarly, the constructions below) also works for the more general class of distributions samplable with postselection (a model introduced by [BGDM, FOCS'23] that generalizes samplable and recognizable sources).","hedge":{"p":1.0,"label":"asserted"},"own_p":0.82,"main_claim_p":0.07,"quantitative":true,"quantitative_p":0.59,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.31,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.6,"interpretation":0.09}},{"i":5,"p":0.55,"id":"s5","own":true,"role":"contribution","text":"Second, we construct an extractor that extracts almost all the entropy, with polynomially small error, for min-entropy $k=n^{\\alpha}$, where $\\alpha>0$ is an arbitrary constant.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.12,"quantitative":true,"quantitative_p":0.96,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.45,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.55,"interpretation":0.0}},{"i":6,"p":0.42,"id":"s6","own":true,"role":"contribution","text":"This result also uses hardness for nondeterministic circuits, and significantly improves upon the recent extractor of [Shaltiel, FOCS'25] which required a much stronger assumption.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.81,"main_claim_p":0.1,"quantitative":true,"quantitative_p":0.9,"role_probabilities":{"gap":0.01,"method":0.02,"result":0.22,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.42,"interpretation":0.33}},{"i":7,"p":0.37,"id":"s7","own":true,"role":"contribution","text":"This extractor is also \\textit{multiplicative}: a stronger notion suggested in [AASY, Comp.","hedge":{"p":0.97,"label":"asserted"},"own_p":0.71,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.08,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.31,"background":0.03,"limitation":0.0,"future_work":0.0,"contribution":0.37,"interpretation":0.28}},{"i":8,"p":0.68,"id":"s8","own":false,"role":"interpretation","text":"Complexity'16; Shaltiel, CCC'25] to make extractors for samplable distributions suitable for selecting keys for cryptographic protocols.","hedge":{"p":0.56,"label":"asserted"},"own_p":0.16,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.09,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.01,"background":0.27,"limitation":0.0,"future_work":0.0,"contribution":0.04,"interpretation":0.68}},{"i":9,"p":0.7,"id":"s9","own":true,"role":"contribution","text":"Third, we construct an extractor that extracts almost all the entropy, with polynomially small error, for min-entropy $k=\\mathrm{polylog}(n)$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.13,"quantitative":true,"quantitative_p":0.93,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.3,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.7,"interpretation":0.0}},{"i":10,"p":0.85,"id":"s10","own":true,"role":"method","text":"This result uses hardness for circuits that have oracle access to $\\Sigma_2^{\\text{P}}$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.85,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.32,"role_probabilities":{"gap":0.0,"method":0.85,"result":0.02,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.13,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":1.0,"text":"In this paper we give three new explicit constructions of extractors for samplable distributions.","location":"abstract s1","hedge_strength":{"p":1.0,"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":8638,"cost_usd_reported":0.0},"compiled_at":"2026-11-06","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13.0","abstract_states":{"claims_first":0.12,"states_limitation":0.29,"human_participants":0.01,"controlled_comparison":0.11,"randomized_assignment":0.01,"states_quantitative_result":0.97,"compares_with_prior_results":0.98,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":0.98,"value":"proof or derivation","probabilities":{"argument":0.01,"literature":0.01,"proof_or_derivation":0.98,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.0}},"contribution_type":{"p":0.8,"value":"theoretical result","probabilities":{"review":0.0,"method_or_tool":0.2,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":0.8,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":1.0,"text":"In this paper we give three new explicit constructions of extractors for samplable distributions.","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":11,"sentences_in_abstract":11},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; 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