This V4.1 release provides a source-clean, externally rebuildable MART/KTA RMEM2 validation package for a fixed effective-response table in CLASS/Cobaya. The release tests a fixed RMEM2 response table in equal-sampled-parameter table-off/table-on comparisons. No additional sampled RMEM2 parameter is introduced in the table-on configuration. The active table-on closure is: ΔKTA = R_mem · S,Σ = 1 + ΔKTA,μ = 1 − R_mem²(Σ − 1),η = 2Σ/μ − 1, with a GR fallback at z > 5. The V4.1 release contains two main joint validation branches: M4g:Planck high-ℓ + BAO DR1 + growth + supernova + direct-S8 data. M4h:Planck high-ℓ + BAO DR2 + growth + supernova + direct-S8 data. The main full-MCMC V4 result is the M4g comparison using Planck, BAO DR1, growth, supernova and direct-S8 data: table-off χ² = 6590.9958352table-on χ² = 6565.2618842Δχ² = ΔAIC = ΔBIC = −25.7339510 The V4.1 BAO DR2 extension is the M4h comparison using Planck, BAO DR2, growth, supernova and direct-S8 data: table-off χ² = 2793.7857table-on χ² = 2784.3369Δχ² = ΔAIC = ΔBIC = −9.4488 Because the table-on and table-off runs use the same sampled cosmological parameter set, ΔAIC and ΔBIC coincide with Δχ² for these fixed-table comparisons. Fitted and tested data combinations included in V4/V4.1: M3D:Planck high-ℓ validation / sigma8-S8 drift audit. M4a:Planck 2018 high-ℓ TTTEEE + low-ℓ TT/EE baseline comparison. M4b:Planck 2018 high-ℓ TTTEEE + low-ℓ TT/EE + BAO DR1 comparison. M4c:Planck 2018 high-ℓ TTTEEE + low-ℓ TT/EE + BAO DR1 comparison. M4d:Planck 2018 high-ℓ TTTEEE + low-ℓ TT/EE + BAO DR1 + growth comparison. M4e:Planck 2018 high-ℓ TTTEEE + low-ℓ TT/EE + BAO DR1 + growth full comparison. M4f:Planck 2018 high-ℓ TTTEEE + low-ℓ TT/EE + BAO DR1 + growth + supernova comparison. M4g:Planck 2018 high-ℓ TTTEEE + low-ℓ TT/EE + BAO DR1 + growth + supernova + direct-S8 comparison. M4h:Planck 2018 high-ℓ TTTEEE + low-ℓ TT/EE+ BAO DR2 + growth + supernova + direct-S8 comparison. Parameter drift audit from M3D to M4h: Run Δχ² ΔH0 ΔΩm Δσ8 ΔS8 ΔωcdmM3D +0.01919 +0.01207 −0.00023 −0.04840 −0.04886 −0.00005M4a −4.23794 +0.86688 −0.01171 −0.03156 −0.04760 −0.00193M4b −1.80050 +0.70774 −0.00892 −0.03644 −0.04861 −0.00138M4c −4.84028 +0.62897 −0.00849 −0.02930 −0.04098 −0.00144M4d −4.44126 +0.58534 −0.00756 −0.02407 −0.03446 −0.00118M4e −16.90111 +0.23660 −0.00289 −0.02116 −0.02519 −0.00043M4f −16.34993 +0.21888 −0.00235 −0.02857 −0.03194 −0.00027M4g −25.73395 −0.12273 +0.00174 −0.01929 −0.01697 +0.00032M4h −9.44880 +0.01342 −0.00002 −0.01551 −0.01551 +0.00002 For M4g, the best-fit values are: Parameter table-off table-on Δ(table-on − table-off)H0 68.579775 68.457043 −0.122732omega_b 0.022476 0.022468199 −0.000007801omega_cdm 0.11835702 0.11867543 +0.00031841tau_reio 0.051289785 0.049876208 −0.001413577A_s 2.072676e−09 2.073223e−09 +5.47e−13n_s 0.96775788 0.96743826 −0.00031962A_planck 0.99916272 1.0001324 +0.00096968 For M4g, the direct sigma8/S8 drift audit gives: Δσ8 = −0.01928819ΔS8 = −0.01697029 For M4h, the full-MCMC BAO DR2 table-off/table-on comparison gives: Parameter Δ(table-on − table-off)χ² −9.448800H0 +0.013418Ωm −0.00002161ωcdm +0.00001802σ8 −0.01550752S8 −0.01550718 The M4h BAO DR2 chains are audit-level converged: M4h table-off:R−1 = 0.018478R−1_cl = 0.089277 M4h table-on:R−1 = 0.010340R−1_cl = 0.085126 The M3D Planck high-ℓ absolute post-processing values are: Parameter table-off table-on Δ(table-on − table-off)χ² 576.76109 576.78028 +0.01919H0 68.416363 68.428429 +0.012066Ωm 0.301921 0.301696 −0.000225σ8 0.863623 0.815224 −0.048399S8 0.866384 0.817525 −0.048859ωcdm 0.118827 0.118775 −0.000052A_s 2.324360e−09 2.180392e−09 −1.43968e−10n_s 0.968222 0.967792 −0.000430A_planck 1.002078 0.998829 −0.003249 The M3D–M4h audit shows that the fixed RMEM2 table mainly affects the growth and lensing-related sector, with repeated negative shifts in σ8 and S8 across the tested configurations, while preserving the equal-sampled-parameter structure of the