{"paper":{"title":"The Type-I Seesaw as a Relativistic Fermionic Proximity Effect: Spectral Moments, EFT Consistency, and Sterile-Sector Reconstruction","arxiv_id":"2609.00888","primary_cat":"hep-ph","submitted_at":"2026-09-01T08:19:29+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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its positive normal support supplies a common annihilator, although anomalous residues can cancel at exact degeneracy.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.75,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.13,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.87,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.13}},{"i":7,"p":0.82,"id":"s7","own":true,"role":"result","text":"We prove normal block-Hankel positivity and positivity of a dimensionally rescaled mixed Nambu-Hankel sequence.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.1,"quantitative":false,"quantitative_p":0.13,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.82,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.18,"interpretation":0.0}},{"i":8,"p":0.48,"id":"s8","own":true,"role":"result","text":"The latter gives matrix Cauchy-Schwarz inequalities between lepton-number-conserving and lepton-number-violating data and can reveal paired directions hidden by a degenerate normal residue.","hedge":{"p":0.68,"label":"hedged_possibility"},"own_p":0.85,"main_claim_p":0.1,"quantitative":false,"quantitative_p":0.37,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.48,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.04,"interpretation":0.46}},{"i":9,"p":1.0,"id":"s9","own":true,"role":"result","text":"Isolated nondegenerate pole residues satisfy an additional nonlinear compatibility identity.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.83,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.09,"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":10,"p":0.42,"id":"s10","own":true,"role":"contribution","text":"These results yield tree-level EFT consistency tests and a matrix-pencil reconstruction of visible pole and aggregate-residue data; selecting a unique ultraviolet Lagrangian requires additional information about sterile-basis multiplicities.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.92,"main_claim_p":0.61,"quantitative":false,"quantitative_p":0.13,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.31,"background":0.0,"limitation":0.07,"future_work":0.0,"contribution":0.42,"interpretation":0.19}},{"i":11,"p":0.62,"id":"s11","own":true,"role":"result","text":"An exact one-generation example distinguishes the static Schur-complement kernel from the physical Takagi pole mass.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.87,"main_claim_p":0.05,"quantitative":true,"quantitative_p":0.53,"role_probabilities":{"gap":0.0,"method":0.06,"result":0.62,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.3,"interpretation":0.02}},{"i":12,"p":0.59,"id":"s12","own":true,"role":"interpretation","text":"The proximity structure applies without a Fermi surface or condensate, and Nambu doubling introduces no new physical degrees of freedom.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.69,"main_claim_p":0.1,"quantitative":false,"quantitative_p":0.17,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.4,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.59}}]},"compiled":{"main_claim":{"p":0.9,"text":"These results yield tree-level EFT consistency tests and a matrix-pencil reconstruction of visible pole and aggregate-residue data; 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