MART/KTA RMEM2 V5: Dynamic Spacetime-Film Reconstruction and Conditional No-Ghost Candidate

MART/KTA RMEM2 V5: Dynamic Spacetime-Film Reconstruction and Conditional No-Ghost Candidate This V5 release extends the fixed-RMEM2 validation baseline established in MART/KTA RMEM2 V4/V4.1 into a broader reconstruction and falsification-stage program. The physical motivation behind MART/KTA is the picture of spacetime as a deformable geometric response medium. In this analogy, the homogeneous FRW universe is the unperturbed expanding spacetime film, similar to a smooth soap-bubble membrane or expanding spacetime fluid. Local deviations from homogeneous expansion generate first-order geometric strain. Nonlinear self-coupling transports this strain, and the accumulated response history produces an effective relaxation memory. MART/KTA uses this analogy only as a structural guide, not as a literal material model. V4.1 was intentionally limited to a fixed effective-response table in CLASS/Cobaya, tested through equal-sampled-parameter table-off/table-on comparisons across M3D, M4a–M4g and the M4h BAO DR2 extension. The V4.1 M4h comparison yielded: χ²_off = 2793.7857χ²_on = 2784.3369Δχ² = ΔAIC = ΔBIC = −9.4488 with no additional sampled RMEM2 parameter. V5 takes this fixed-table baseline as a reproducible validation anchor and asks whether the same response pattern can be dynamically reconstructed, stress-tested or falsified without introducing unconstrained new degrees of freedom. The V5 release contains six main development branches. 1. Dynamic RMEM2 reconstruction V5 introduces a no-free-parameter dynamic RMEM2 reconstruction candidate. In the spacetime-film analogy, RMEM² is not an externally imposed table. It is the effective memory of the geometric response medium: local deformation generates transport activity, and the causal relaxation history of this activity produces the memory state. The aim is to test whether the fixed RMEM2 response used in V4/V4.1 can be recovered, approximated or falsified from the M3D–M4h validation sequence without treating RMEM2 as a fitted table amplitude. For M4h / BAO DR2, the V5m dynamic RMEM2 candidate reproduces the fixed-RMEM2 table-on branch essentially exactly: χ²_off = 2793.7857χ²_fixed = 2784.3369χ²_V5m = 2784.3339Δχ²_V5m−off = −9.4518Δχ²_V5m−fixed = −0.0030 Thus, in the M4h BAO DR2 test, the dynamic V5m reconstruction recovers the fixed-response improvement to within numerical diagnostic precision. For M4g, V5m remains on the RMEM2 improvement branch but is weaker than the fixed-table diagnostic: Δχ²_V5m−off = −7.3246Δχ²_V5m−fixed = +2.2843 This supports V5m as an empirically viable dynamic reconstruction candidate, while keeping the comparison falsifiable. 2. Fixed versus dynamic RMEM2 comparison V5 directly compares the fixed V4/V4.1 RMEM2 table against the dynamic V5m reconstruction. The fixed table is not treated as fundamental. It is used as a validation anchor for testing whether a dynamic no-free-parameter response can reproduce the same growth/lensing branch across the likelihood ladder. The M4h result provides the strongest fixed-versus-dynamic agreement: Δχ²_fixed = −9.4488Δχ²_V5m = −9.4518 The M4g result remains positive relative to table-off but weaker than fixed table-on, making it a useful stress test rather than a trivial confirmation. 3. CDM-sector stress test V5 includes controlled CDM-sector stress tests to probe how strongly the RMEM2 response depends on the assumed cold-dark-matter contribution. This branch is explicitly falsification-oriented. It is not a claim that MART/KTA replaces dark matter. Allowed statement: The CDM-sector tests provide diagnostic evidence about the dependence of the RMEM2 response on the assumed CDM contribution. Not claimed: MART/KTA replaces cold dark matter. 4. Boundary-phase and membrane stress tests V5 explores whether the same relaxation-memory structure can act as a boundary-phase diagnostic for early-universe and black-hole-like regimes. In the spacetime-film analogy, expansion corresponds to relaxation of the film-like response medium, while collapse can drive the memory sector into an anti-damping branch. V5 treats this not as a completed black-hole or big-bang transition theory, but as a possible signal that the effective cosmological response approaches a boundary-phase or reset regime. Allowed statement: V5 introduces exploratory boundary-phase diagnostics motivated by the relaxation-memory structure. Not claimed: V5 proves singularity avoidance or black-hole/big-bang transition physics. 