History-Based Evolution (HBE) v3: A Covariant Completion of the Survival-Constraint Framework

History-Based Evolution (HBE) v3 presents the complete covariant formulation of a geometric framework in which late-time cosmic acceleration emerges as a backreaction sourced by the accumulated survival history of matter structures. The framework introduces a constrained auxiliary sector that localizes causal memory accumulation while preserving diffeomorphism invariance and standard General Relativity. Starting from CPT-symmetric boundary regularity at the cosmological origin (the Janus point), HBE v3 constructs a master action that yields a covariantly conserved total stress–energy tensor and a retarded Green’s function governing the evolution of the history field. The formulation ensures that the backreaction sector remains dynamically dormant during radiation and early matter domination, thereby preserving Big Bang Nucleosynthesis and Cosmic Microwave Background observables. The activation threshold Φ₀ is calibrated to the primordial entanglement amplitude r₀ ≈ 0.09 (inferred from large-scale CMB power deficits) via conformal time matching, naturally reproducing the observed onset of acceleration at redshift z ≈ 0.6. The framework identifies mechanisms that may provide partial relief to the Hubble (H₀) and growth (fσ₈) tensions, while maintaining perturbative stability through a constraint-enforced auxiliary sector that is ghost-free and gradient-stable. HBE v3 supersedes earlier phenomenological versions by providing the full covariant foundation underlying history-dependent backreaction and serves as the interior (infrared) completion of the Unified Survival-Constraint (USC) framework. No modification of General Relativity is introduced, and no new particle degrees of freedom are assumed; all effects arise from a covariantly conserved geometric backreaction sourced by realized cosmic history. Version NoteThis version (v3) provides the complete covariant formulation with a first-principles derivation of the backreaction sector and total stress–energy conservation, a retarded Green’s function structure governing causal memory accumulation, and a calibrated r₀ → Φ₀ linkage connecting late-time activation to primordial boundary physics. It clarifies conservation statements to explicitly refer to covariant conservation of the total stress–energy tensor guaranteed by diffeomorphism invariance, tightens the treatment of phenomenological activation parameters, and establishes HBE as the covariant interior completion within the Unified Survival-Constraint framework. No equations, results, numerical estimates, or physical claims are changed relative to earlier v3 drafts. Version Historyv1 (DOI: 10.5281/zenodo.18055910): Initial phenomenological background-level formulationv2 (DOI: 10.5281/zenodo.18067611): Unified survival-constraint framework with regime structurev3 (this version): Complete covariant formulation with master action and first-principles conservation structure