From Density-Matrix GKSL–Optimal-Transport Dynamics to Cosmological Growth and Weak-Lensing Shear Suppression: CAMB/Cobaya and CosmoSIS/kcap Stress Tests with Planck, DESI, S8, and KiDS1000

Stage31–Stage32 Summary Native GKSL–OT Source/Readout
Stage31–Stage32: Native GKSL–Optimal-Transport
Source/Readout Stress Tests in Precision Cosmology and Tomographic Shear  reproducibility summary
Prepared for the Stage31–Stage32 reproducibility archive June 2026

Archive scope. This summary documents the Stage31 CAMB/Cobaya stress test of a native GKSL–optimal-transport source/readout implementation for precision cosmology, and its Stage32 post-freeze propagation into the KiDS1000 Flinc tomographic cosmicshear pipeline. The tested object is not a phenomenological growth multiplier, not a posterior rescaling of chains, and not a fitted extension of ΛCDM. It is a fixed, traceable core-to-cosmology object: a density-matrix source dynamics, a source/readout response table, a patched CAMB implementation, paired posterior exposure, and independent shear propagation.

Contents of this reproducibility deposit:
This deposit provides the files required to inspect, audit, and independently reproduce the Stage31–Stage32 stress-test chain. It includes compressed reproducibility archives and sanitized working directories containing the native source/readout outputs, CAMB and CosmoSIS/kcap configuration files, patched source-code snapshots, compiled CAMB libraries, KiDS1000 Flinc data products, execution scripts, logs, MCMC chains, summary tables, SHA256 manifests, and PDF audit reports.

The shared material includes, in particular:

1. a Stage31 posterior audit package containing the native density-matrix/GKSL source/readout outputs, the CAMB-facing response table, patched CAMB files, Cobaya configurations, logs, chains, weighted summaries, and SHA256 records;

2. a Stage32 KiDS1000 Flinc reproducibility bundle containing the OFF and active-branch shear runs, fixed-cosmology outputs, (A_s)-only MCMC outputs, six-parameter MCMC outputs, CosmoSIS/kcap INI and values files, likelihood modules, logs, chains, summary JSON files, and run manifests;

3. compressed source-code archives for the patched CAMB build and the external CosmoSIS/kcap software environment used to run the shear pipeline;

4. the KiDS1000 Flinc input data required for the tomographic-shear exposure, including the binned data vector, covariance, redshift-distribution inputs, and mapping convention used to construct the 195-dimensional vector;

5. execution scripts and configuration files documenting how the OFF and active branches were launched, how the likelihoods were evaluated, and how the summary quantities were computed;

6. SHA256 checksum manifests allowing the deposited files and compressed archives to be verified after download;

7. PDF audit summaries describing the methodology, physical implementation, run results, interpretation, and reproducibility surface.

The archive is intended to make the result inspectable at file level: which response table was used, which CAMB and CosmoSIS/kcap configurations were run, which chains and logs support the reported likelihood comparisons, and which checksum manifests identify the frozen reproducibility objects. Local personal paths are not part of the scientific claim; the reproducibility object is defined by the deposited files, configuration state, code snapshots, chains, summaries, and hashes.

1 What is being tested:
The framework addresses the quantum–classical gravity interface by treating classical gravitational source terms as certified low-energy readouts of open quantum source dynamics. Classical geometry and classical source terms are not used as primitive objects before the quantum-to-classical interface has been specified. They are readout structures obtained in a certified low-energy window. The native numerical object is a density matrix ρ(λ), where λ is the internal evolution parameter of the open-system solver. The state evolves under a GKSL/Lindblad generator, dρ/dλ= -i[H, ρ] + Somme_ j (LjρL†j -1/2 {L†jLj , ρ}) 

The solver records trace preservation, positivity, Hermiticity, purity, coherence, entropy, relative entropy, entropy production, and Bures/optimal-transport diagnostics before any cosmological likelihood evaluation. The central implementation chain is ρ -> GKSL/Lindblad -> coherence/entropy/transport -> source/readout -> CAMB/Cobaya. Here source/readout denotes the map from native source diagnostics to the effective gravitational source seen by classical growth and shear observables. Transport denotes the information-geometric or optimal-transport diagnostic layer used to quantify motion and distinguishability on state space. The CAMB table is therefore a traceable output of the native ρ-based source/readout core. 2 Einstein-locked placement The implementation keeps the Einstein–Hilbert kinetic sector fixed:
SEH = (c3/16πG0) int (d^4x p(-g)^1/2 R[g])
No state-dependent factor multiplies R[g]. The test does not introduce a sampled Geff(z, k), μ(z, k), or Σ(z, k), and it does not add a scalar-field relief sector, primitive dark-fluid sector, or new sampled cosmological amplitude parameter. The state dependence is assigned to 1 of 5 Stage31–Stage32 Zenodo Summary Native GKSL–OT Source/Readout the source/readout side: the effective source seen by classical observables is generated from the native density-matrix dynamics.

