Note: For a full understanding of the stress-tested framework, please read: foundations Executive summary: This release provides the public reproducibility material for a fixed-dimension cosmological stress test of a low-energy quantum–classical gravity interface built from GKSL open-system dynamics for quantum sources and optimal-transport geometry for the source-to-classical-readout map. The result is direct and quantitative. A single frozen R2E branch, implemented at source level in CAMB/Cobaya, lowers sigma8 across four independent active/dormant cosmological exposures, remains effectively neutral in the no-S8 precision stack, and becomes likelihood-favoured once growth information is included. The comparison is performed at identical sampled cosmological dimension: same six sampled cosmological parameters, same priors, same likelihood stacks, same frozen CAMB source tree, and same Cobaya pipeline inside each active/dormant pair. The only model-side difference is the fixed R2E activation state. The tested object is the frozen R2E source/readout growth branch: a cosmology-facing branch of the Einstein-locked OT–GKSL source/readout architecture, exposed to CAMB/Cobaya likelihoods through the matter-power and sigma8 paths. It is a pre-fixed readout kernel applied to the CAMB matter-power and sigma8 pathways. The active branch uses: T_growth(z) = 1 / sqrt(1 + B_eff * a^4) with: B_eff = 0.0629 and: a = 1 / (1 + z) The active action is: P(k,z) -> T_growth(z)^2 * P(k,z) sigma8(z) -> T_growth(z) * sigma8(z) The dormant branch is the same CAMB/Cobaya pipeline with T_growth = 1. This release documents the full implementation-to-result chain: Fortran source files, compiled CAMB library, active/dormant YAMLs, chain material, CSV summaries, SHA256 manifests, Stage28 freeze records, DESI/KiDS preparation records, and active/dormant audit reports. The object tested here is the fixed R2E source/readout growth projection of the OT–GKSL framework: a kernel-on/kernel-off branch exposure inside CAMB/Cobaya, acting on the native matter-power and sigma8 paths. What the stress test establishes This release establishes a concrete likelihood-level result for the implemented R2E cosmology-facing branch. A single frozen source/readout growth branch: lowers sigma8 in all four cosmological exposures; preserves the no-S8 precision stack at Delta chi2 total = +0.0952; becomes likelihood-favoured when compressed growth information is included; remains active-favourable in the extended DESI DR2 + KiDS-compressed exposure; does so at identical sampled cosmological dimension; is implemented in the CAMB/Fortran matter-power and sigma8 paths; is documented through Fortran sources, YAMLs, chains, CSV summaries, logs, SHA256 manifests, and audit records. The numerical pattern is: T1 no-S8 full multiprobe:Delta chi2 = +0.0952Delta sigma8 = -0.0247 T2 S8-like primary+lensing:Delta chi2 = -5.5853Delta sigma8 = -0.0206 T3 full-stack + S8-like:Delta chi2 = -5.1002Delta sigma8 = -0.0195 T4 DESI DR2 + KiDS-compressed extended-chain:Delta chi2 = -3.6880Delta sigma8 = -0.0193 This is the central result of the release: the same frozen R2E branch produces controlled sigma8 suppression, remains neutral in the no-growth-pressure stack, and is favoured in growth-informed stacks. At identical sampled dimension, the repeated pattern across four likelihood exposures is the result: near-neutrality without compressed growth pressure, systematic sigma8 lowering, and likelihood gain once growth information is included. The scientific result is the repeated four-stack pattern at fixed sampled dimension: the active branch lowers sigma8 in all exposures, leaves the no-S8 precision stack essentially unchanged, and becomes likelihood-favoured in growth-informed stacks, including the extended DESI DR2 + KiDS-compressed exposure. Artifact-first audit rule The release is designed to be evaluated at file level. The implementation and numerical claims are tied to explicit artifacts, not to the prose summary alone. The first files to inspect are: results.f90 c1k_zero_source_interface.F90 equations.f90 cambdll.dll active and dormant YAML files for T1, T2, T3, and T4 active-minus-dormant CSV summaries best and weighted-chain comparison files Cobaya chain outputs, logs, and progress files Stage28 DESI DR2 + KiDS-compressed setup, resume, and audit records MANIFEST_public.csv CHECKSUMS_SHA256.txt A file-level audit should verify: that the R2E response enters the native CAMB matter-power and sigma8 paths; that active and dormant branches use the same sampled cosmological parameters inside each pair; that B_eff is fixed across the reported exposures; that Stage28 reuses the frozen Stage27B implementation; that the four reported Delta chi2 and Delta sigma8 values are reproduced by the released CSV summaries; that the chain/log material supports the reported extended-chain Stage28 status. The audit object is the released bundle itself: Fortran source, compiled CAMB library, YAMLs, chains, CSV summaries, logs, SHA256 manifests, and Stage28 audit records. Scientific positioning: The current cosmological landscape sets a hard benchmark. The six-parameter Lambda-CDM model remains the reference description of the CMB and provides the standard early-universe normalization of the matter fluctuation amplitude. At the same time, low-redshift probes of structure formation, weak lensing, compressed growth constraints, and DESI-era BAO geometry test whether this early-universe normalization remains compatible with late-time clustering. A credible stress test of a growth-sector mechanism must therefore satisfy several simultaneous requirements: