lin-0224
18.7 The SID controller
Sheaf Infinitesimal Descent
Estimate local predictive updates \(u_i\)
Evaluate typed compatibility and effectivity witnesses
Localize each witness to its incident cover simplices
Solve for admitted tangent corrections \(a_i\)
Retract \(x_i\leftarrow \operatorname {Ret}_{x_i}(u_i+a_i)\)
Audit pair, triple-overlap, and global-realizability conditions
Promote, damp, quarantine, collect data, or revise the cover
|
Method |
Primitive |
Structural consequence |
|---|---|---|
|
Glue loss |
scalar tradeoff |
approximate pair agreement |
|
Augmented Lagrangian |
equality plus duals |
solver-dependent feasibility |
|
Projection |
realized constraint |
direct local feasibility |
|
SID |
descent sketch and repair lift |
typed compatibility, effectivity, localization, and admission |