At the CAMB-facing level, the generated response acts inside the matter-growth and derived growth-amplitude paths:
P(k, z) -> T^2 _growth(k, z) P(k, z) ;        σ8(z) -> Tgrowth(keff, z) σ8(z),    keff = 0.125 h Mpc−1 
.
A stored fσ8-response carries the velocity-density channel. The sampled cosmological parameter dimension is unchanged in the paired Stage31 posterior comparison.
3 Stage31C: causal ablation layer Stage31C is the evaluate-only causal exposure. It verifies that the cosmology-facing response follows the native branch structure rather than only the CAMB activation path. It compares OFF, FULL_COHERENT, DEPHASED, NO_DISSIPATOR, and IDENTITY_DYNAMICS.

This ordering identifies the active native ingredients of the cosmological response. Coherence contributes to the generated growth signal. The dissipative GKSL sector supplies additional strength beyond the Hamiltonian-only branch. The identity branch verifies the dormant reference.

4 Stage31D: posteriorized OFF/FULL_COHERENT comparison Stage31D posteriorizes the main OFF versus FULL_COHERENT comparison in paired MCMC chains.

The two branches use the same six sampled cosmological parameters, priors, likelihood stack, sampler covariance, patched CAMB implementation, and frozen code/data objects. The controlled difference is the native branch state. The post-burn weighted means give

σ8,OFF = 0.803989601, σ8,FULL = 0.7988012772,

so that Δσ8 = -0.005188323858.
The coherent native branch lowers the posterior mean growth amplitude by approximately 0.65%.
At likelihood level, χ2OFF = 12520.82559, χ2FULL = 12519.80327, with Δχ2 total = χ2 FULL - χ2 OFF = -1.022320612.
The compressed growth-amplitude block carries the leading contribution, Δχ2 S8 = -0.9584826635.

The blockwise decomposition is growth-led: the S8 block dominates the improvement, Planck high-ℓ, native Planck lensing, and Pantheon+ are mildly aligned with FULL_COHERENT, and DESI DR2 BAO gives a mild counter-shift absorbed by the total comparison. Both Stage31D chains pass the adopted mean-convergence criterion

R -1means 0.01: R - 1means = 0.009912 for OFF, R - 1means = 0.008521 for FULL_COHERENT.

Posterior-bound diagnostics converge more slowly and are retained as chain-diagnostic metadata. The reported Stage31D result is therefore a post-burn weighted mean-level posterior stress-test summary.

5 Stage32D: KiDS1000 Flinc 195D evaluate-only shear propagation Stage32D exposes the same frozen Stage31 FULL_COHERENT branch to the KiDS1000
Flinc tomographic cosmic-shear pipeline. A Linux build of the patched Stage31 CAMB engine is used inside the existing CosmoSIS/kcap B13 shear pipeline. The propagation chain is CAMB -> nKiDS(z) -> Cγγ ℓ -> ξ± -> ξbinned ± -> d195.
The mapping uses upper-convention tomographic pairs, all ξ+ followed by all ξ−, ξ+ theta bins 2–8, and ξ− theta bins 4–9:
15 7 + 15 6 = 195. The vector response is max jΔd195j = 6.72671461059073 10−7,  hΔd195i = -5.8540684729357585 10−8,

max Δd_195 dOFF 195= 0.004893677248413424, 
Δd_195 dOFF 195 = -0.004427249826950027, median

Δd_195 dOFF 195 = -0.00449422517837458.
FULL_COHERENT therefore produces a coherent 0.44%–0.49% suppression of the KiDS1000
Flinc 195-component tomographic shear vector.
Using the KiDS1000 Flinc data vector and covariance, the evaluate-only chi-square
comparison gives χ2 OFF,shear,195D = 781.3570775663435,
χ2 FULL,shear,195D = 779.1437152289436,
with
Δχ2 shear,195D = χ2
FULL,shear,195D - χ2
OFF,shear,195D =-2.2133623373998716.
This is a differential OFF/FULL propagation result at fixed cosmology, identical data vector, identical covariance, identical mapping, and identical downstream shear settings.
6 Stage32E:

As-only shear MCMC exposure Stage32E exposes the same KiDS1000 Flinc shear likelihood to an As-only CosmoSIS MCMC comparison. The best sampled OFF and FULL_COHERENT points remain separated in favour of the frozen native response: χ2 OFF,min = 724.9175685656735, χ2 FULL,min = 724.7394765413381,
3 of 5 Stage31–Stage32 Zenodo Summary Native GKSL–OT Source/Readout so that Δχ2 As-only = -0.1780920243353421.
The corresponding best sampled scalar amplitudes are As,OFF,min = 1.665064110215694 10−9, As,FULL,min = 1.6714023922556927 10−9.
This intermediate posterior exposure shows that the Stage31 response is not erased by a single-amplitude re-adjustment of the primordial scalar amplitude inside the shear pipeline.

