{"paper":{"title":"Non-singlets and the phase diagram of Matrix Quantum Mechanics","arxiv_id":"2610.32856","primary_cat":"hep-th","submitted_at":"2026-10-23T16:29:59+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":"The quantum mechanics of one $N\\times N$ Hermitian matrix in the infinite $N$ limit is well known to define a two-dimensional string theory when the quartic coupling constant $g$ is tuned to a special negative value $g_*$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.05,"main_claim_p":0.05,"quantitative":true,"quantitative_p":0.6,"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":0.86,"id":"s1","own":true,"role":"contribution","text":"We study the thermodynamics of this Matrix Quantum Mechanics (MQM), treating the SU$(N)$ symmetry as a global symmetry.","hedge":{"p":0.91,"label":"asserted"},"own_p":0.9,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.12,"result":0.0,"background":0.02,"limitation":0.0,"future_work":0.0,"contribution":0.86,"interpretation":0.0}},{"i":2,"p":0.76,"id":"s2","own":false,"role":"interpretation","text":"Crucially, the non-singlets, i.e. states in non-trivial representations of SU$(N)$, implement the effects of vortices on the discretized worldsheets.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.38,"main_claim_p":0.13,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.04,"result":0.02,"background":0.05,"limitation":0.0,"future_work":0.0,"contribution":0.13,"interpretation":0.76}},{"i":3,"p":0.9,"id":"s3","own":true,"role":"result","text":"This random lattice model has the low-temperature $c=1$ and high-temperature $c=0$ phases, with the Berezinskii-Kosterlitz-Thouless (BKT) transition separating them.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.54,"main_claim_p":0.19,"quantitative":true,"quantitative_p":0.88,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.9,"background":0.04,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.05}},{"i":4,"p":0.6,"id":"s4","own":true,"role":"result","text":"We map out the phase diagram in the coupling--temperature plane, which is separated by the critical stability curve $T_c(g)$ extending from $g_*< g <0$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.9,"main_claim_p":0.17,"quantitative":true,"quantitative_p":0.76,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.6,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.4,"interpretation":0.0}},{"i":5,"p":0.89,"id":"s5","own":true,"role":"method","text":"We study this curve using the non-perturbative matrix bootstrap and low- and high-temperature perturbation theory, which explain the thermal instability.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.11,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.89,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.11,"interpretation":0.0}},{"i":6,"p":0.67,"id":"s6","own":true,"role":"result","text":"At low temperatures, thermally excited non-singlets backreact on the Fermi sea of matrix eigenvalues, causing it to spill over.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.78,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.67,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.33}},{"i":7,"p":0.68,"id":"s7","own":true,"role":"result","text":"At high temperatures, the theory is described by an effective matrix integral obtained by dimensional reduction on the thermal circle; the eigenvalue distribution of the zero mode becomes unstable at the critical coupling.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.73,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.13,"result":0.68,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.04,"interpretation":0.15}},{"i":8,"p":0.48,"id":"s8","own":true,"role":"interpretation","text":"We conjecture that the BKT transition occurs at a special point on the critical curve and estimate its position.","hedge":{"p":1.0,"label":"speculative"},"own_p":0.83,"main_claim_p":0.22,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.34,"background":0.0,"limitation":0.0,"future_work":0.01,"contribution":0.17,"interpretation":0.48}},{"i":9,"p":0.82,"id":"s9","own":true,"role":"contribution","text":"Finally, we switch to the regular square lattice and study the MQM-inspired Villain model, where the link factor is the one-dimensional propagator on a circle.","hedge":{"p":0.96,"label":"asserted"},"own_p":0.92,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.09,"role_probabilities":{"gap":0.0,"method":0.18,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.82,"interpretation":0.0}},{"i":10,"p":0.44,"id":"s10","own":true,"role":"contribution","text":"Using Monte Carlo simulations, we map out the BKT transition in this model.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.94,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.42,"result":0.14,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.44,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":0.37,"text":"We map out the phase diagram in the coupling--temperature plane, which is separated by the critical stability curve $T_c(g)$ extending from $g_*< g <0$.","location":"abstract s4","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":8390,"cost_usd_reported":0.0},"compiled_at":"2026-10-26","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13.0","abstract_states":{"claims_first":0.04,"states_limitation":0.16,"human_participants":0.01,"controlled_comparison":0.03,"randomized_assignment":0.01,"states_quantitative_result":0.15,"compares_with_prior_results":0.29,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":0.84,"value":"simulation or computation","probabilities":{"argument":0.01,"literature":0.0,"proof_or_derivation":0.15,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.84}},"contribution_type":{"p":0.81,"value":"theoretical result","probabilities":{"review":0.0,"method_or_tool":0.0,"empirical_study":0.0,"simulation_study":0.19,"theoretical_result":0.81,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":0.6,"text":"We map out the phase diagram in the coupling--temperature plane, which is separated by the critical stability curve $T_c(g)$ extending from $g_*< g <0$.","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 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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