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