5. Covariant MART/KTA V5.0-M0 candidate V5 introduces V5.0-M0 as a closed mathematical candidate for a Bianchi-compatible MART/KTA response hierarchy. The candidate structure is: MART^(1) → KTA^(2) → R_mem² → X_μν → V_ν → ΔG_μν^(V5.0) MART is defined as a first-order local geometric-flow deviation from homogeneous FRW expansion. KTA is defined as a second-order trace-free self-coupled transport response. RMEM² is defined as a third-order causal memory state generated by the KTA activity history. The raw memory-stress response X_μν is completed by an induced relaxation current V_ν, so that the final geometric response is divergence-free: ∇^μ ΔG_μν^(V5.0) = 0 This makes V5.0-M0 a Bianchi-compatible mathematical candidate, but not yet a completed fundamental theory. Open tasks remain: action derivation, causal Green-function prescription, well-posedness, perturbation reduction, strong-gravity extension and full stability proof. 6. Ghost and stability-boundary diagnostics V5 adds an explicit ghost- and stability-boundary layer to the MART/KTA reconstruction program. The release includes a bounded no-ghost analysis within the explicitly defined localized first-order auxiliary/constrained V5-M0 completion. Allowed interpretation: V5 provides conditional no-ghost evidence within the explicitly defined localized first-order auxiliary/constrained V5-M0 action/completion class. This means that the no-ghost statement is restricted to the defined auxiliary/constrained completion in which the induced current V_ν is not introduced as an arbitrary freely propagating new vector sector with unconstrained couplings. Not claimed: V5 proves universal covariant ghost freedom for all MART/KTA theories. The full universal ghost/stability question remains open and requires a complete covariant perturbation analysis. Package contents The V5 release candidate includes: dynamic RMEM2 reconstruction evidence, fixed-versus-dynamic RMEM2 comparisons, M4g and M4h V5m full-MCMC audit material, CDM-sector stress-test diagnostics, boundary-growth and membrane-style exploratory stress tests, V5.0-M0 covariant mathematical candidate material, conditional no-ghost / stability-boundary analysis, claim-boundary validation, unit tests, smoke tests, artifact-reference audit, source-clean and privacy-clean checks, documentation distinguishing V4.1 fixed-response claims from V5 candidate-level claims. Scientific scope and claim boundary This release is a V5 reconstruction and falsification-stage candidate. It does not claim that MART/KTA is already a completed fundamental theory. It does not claim that RMEM2 replaces dark matter. It does not claim to solve the Hubble tension or the S8 tension. It does not claim singularity avoidance. It does not claim universal covariant ghost freedom. The central V5 claim is narrower: V5 fulfills the V4.1 outlook as a stress-test and reconstruction-stage candidate: it tests dynamic RMEM2 reconstruction against the fixed response, compares fixed and dynamic branches across M4g and M4h, includes CDM-sector stress tests, develops boundary-phase diagnostics, introduces a Bianchi-compatible V5.0-M0 covariant candidate, and adds a bounded no-ghost/stability analysis within an explicitly defined auxiliary/constrained completion. Outlook The next stage, V6, will focus on the induced relaxation-current sector V_ν. In V5.0-M0, V_ν is introduced as a constrained Bianchi-completion current. V6 will investigate whether V_ν should be understood as a non-propagating projection/constraint current or as a physical relaxation-flow degree of freedom. The V6 program will require: causal Green-function prescription, action-level treatment of V_ν, well-posedness analysis, perturbative cosmological reduction, ghost/tachyon diagnostics, strong-gravity and boundary-phase consistency tests. Thus, V5 does not close the MART/KTA theory program. It converts the V4.1 fixed-response validation into a dynamic reconstruction, stress-test, boundary-diagnostic and conditional stability-analysis program.