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The upper estimates can exceed the actual errors and do not imply a uniform bound in time.","blocks":[{"kind":"text","nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]}]}},"resolvent_amplification":{"name":"resolvent_amplification","plate":23,"source":"papers/paper-ii/current/editable/traditional/visual_graphics/resolvent_amplification.tex","source_sha256":"530d7d523419e990e1094b5ad83ebd30f319cf5b305b6662b23cc837f8b2bd7f","image":"assets/atlas/paper-ii/resolvent_amplification.png","image_sha256":"41ad51e1d87b46dfb0aec07def910c949c71025d439f649ebe5b4d9b3b63207a","pdf_page":25,"crop_pdf_points":[55,225,557,516],"nodes":[{"text":"$\\frac{5}{2}$","source_text":"$\\frac{5}{2}$","position":[-0.2,4.03],"line":2},{"text":"$\\frac{4}{3}$","source_text":"$\\frac{4}{3}$","position":[0.3,4.03],"line":4},{"text":"$\\frac{11}{5}$","source_text":"$\\frac{11}{5}$","position":[-0.2,3.11],"line":5},{"text":"$\\frac{25}{6}$","source_text":"$\\frac{25}{6}$","position":[0.5125,3.11],"line":7},{"text":"$\\frac{21}{10}$","source_text":"$\\frac{21}{10}$","position":[-0.2,2.19],"line":8},{"text":"$\\frac{100}{11}$","source_text":"$\\frac{100}{11}$","position":[0.88182,2.19],"line":10},{"text":"$\\frac{41}{20}$","source_text":"$\\frac{41}{20}$","position":[-0.2,1.27],"line":11},{"text":"$\\frac{400}{21}$","source_text":"$\\frac{400}{21}$","position":[1.62857,1.27],"line":13},{"text":"$\\frac{201}{100}$","source_text":"$\\frac{201}{100}$","position":[-0.2,0.35],"line":14},{"text":"$\\frac{10000}{101}$","source_text":"$\\frac{10000}{101}$","position":[7.62574,0.35],"line":16},{"text":"$z$","source_text":"$z$","position":[-0.2,4.65],"line":17},{"text":"$\\|C R_f-R_c C\\|_\\infty/\\varepsilon$","source_text":"$\\|C R_f-R_c C\\|_\\infty/\\varepsilon$","position":[4.0,4.65],"line":18},{"text":"Exact rational samples; the point $z=2$ itself is excluded.","source_text":"Exact rational samples; the point $z=2$ itself is excluded.","position":[4.7,-1.15],"line":19}],"node_order":[0,1,2,3,4,5,6,7,8,9,10,11,12],"reading_aid":{"alt":"Five exact amplification samples near a pole","description":"Each bar corresponds to its labeled rational spectral parameter. The rows are separate samples rather than equally spaced axis values; the local defect coefficient is divided out.","blocks":[{"kind":"text","nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12]}]}}},"included_sources":{"generated/current_visual_scope.tex":{"source":"papers/paper-ii/current/editable/traditional/generated/current_visual_scope.tex","sha256":"427113db02cb17d7642fbf048d9cb1c5a1f20452d769eb3d132d0d4ab25a0480","text":"\\textbf{Current Lean scope.} 53 of 53 proof-level source records have kernel checked, semantically accepted scope. No partial or pending proof records are listed in this correspondence. 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