10.8 DIAL-ALLORA: the target is an admitted adapter composition

ALLORA studies ordered adapter composition. Its operational target is a deployable composite of task, domain, capability, or safety adapters. Its structural target is the adapter incidence and factorization sketch, including which adapters share a backbone, which quotient directions are identified, and which orders are promised to agree. Its epistemic target combines held-out task behavior, safety constraints, order robustness, and resource cost.

For two typed adapter updates \(U_i\) and \(U_j\), the two DIAL sides are their separately coherent specialization processes. The first mixed proxy is the order defect

augmented by cross- and nested-bracket observers when the application declares them. Small or quotient-null interaction may be assimilated by an ALLORA regularizer or order schedule. Persistent localized interaction may instead motivate a finite composition test. The system applies the proposed composite over a registered sequence of contexts or layers and tests path-order stability, capability retention, and safety persistence. If the candidate remains coherent, it is an integrated repair inside the current adapter theory. Reproducible failure triggers stronger-search, observer, and representability controls. Only a registered argument ruling out the relevant in-theory repair class opens a typed proto-accommodation proposal: refactor the adapters, introduce a shared module, change the quotient, split capability from safety, or revise the declared composition graph.

The target is not a zero commutator at any cost. Two adapters can commute by becoming behaviorally useless. Conversely, a nonzero interaction may be admissible when it is typed, localized, and improves the declared task without violating safety. DIAL-ALLORA therefore retains both the structural witness and the behavioral certificate.

Here the creativity distinction is especially concrete. Searching for a new useful ordering or composite of known adapters is combinational creativity if the composite is absent from the reference library. Exploring a large typed composition space is exploratory creativity. Introducing a new shared module, adapter type, or composition rule is transformational. Merely selecting the best registered ordering is optimization, even when DIAL supplies the routing signal.