FCD-HAT: Frame-Constrained Dynamics (FCD)

FCD-HAT introduces Frame-Constrained Dynamics (FCD) as a transversal research program devoted to the conditions, limits, and consequences of finite implemented access. FCD studies what can and cannot be jointly guaranteed when observation, prediction, representation, control, inversion, and validation are performed through finite operational frames. It does not deny the possibility of successful local science: measurements, proofs, models, reconstructions, and control procedures may remain valid, robust, and useful for their declared tasks. Its central question is whether all relevant guarantees can be preserved simultaneously within one finite implementation. The current working basis of FCD is defined through finite informational access, operational locality, constrained feedback, and scale separation through non-isomorphic projections. Implemented access is represented structurally as a pipeline involving interaction or execution, finite encoding, and task-dependent restriction or projection. Under sufficiently rich and explicitly declared conditions, local closure may remain operable while complete observability, control, prediction, stable inversion, frame-independent accessible content, exhaustive validation, and global closure cannot in general be jointly maintained. FCD is presented here as a versioned research basis rather than a completed solution. Its present axioms and structural principles define the current domain of investigation, but their minimality, independence, and possible reduction to a smaller basis remain open research questions. Exact theorem statements, proofs, calculations, and paper-level falsification conditions remain those of the cited source papers. A colour-and-scale example provides an accessible illustration of the framework. A fine frame may preserve distinct local colour components and their positions, while a coarser frame may produce a stable global white or achromatic record. The global record can be real and useful within its frame while no longer preserving the unique local decomposition that produced it. The example illustrates frame dependence without arbitrariness, non-injective closure, loss of local distinctions under globalisation, and the persistence of compatible possibilities outside the current record. It is an explanatory example, not a proof of FCD or a general theory of vision. The paper organizes the research program through a canonical 3+1 architecture: FCD-CORE contains the current working assumptions, foundational limits, conjunctive non-totalization problems, finite certification bounds, implemented-pipeline structures, and methodological rules. FCD-TITAN studies the general consequences that may follow when persistent non-closure is combined with continued operability, including constrained reorganization, ordering, historical dependence, and pre-metric temporal asymmetry. Domain papers formalize, calculate, test, reproduce, restrict, or reject precise claims in mathematics, physics, quantum and classical systems, spectral analysis, particle physics, and other concrete domains. These routes may originate directly in CORE, through TITAN, or through both. FCD-ONTO is an optional and firewalled downstream branch exploring stronger reconstructions concerning time, law, matter, mathematics, and observable reality. ONTO cannot validate CORE or TITAN retroactively. The distinction between CORE and domain-level mathematics is made explicit. Mathematics at the CORE level concerns the general conditions and limits of implemented mathematical representation, construction, inversion, translation, and verification. Domain Mathematics concerns particular theorems, formal proofs, Lean developments, dependency audits, and exact mathematical constructions. The HAT also identifies four high-value research directions that could support, but not confirm, FCD: the derivation of temporal structure from persistent non-closure and continued operability; the emergence of distinct mathematical and physical organizations from a common pre-domain closure deficit or residual burden; the derivation of matter-like carriers without assuming matter as primordial; the derivation of laws, constants, fixed points, or attractor-like structures through explicit constrained dynamics and compatibility filtering. FCD-HAT states equally explicit directions by which the program may be restricted or falsified. These include a finite totalization witness under the exact hypotheses of a declared CORE statement, a lossless finite unification of predeclared distinct frames under a fixed resource envelope, or a demonstrated persistent overload that remains operable without restriction, transfer, compression, reorganization, or hidden resources. No paper is protected merely by belonging to the FCD corpus. Each paper is required to state: its central claim; an explicit kill condition. If the kill condition is satisfied under the declared hypotheses and scope, the claim must be revised, restricted, or abandoned. Failure propagation applies only through genuine dependencies: the rejection of a domain result does not automatically refute CORE, but no adverse result may be immunized by being relocated to another layer after the fact. This preprint serves as the conceptual and navigational HAT of the FCD corpus. It provides the current structural basis, explains the 3+1 architecture, clarifies the status of claims and axioms, maps the currently verified public papers, and offers reading routes through the program. It is not a fifth scientific layer and does not replace the detailed manuscripts, formal proofs, datasets, scripts, reproducibility packages, or limitations of the papers it references. FCD can die. So can every paper written in its name. Once their falsification conditions are public, evidence—not authorship—must decide what survives.