lin-0049

2.6 One pattern, different domains

The common architecture does not make the applications interchangeable. Each domain chooses a different sketch, obstruction, quotient, cover, repair language, and admission rule.

Application	Structural promise	Characteristic failure	Repair gate
BRIDGE/SKFM	Visible intervention fields support causal discovery	Lie-bracket nonclosure or unstable extraction	Falsified screen followed by an identified downstream learner
LINCS-KET	Direct and Kan routes agree	Base or tangent route incompatibility	Held-out, blockwise post-training admission
ALLORA	Adapter composition respects intended order	Noncommuting low-rank interventions	Capability and safety preservation
LASKO	Skill sections remain executable under composition	Anchor, bracket-closure, or feasibility failure	Executability and workflow validation
GIRL	Bellman structure factors across computation	Base or tangent Bellman obstruction	Layered policy admission and recovery
LINCS-RLHF	Pairwise preferences support the claimed representation	Cyclic or statistically unsupported scalar reward	Integrability test or relational fallback
RADAR	Private relational charts descend to a shared geometry	Incidence, cocycle, or apex incompatibility	Sparse, decision-preserving repair
SID	Compatible local predictive states realize globally	Compatibility or effectivity failure	Tangential preservation and transverse repair
LINCS-Toulmin	Typed argument roles glue across sources	Warrant, source, qualifier, or rebuttal failure	Typed structural repair certificate

Table 2.1 Nine application-specific realizations of the same LINCS pattern.

Design principle Design principle: What an empirical chapter must retain

An application chapter reports not only the best admitted result, but also the registered probes, failed repairs, incomplete covers, and boundary between the measured object and the broader claim. Negative results are part of the design evidence.