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Contents 1 Preface 2 Views and coherent realizations 3 The additive obstruction and the space of extensions 4 Changing what is prescribed 5 Resolution towers and exact transport 6 Finite observations and realized transformations 7 Banach repair and constructed split coordinates 8 Repair under a change of representation 9 Multiscale residuals and the limits of reconstruction 10 Nonabelian coherence and relative trivialization 11 A boundary identification is data 12 Coherence need not mean removable phase 13 Graph views, holonomy, and reconstruction 14 Reading a stability certificate 15 A geometry of transformations needs its own cost 16 Exactification without a fixed contraction rate 17 The residual floor and the closure of admissible changes 18 Exact finite repairs can escape the intended ambient space 19 A bounded repair budget can recover existence 20 The attainable residual at a fixed correction budget 21 Regularization selects a protected correction 22 A complete regularization diagnostic for the escaping model 23 Certifying an inexact protected correction 24 Coordinates, noise, and a justified stopping rule 25 A closed signal loop 26 Mathematical meaning and the remaining boundaries 27 A reader's workshop 28 A hypothesis atlas 29 Notation and formal correspondence 30 Claim correspondence 31 Using the correspondence 32 Proof and formal verification 33 Analytic facts used in the proofs 34 Background and references 35 References PDF and companion guides The chapters retain the manuscript wording, hypotheses, and recorded limits. The original PDF and companion files remain available above.