comparison. The package includes: - patched CLASS/Cobaya solver source tree,- fixed RMEM2 μ/Σ table,- table-off and table-on YAML configurations for M4g and M4h,- custom likelihood modules for BAO DR1, BAO DR2, growth, SN and S8 tests,- local BAO DR1 and BAO DR2 data files,- local SN data files used by the custom likelihoods,- M3D–M4h audit material,- sigma8/S8 drift tables,- M4g direct-S8 likelihood result,- M4h BAO DR2 full-MCMC result,- manuscript and supplement source/PDF files,- README_REPRODUCE,- README_SOLVER,- README_PHYSICS_LIMITS,- run_unit_tests.sh,- run_smoke_tests.sh,- run_solver_build_smoke_tests.sh,- SHA256 checksums. The release archive is source-clean: compiled solver binaries, object files, shared libraries, build directories and local-path build artifacts are intentionally excluded. The solver can be rebuilt from source using the included build-smoke script. The package passed smoke and unit tests, including: - required release-structure checks,- source-clean checks for forbidden precompiled artifacts,- text privacy scan,- binary/string privacy scan,- RMEM2 table integrity check,- M4g/M4h YAML file-reference checks. Scientific scope and claim boundary: This release validates a fixed RMEM2 effective-response table as an externally rebuildable and reproducible comparison package across M3D, M4a–M4g and the V4.1 M4h BAO DR2 extension. It does not claim that RMEM2 is a fundamental theory, does not claim to replace dark matter, does not claim to solve the H0 or S8 tensions, and does not claim to prove singularity avoidance or black-hole/big-bang transition physics. V5m and other dynamic RMEM2 reconstructions are not part of the V4.1 main release claim. Outlook This V4.1 release is intentionally limited to a fixed-RMEM2 effective-response validation. It establishes a reproducible source-clean baseline for equal-sampled-parameter table-off/table-on comparisons across M3D, M4a–M4g and M4h, including the M4g direct-S8 result and the M4h BAO DR2 extension. The next development stage will extend this fixed-table validation into a broader MART/KTA stress-test and reconstruction program. The planned V5 directions are: 1. Dynamic RMEM2 reconstruction A dynamic RMEM2 reconstruction will be developed from the M3D–M4h validation sequence. The goal is to test whether the fixed RMEM2 response used in V4/V4.1 can be recovered, approximated, or falsified by a data-driven reconstruction without introducing unconstrained new degrees of freedom. 2. Fixed versus dynamic RMEM2 comparison The fixed V4/V4.1 response table will be compared against the dynamic RMEM2 reconstruction. This comparison will test whether the fixed-table approximation is merely phenomenological or whether it captures a stable response pattern across the likelihood ladder. 3. CDM stress test A controlled CDM-sector stress test will probe how strongly the RMEM2 response depends on the assumed cold-dark-matter contribution. This will be treated as a falsification-oriented diagnostic, not as a claim that MART/KTA replaces dark matter. 4. Boundary-phase and membrane stress tests Future work will explore whether the same relaxation-memory structure can be formulated as a boundary-phase diagnostic for early-universe and black-hole-like regimes. This is an exploratory structural program only; V4.1 does not claim singularity avoidance or black-hole/big-bang transition physics. 5. Covariant MART/KTA formulation A longer-term objective is to investigate whether the effective RMEM2 closure can be embedded in a covariant MART/KTA formulation with explicit consistency limits, stability diagnostics, and falsifiable observational consequences. The immediate next milestone is therefore not a stronger theoretical claim, but a stricter falsification program: dynamic reconstruction, solver-level stress tests, controlled comparison between fixed and reconstructed RMEM2 responses, CDM-sector stress tests, and explicit claim-boundary validation.