7 Stage32F: six-parameter KiDS1000 Flinc shear MCMC stress test Stage32F promotes the KiDS1000 Flinc exposure to a six-parameter CosmoSIS/kcap MCMC
stress test. The varied cosmological parameters are fΩm, h, Ωb, ns, As, τg.

The OFF and FULL_COHERENT branches use the same KiDS1000 Flinc data vector, covariance, redshift distributions, CosmoSIS/kcap modules, sampler settings, patched
CAMB implementation, and frozen code/data objects. The completed run contains 12800 chain rows per branch. At the best sampled points,

χ2  OFF,min = 706.5713695461471, χ2FULL,min = 705.5031943137622,
so that Δχ2 6p,shear = -1.0681752323849878.

The maximum sampled posterior value also shifts in favour of FULL_COHERENT:
Δlog Pmax = +0.5340876161924939. Thus the same frozen native source/readout branch remains favoured at the best sampled point after six-parameter shear re-adjustment. 8 Scientific interpretation The Stage31–Stage32 result establishes a concrete core-to-cosmology implementation of the GKSL–optimal-transport source/readout programme. It does not claim to validate the entire foundational framework or every possible source/readout sector. It establishes a narrower and operationally meaningful result: the implemented branch can be generated natively from a density-matrix GKSL/coherence/transport core, inserted into CAMB as a traceable response table, resolved by identity, dephasing, and no-dissipator controls, posteriorized against OFF at fixed sampled cosmological dimension, propagated to an independent KiDS1000 Flinc tomographic-shear observable, and retained under both Asonly and six-parameter shear posterior exposure. The physical interpretation is correspondingly precise. The suppression of σ8 and the suppression of the KiDS1000 Flinc shear vector are not interpreted as free late-time amplitude retunings. They are interpreted as CAMB/Cobaya and CosmoSIS/kcap readouts of a frozen native source-side branch generated from open quantum source dynamics. The Einstein–Hilbert sector remains fixed; the effective classical source read by the growth and shear channels carries the state dependence. 4 of 5 Stage31–Stage32 Zenodo Summary Native GKSL–OT Source/Readout

9 Low-energy testability:
The cosmological stress tests are one exposure surface of a broader testable programme. The same Einstein-locked source/readout placement also leads to low-energy laboratory protocols in which a prepared source-state coordinate is modulated at fixed geometry and searched for through phase-coherent lock-in readouts.
A minimal fixed-geometry source-side template is δgsrc(Ω)/ ggeo  ~ -β⋆ δpκ(Ω),  β⋆= - ∂pκ( ln μ(pκ)) _ pκ,⋆
.
In a clock-comparison version, the analogous fractional-frequency response is δyΩ(t) ~ -β⋆ δpκ ϕgeo cos(Ωt + ϕp). These protocols use calibrated source proxies, lock-in demodulation, placebo or isopurity controls, phase reversal, geometry scaling, and monitor regression to veto Newtonian motion, mass redistribution, electromagnetic pickup, thermal leakage, vibration, and linksystematic mimics. They test whether the effective source-to-readout map is strictly state blind once geometry and ordinary Newtonian flow-downs are controlled. 10 Reproducibility bundle The Stage31 archive records the native solver outputs, density-matrix diagnostics, readout
tables, traceability products, patched Fortran sources, compiled CAMB library, Cobaya YAML files, execution scripts, logs, MCMC chains, CSV summaries, SHA256 manifests,
and portable audit package.

The final posterior audit package is STAGE31D_FINAL_POSTERIOR_AUDIT_PACKAGE.zip, with manifest count OK 18 and SHA256
B4E4764B2EF74A3E6E22E082BCB1D2C47E6338F09D7904AEA9383724FB5F5F08. 

The Stage32 reproducibility record extends the bundle with the frozen Stage31 FULL_COHERENT response table, the patched Linux CAMB build, CosmoSIS/kcap configuration and modules, KiDS1000 Flinc data vector and covariance, fixed-cosmology logs, As-only and sixparameter shear chains, summary JSON files, mapped shear vectors, SHA256 manifests, and the Stage32 H16 reproducibility bundle.
Archive reading. Stage31 links native source dynamics, CAMB implementation, causal ablations, and paired MCMC posteriorization in one reproducible core-to-cosmology
chain. Stage32 extends the same frozen branch to an independent KiDS1000 Flinc tomographic-shear surface, where it suppresses the mapped 195D shear vector, improves the fixed-cosmology shear comparison, survives As-only re-adjustment, and remains favoured at the best sampled point in a six-parameter shear MCMC stress test. 5 of 5