A minimal realized bounded-transient extension around the GR-exact branch in flux-fixed GR

A minimal realized bounded-transient extension around the GR-exact branch in flux-fixed GR (v2.0.0) On the GR-exact, flux-fixed branch of the gauged constant vacuum-mode (GCV) framework, local gravity obeys the Einstein equation with a flux-fixed integration constant Λeff, while the strictly spacetime-constant vacuum mode is excluded from local sourcing. A previous note defined a conservative bounded-transient extension class around that baseline. The present paper realizes that extension class explicitly. Two minimal realized profiles are studied. The first is a matter-tracking transient that serves as a proof of concept that the bounded-transient class is non-empty. The second is a normalized hump-shaped transient designed to localize the geometry excursion inside the late-time survey window while preserving the same bounded-transient requirements. The realized departures are constructed to remain: excitation-driven vacuum-subtracted (no new constant mode) bounded by a small parameter transient relative to the flux-fixed Λ background The paper derives the induced geometry departure, the corresponding fractional shift in the Hubble rate, and the associated ruler-free Alcock–Paczynski geometry signal. For benchmark realizations, the hump-shaped profile produces a small, localized late-time geometry excursion with peak effect near the matter–Λ transition and a structured AP signature, including a sign change at higher redshift. This provides a concrete survey-facing realization of the bounded-transient class. Scope and claim boundary This paper does not claim evidence for departures in current data. It does not claim to disprove evolving dark energy with present observations. It does not modify the core GCV claim that the cosmological-constant problem is closed on the GR-exact branch. It does not propose a unique UV completion for the realized excitation sector. Its purpose is narrower: to show that the bounded-transient extension class is explicitly realizable, to characterize the resulting late-time geometry signatures, and to provide a concrete falsifier-oriented interface for future observational tests. Positioning within the GCV programme The published GCV default remains the GR-exact late-time branch. The previously released optional response sector remains growth-only on a fixed background. The present note studies a stronger but still controlled extension in which small bounded transient geometry excursions are allowed without reintroducing a local constant mode. Files in this record PDF manuscript Project homepage: https://johansson.digital Project overview hub: https://github.com/gcv-framework/gcv-vacuum-energy