7. Sources and conceptual synthesis

Fong and Spivak’s Seven Sketches in Compositionality develops category-theoretic constructions through several applications. The available MATH bodies use particular constructions, including paths and interpretation; they retain direct finite calculation as an alternative when it suffices. The Suite uses composition across practices without requiring one mathematical foundation for every inquiry. The MATH Preface supplies further source comparisons for universal algebra, constructive proofs, symmetry and variation.

Sussman and Wisdom’s Structure and Interpretation of Classical Mechanics, Preface, connects physical investigation, mathematical notation and executable procedures. Its functional notation exposes operations hidden by conventional expressions. This supports an important direction here: recover what each expression asks its interpreter to do. Mechanics and Scheme are the book’s worked setting; they do not set the Suite’s subject or language requirements.

Frigg and Hartmann’s Models in Science distinguishes questions about what models are, how they represent and how they support knowledge. The MMP Preface develops its adopted source comparisons further, including Nguyen and Frigg, SIMULA history and equation-based modeling. The Suite consequently asks which use of a model is intended and how its result is obtained and interpreted, instead of prescribing one carrier for every model.

Rodin’s Axiomatic Method and Category Theory compares different ways of forming axiomatic theories, including constructive and categorical approaches. Its methodological question helps explain why this architecture includes operations as objects, comparison of interpretations and changes of axioms. A difference in permitted constructions or equality can itself be investigated. The selected methods let the reader examine such a difference while retaining the grounds specific to each mathematical account.

Dutilh Novaes’s Formal Languages in Logic studies formal languages as tools used in human reasoning, including their historical and cognitive effects. This contributes a different question from whether a string is well formed: which reasoning operations does the notation make accessible, difficult or implicit? Notational Engineering therefore includes interpretation and reader-use changes, alongside expression rules. Extending these methods to AI or embodied carriers is part of this Suite’s synthesis; claims about human cognition retain their own scope.

Marletto, Deutsch and Vedral’s Tests of Constructor Theory, especially §§1.4 and 3.2, compares allowed evolution with repeatable performance of a transformation. This informs the separate attention to preparation, physical means, attainable transformations and their limits. Its new physical principles are proposals accompanied by tests. A physical method here must state the principles its consequence uses, so that a different physical account can be compared at the affected premise. This preserves the source’s methodological contribution without making acceptance of its whole physical programme a prerequisite.

Risi, Tang, Ha and Miikkulainen’s Neuroevolution: Harnessing Creativity in AI Agent Design develops complete constructions for obtaining, combining and continuing neural behavior. Section 3.10 connects those constructions to their receiving uses and the existing FPF, computational and modeling methods. The book provides the sustained applied explanation; particular primary accounts supply algorithm details and comparisons. The application retains corrections where they change the work, including the walking environment’s observations and reward, the complete CMA-ES update, stochastic action, bounded retention and the salamander model’s actual construction. Evolutionary search, gradient learning, direct design and their combinations are alternatives whose task, information and complete costs must be compared. The cited newer constructions change particular available choices; neither the book nor this synthesis establishes an exhaustive current ranking or a verified implementation of every method.

The organization here is a conceptual synthesis: retaining each contribution’s conditions, connecting knowledge with its application, and making the methods themselves available for criticism and change. The small cross-practice cases explain this construction; they do not establish a general learning effect. A changed source matters when it changes an operation, premise, cost, interpretation or useful result. Return to that body’s source discussion for the corresponding decision.