Stochastic Rupture as an Information-Bounded Mechanism for Objective Wave-Function Collapse: Field Dynamics, Trigger Regime, and the Arrow of Time

We present a consolidated formulation of Stochastic Rupture (SR), an objective wave-function collapse framework in which branch selection is triggered bythe local saturation of an informational bound on covariant causal-diamond surfaces. The framework is built on three interlocking layers: (i) a Lindblad masterequation with collapse operator Lˆ = x/σ ˆ x, modulated by a divergent saturationfeedback F(χ) = (1 − χ)−1 where χ = SvN/(η IBek); (ii) a covariant field equation ∇µ∇µχ = S −Γ0χ−αχ2 for the saturation scalar promoted to a dynamical degree offreedom; and (iii) a trigger regime hierarchy establishing that pruning fires only whenlocal saturation crosses threshold, leaving isolated microscopic systems empirically Equivalent to standard quantum mechanics. We make six principal contributions inthis consolidated edition: we derive the decoherence rate Γdec = γ(t) d 2/(4σ 2x) from the Lindblad structure rather than postulating it; we identify a qualitatively new prediction (Regime IV) for high-entanglement systems with no spatial superposition,absent from both Di´osi–Penrose and Continuous Spontaneous Localization; we derivethe arrow of time as a structural consequence of the nonlinear sink −αχ2 via Lan-dauer’s principle, unifying the thermodynamic, radiation, and quantum measurementarrows; we compute cosmological heating rates 15–27 orders of magnitude belowCSL in diffuse environments; we develop the 4D Rose as a visualization choicethat preserves parity violation and unequal-amplitude branching; and we articulate framework scope explicitly. The framework is observationally indistinguishable from standard quantum mechanics—and indeed from Di´osi–Penrose—in all currently accessible regimes, because the saturation feedback F(χ) is essentially unity throughout the parameter space of contemporary matter-wave interferometry and levitated optomechanics. Discrimination from DP and CSL is therefore concentrated in three structurally distinct regimes: macroscopic entangled-memory systems with no spatialsuperposition (Regime IV), time reversed interferometric protocols, and precisionthermodynamic measurements in varying gravitational potential