MART/KTA RMEM2 V4: Fixed RMEM2 Full-MCMC Validation on Planck High-ℓ, BAO DR1, Growth, SN and Direct-S8 Data, Δχ² = ΔAIC = ΔBIC = −25.73

This V4 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 main full-MCMC V4 result is the M4g comparison using Planck, BAO, growth, supernova and direct-S8 data: table-off χ² = 6590.9958352table-on χ² = 6565.2618842Δχ² = ΔAIC = ΔBIC = −25.7339510 Because the table-on and table-off runs use the same sampled cosmological parameter set, ΔAIC and ΔBIC coincide with Δχ² for this fixed-table comparison. Fitted and tested data combinations included in V4: M3D:Planck high-ℓ validation / sigma8-S8 drift audit. M4a:Planck baseline comparison. M4b:Planck + BAO comparison. M4c:Planck + BAO DR1 comparison. M4d:Planck + BAO DR1+ growth comparison. M4e:Planck + BAO DR1+ growth full comparison. M4f:Planck + BAO DR1+ growth + supernova comparison. M4g:Planck + BAO DR1+ growth + supernova + direct-S8 comparison. Parameter drift audit from M3D to M4g: 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 — — — +0.00032 Note: For M4g, this Zenodo summary table lists the directly audited best-fit parameter shifts available in the summary record. Additional run-level audit files are included in the release package. 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 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–M4g 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,- custom likelihood modules for BAO DR1, growth, SN and S8 tests,- M3D–M4g audit material,- sigma8/S8 drift tables,- M4g direct-S8 likelihood 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. Scientific scope and claim boundary: This release validates a fixed RMEM2 effective-response table as an externally rebuildable and reproducible comparison package across M3D and M4a–M4g. 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. Outlook This V4 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 and M4a–M4g, including the M4g direct-S8 result. 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. M4h BAO DR2 extension The M4h branch will extend the V4 likelihood ladder with BAO DR2 information and test whether the fixed RMEM2 response remains stable under the updated BAO sector. 2. 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 can be recovered, approximated, or falsified by a data-driven reconstruction without introducing unconstrained new degrees of freedom. 3. Fixed versus dynamic RMEM2 comparison The fixed V4 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. 4. 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. 5. 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 does not claim singularity avoidance or black-hole/big-bang transition physics. 6. 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: M4h validation, dynamic reconstruction, solver-level stress tests, and controlled comparison between fixed and reconstructed RMEM2 responses.