The c-Budget: Speed, Structure, and the Seam A First-Principles Exploration of the Twin Paradox and Wave-Particle Duality

This paper explores what follows when the speed of light is understood not as a constraint on a single physical process but as the total structural budget distributed across the seven-operator chain of Structural Primitive Architecture (SPA). Beginning with the twin paradox and working toward wave-particle duality and wave-function collapse, I trace a continuous argument from first structural principles. The central claims have different evidential weights, which I flag throughout: (1) time and space are structural inverses grounded in the H/K operator duality, and the Minkowski metric signature may encode this inversion — proposed, derivation open; (2) the twin paradox is a redistribution of c-budget from temporal Actualization into spatial Orientation, made permanent by K-irreversibility — argued structurally; (3) the photon is a limiting structural case, absent from the K-type operator dimensions and propagating as a wave because it cannot localize — argued structurally; (4) wave-function collapse is seam-breaking by an external H > K structure — argued structurally, with the uniqueness-of-outcome question left explicitly open; and (5) the Born rule may find a structural reading in the Gradientation operator, for monochromatic plane waves only — suggested, generalization open. This is theoretical philosophy of physics: an exploration from first principles whose goal is to open a direction of inquiry, not to close one.