{"paper":{"title":"Free-energy distribution of the directed polymer at high temperature","arxiv_id":"1002.4560","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-02-24T15:12:35+00:00","version_compiled":"v2"},"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 v2","sentences":[{"i":0,"p":0.94,"id":"s0","own":true,"role":"contribution","text":"We study the directed polymer of length $t$ in a random potential with fixed endpoints in dimension 1+1 in the continuum and on the square lattice, by analytical and numerical methods.","hedge":{"p":0.93,"label":"asserted"},"own_p":0.95,"main_claim_p":0.03,"quantitative":true,"quantitative_p":0.63,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.0,"background":0.04,"limitation":0.0,"future_work":0.0,"contribution":0.94,"interpretation":0.0}},{"i":1,"p":0.74,"id":"s1","own":true,"role":"method","text":"The universal regime of high temperature $T$ is described, upon scaling 'time' $t \\sim T^5/\\kappa$ and space $x = T^3/\\kappa$ (with $\\kappa=T$ for the discrete model) by a continuum model with $\\delta$-function disorder correlation.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.66,"main_claim_p":0.08,"quantitative":true,"quantitative_p":0.61,"role_probabilities":{"gap":0.0,"method":0.74,"result":0.08,"background":0.01,"limitation":0.0,"future_work":0.0,"contribution":0.16,"interpretation":0.01}},{"i":2,"p":0.75,"id":"s2","own":true,"role":"method","text":"Using the Bethe Ansatz solution for the attractive boson problem, we obtain all positive integer moments of the partition function.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.17,"role_probabilities":{"gap":0.0,"method":0.75,"result":0.14,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.11,"interpretation":0.0}},{"i":3,"p":0.99,"id":"s3","own":true,"role":"result","text":"The lowest cumulants of the free energy are predicted at small time and found in agreement with numerics.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.91,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.39,"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":4,"p":0.9,"id":"s4","own":true,"role":"result","text":"We then obtain the exact expression at any time for the generating function of the free energy distribution, in terms of a Fredholm determinant.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.3,"quantitative":false,"quantitative_p":0.08,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.9,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.1,"interpretation":0.0}},{"i":5,"p":0.99,"id":"s5","own":true,"role":"result","text":"At large time we find that it crosses over to the Tracy Widom distribution (TW) which describes the fixed $T$ infinite $t$ limit.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.31,"quantitative":false,"quantitative_p":0.35,"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":6,"p":0.82,"id":"s6","own":true,"role":"result","text":"The exact free energy distribution is obtained for any time and compared with very recent results on growth and exclusion models.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.18,"quantitative":true,"quantitative_p":0.53,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.82,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.16,"interpretation":0.02}}]},"compiled":{"main_claim":{"p":0.43,"text":"The exact free energy distribution is obtained for any time and compared with very recent results on growth and exclusion models.","location":"abstract s6","hedge_strength":{"p":1.0,"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":5635,"cost_usd_reported":0.000237},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13-20260917","abstract_states":{"claims_first":0.04,"states_limitation":0.11,"human_participants":0.01,"controlled_comparison":0.04,"randomized_assignment":0.01,"states_quantitative_result":0.56,"compares_with_prior_results":0.95,"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":1.0,"value":"theoretical result","probabilities":{"review":0.0,"method_or_tool":0.0,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":1.0,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":0.92,"text":"We then obtain the exact expression at any time for the generating function of the free energy distribution, in terms of a Fredholm determinant.","location":"abstract s4"}},"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 v2"],"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}}