Signposts for the journey

Three distinctions prevent most misreadings of the framework.

1. Obstruction is not loss. A scalar may observe or rank a typed failure, but it does not exhaust the failed structural promise.

2. Diagnosis is not authority. A localized obstruction may motivate a repair without identifying its cause or licensing a change.

3. Infinitesimal coherence is not finite success. Tangent agreement must be transported, tested, and admitted before it supports a deployment or scientific claim.

With those signposts in view, the long theoretical ascent has a practical destination. The applications do not merely illustrate category theory. They test whether one disciplined sequence—declare, differentiate, quotient, localize, repair, and admit—can make very different learning systems more inspectable and actionable.