MART/KTA RMEM2 V4.1: Fixed-RMEM2 Full-MCMC Validation on Planck 2018 high-ℓ TTTEEE + low-ℓ TT/EE, BAO DR2, Growth, SN and Direct-S8 Data, Δχ² = ΔAIC = ΔBIC = −9.4488

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 = 6590.9958352
table-on  χ² = 6565.2618842
Δχ² = 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 = 2793.7857
table-on  χ² = 2784.3369
Δχ² = 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        Δωcdm
M3D        +0.01919      +0.01207   −0.00023    −0.04840   −0.04886   −0.00005
M4a        −4.23794      +0.86688   −0.01171    −0.03156   −0.04760   −0.00193
M4b        −1.80050      +0.70774   −0.00892    −0.03644   −0.04861   −0.00138
M4c        −4.84028      +0.62897   −0.00849    −0.02930   −0.04098   −0.00144
M4d        −4.44126      +0.58534   −0.00756    −0.02407   −0.03446   −0.00118
M4e        −16.90111     +0.23660   −0.00289    −0.02116   −0.02519   −0.00043
M4f        −16.34993     +0.21888   −0.00235    −0.02857   −0.03194   −0.00027
M4g        −25.73395     −0.12273   +0.00174    −0.01929   −0.01697   +0.00032
M4h        −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        −0.122732
omega_b        0.022476         0.022468199      −0.000007801
omega_cdm      0.11835702       0.11867543       +0.00031841
tau_reio       0.051289785      0.049876208      −0.001413577
A_s            2.072676e−09     2.073223e−09     +5.47e−13
n_s            0.96775788       0.96743826       −0.00031962
A_planck       0.99916272       1.0001324        +0.00096968

For M4g, the direct sigma8/S8 drift audit gives:

Δσ8 = −0.01928819
ΔS8 = −0.01697029

For M4h, the full-MCMC BAO DR2 table-off/table-on comparison gives:

Parameter      Δ(table-on − table-off)
χ²             −9.448800
H0             +0.013418
Ωm             −0.00002161
ωcdm           +0.00001802
σ8             −0.01550752
S8             −0.01550718

The M4h BAO DR2 chains are audit-level converged:

M4h table-off:
R−1 = 0.018478
R−1_cl = 0.089277

M4h table-on:
R−1 = 0.010340
R−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        +0.01919
H0             68.416363        68.428429        +0.012066
Ωm             0.301921         0.301696         −0.000225
σ8             0.863623         0.815224         −0.048399
S8             0.866384         0.817525         −0.048859
ωcdm           0.118827         0.118775         −0.000052
A_s            2.324360e−09     2.180392e−09     −1.43968e−10
n_s            0.968222         0.967792         −0.000430
A_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.