Relational Continuity: A Unified Framework of Geometry, Perspective, Memory, and Physical Invariance Foundational Architecture, Symmetry, Synchronization, Holonomy, Observability, and Conditional No-Go Results

This research collection presents the development of Relational Continuity, a unified theoretical framework investigating the mutual determination of physical relations, geometry, boundaries, time, observer perspectives, memory, and recursive organization. The central hypothesis proposes that these are not independent foundational mechanisms subsequently connected, but mutually constrained aspects of a single physically realized relational configuration. Different internal perspectives may produce distinct observable descriptions while preserving appropriately defined physical invariants. The collection brings together three complementary manuscripts: 1. Foundational Architecture — One Boundary and Internal Perspectives (MASTER v17, October 28, 2026). Develops the relational foundation through a single boundary organization, endogenous perspectives, geometric compatibility, Formation, Relic, Re-entry, and the preservation of physically consequential distinctions. 2. Symmetry and Synchronization (MAIN v41, November 10, 2026). Extends the framework through recursive mutual perspectives, symmetry, synchronization, higher-order relational structure, observer–observed identity at the level of relational organization, and the compatibility of local descriptions within a shared whole. 3. Physical Realization — Holonomy, Observability, and No-Go (MAIN v44, November 13, 2026). Introduces an explicit photonic-network realization connecting propagation, internal observer access, gauge-invariant loop holonomy, and exact effective descriptions. A three-resonator model demonstrates that configurations with identical spectra and graph connectivity can produce different measurable responses at fixed observation ports. This establishes a model-specific obstruction to reductions that discard physically consequential relational information. The mathematical framework distinguishes established model-dependent results, conditional no-go statements, foundational hypotheses, and unresolved physical questions. Together, the manuscripts consolidate the broader Ψ–SAF–FRDL–SERA–Relational Continuity research program and establish a foundation for investigating whether a stronger, substrate-independent physical constraint can be derived from relational compatibility, recursive organization, and the preservation of observable consequences.