Public articles linked to the same research event.
arXiv The authors propose a topological model representing knowledge states and preregistered capability probes as subcomplexes of a finite regular CW complex, prove that attaching a single n-cell can only create a class in H_n or kill a class in H_{n-1}, treat the reliability threshold and the training checkpoint as two parameter axes so that capability gains and losses make the spaces along the training axis nonnested, use union or intersection bridges to build zigzag persistence modules distinguishing checkpoint, transition, and bridge-sensitive classes, and compute a finite four-stage example via boundary matrices.
The authors propose a topological model representing knowledge states and preregistered capability probes as subcomplexes of a finite regular CW complex, prove that attaching a single n-cell can only create a class in H_n or kill a class in H_{n-1}, treat the reliability threshold and the training checkpoint as two parameter axes so that capability gains and losses make the spaces along the training axis nonnested, use union or intersection bridges to build zigzag persistence modules distinguishing checkpoint, transition, and bridge-sensitive classes, and compute a finite four-stage example via boundary matrices.
The authors propose a topological model representing knowledge states and preregistered capability probes as subcomplexes of a finite regular CW complex, prove that attaching a single n-cell can only create a class in H_n or kill a class in H_{n-1}, treat the reliability threshold and the training checkpoint as two parameter axes so that capability gains and losses make the spaces along the training axis nonnested, use union or intersection bridges to build zigzag persistence modules distinguishing checkpoint, transition, and bridge-sensitive classes, and compute a finite four-stage example via boundary matrices.
The authors propose a topological model representing knowledge states and preregistered capability probes as subcomplexes of a finite regular CW complex, prove that attaching a single n-cell can only create a class in H_n or kill a class in H_{n-1}, treat the reliability threshold and the training checkpoint as two parameter axes so that capability gains and losses make the spaces along the training axis nonnested, use union or intersection bridges to build zigzag persistence modules distinguishing checkpoint, transition, and bridge-sensitive classes, and compute a finite four-stage example via boundary matrices.