{"paper":{"title":"Moments of Random Permanents and Hafnians: A Replica Approach","arxiv_id":"2610.27872","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-10-20T08:54:29+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. 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higher cumulants affect only the prefactor and the $1/N$ term.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.89,"main_claim_p":0.17,"quantitative":false,"quantitative_p":0.28,"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":3,"p":1.0,"id":"s3","own":true,"role":"result","text":"At $k=2$ the replica-symmetric solution becomes unstable, separating a power-law bulk of the distribution from a large-deviation tail, which we compute.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.14,"quantitative":true,"quantitative_p":0.66,"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":4,"p":0.93,"id":"s4","own":false,"role":"interpretation","text":"The results apply to boson sampling with single photons and with squeezed light.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.48,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.04,"background":0.0,"limitation":0.0,"future_work":0.01,"contribution":0.02,"interpretation":0.93}}]},"compiled":{"main_claim":{"p":0.97,"text":"For the $2k$-th moment of $N\\times N$ matrices with independent entries, the dominant saddle point is replica symmetric for $k>2$, and we obtain in closed form the exponential growth rate, the prefactor and the first $1/N$ correction, in agreement with exact enumerations.","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":4386,"cost_usd_reported":0.0},"compiled_at":"2026-10-21","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13.0","abstract_states":{"claims_first":0.03,"states_limitation":0.48,"human_participants":0.01,"controlled_comparison":0.03,"randomized_assignment":0.02,"states_quantitative_result":0.66,"compares_with_prior_results":0.82,"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":0.83,"text":"Using contour-integral representations of the permanent and of the Hafnian, we turn the computation of their moments for random matrices into a replica calculation, analogous to that of the moments of the partition function of a mean-field spin glass.","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":5,"sentences_in_abstract":5},"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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