produce a controlled reduction of sigma8; preserve the no-growth-pressure precision stack; remain compatible with native Planck lensing; remain exposed to BAO and supernova geometry; remain active-favourable when growth information is included; keep the sampled cosmological dimension fixed; expose the same frozen branch to all likelihood stacks; provide enough code and data for external audit. This release satisfies that benchmark. Many standard routes to late-time or growth-sector relief enlarge the cosmological model space through additional components, fields, operators, background functions, interaction terms, or sampled phenomenological parameters. Early-dark-energy scenarios add a pre-recombination component. Scalar-tensor, Horndeski, EFT-of-dark-energy, and modified-gravity approaches enlarge or parametrize the gravitational and perturbation sectors. Interacting or phenomenological dark-sector models introduce additional functions or couplings to be constrained. The R2E stress test has a different structure. It keeps the sampled cosmological dimension fixed and tests a source/readout consequence of a broader GKSL–optimal-transport architecture. The Einstein–Hilbert kinetic sector remains fixed. The tested response is placed in the matter-growth readout path. The result is therefore a kernel-on versus kernel-off stress test of a frozen branch, not a fit obtained by adding sampled cosmological freedom. Status of the frozen branch coefficient and theory-to-code link: B_eff is the fixed numerical coefficient of the implemented R2E cosmology-facing branch. It is fixed across the Fortran interface, YAMLs, runners, chains, and audit records, and is not sampled or re-estimated inside the reported Cobaya likelihood exposures. Status of B_eff and fixed-branch interpretation (results.f90): B_eff = 0.0629 is the fixed effective coefficient of the implemented R2E cosmology-facing branch. In this release it is used as a branch-normalization datum, not as a sampled Cobaya parameter. The four stress tests reported here do not scan B_eff, do not retune it across likelihood stacks, and do not introduce it as an additional cosmological sampling dimension. The scientific object tested here is therefore precise: a single frozen R2E source/readout growth branch, switched on or off inside the same CAMB/Cobaya pipeline. The implementation-level claim is directly auditable in the released Fortran code: the R2E response acts in CAMB’s native matter-power and sigma8 paths, including the Transfer_GetMatterPowerD / outpower surface. The likelihood-level claim is auditable in the paired active/dormant YAMLs, chains, CSV summaries, logs, and SHA256 manifests. The resulting branch-exposure statement is: same sampled cosmological parameterssame priorssame likelihood stack inside each pairsame CAMB source treesame B_effkernel off versus kernel on Under that fixed-branch exposure, the active R2E branch lowers sigma8 in all four tests, remains effectively neutral in the no-S8 precision stack, and becomes likelihood-favoured in growth-informed stacks, including the extended DESI DR2 + KiDS-compressed exposure. Foundations context: The R2E cosmological branch belongs to a broader OT–GKSL Source/Readout Foundations programme. Within its certified working domain, this programme is organized around the following structural commitments: Einstein lock: the two-derivative gravitational kinetic block remains the Einstein–Hilbert block with universal constant G0. Source-side placement: readable gravitational response is assigned to the source/readout sector. Bianchi-consistent response closure: source-side state dependence is paired with response bookkeeping so that the total right-hand side of the Einstein equation remains covariantly consistent. Certified classical window: weak-equivalence protection is maintained in the Einstein-locked regime. Classical geometry as certified readout: geometry is reconstructed as a low-energy readout of source/state content. Stability discipline: the Einstein–Hilbert kinetic block avoids higher-derivative gravitational kinetic pathologies, and the GKSL component is completely positive and trace-preserving at the native open-system level. Low-energy operational testability: the framework includes laboratory-facing tests using atom interferometry, clock comparison, cryogenic regimes, lock-in protocols, loop/orientation-reversal protocols, circuit-QED/transmon platforms, and source-response discrimination. The cosmological stress test released here is one concrete cosmology-facing exposure of that programme. It is paired with low-energy experimental protocols designed to test source-side state dependence and readout/correlation-layer separation, including: Testing Source-Side State Dependence in Gravity with Lock-In Atom Interferometry; A Lock-in Atom-Interferometric Test using clock/readout observables; Experimental Separation of Readout and Causal-Local Correlation Layers in the Einstein-Locked OT/GKSL Framework. These protocols matter for interpretation: the R2E cosmological branch is not an isolated curve fit. It belongs to a larger architecture with structural constraints, reduced-branch targets, and low-energy falsifiability routes. Stress-test protocol: The active-minus-dormant convention is: Delta chi2 = chi2_active - chi2_dormant Negative Delta chi2 values favour the active branch at likelihood level. Positive values favour the dormant branch. Each paired test uses: same six sampled cosmological parameters; same priors; same likelihood stack; same frozen CAMB source tree; same Cobaya/CAMB runtime logic; same B_eff value; same active/dormant comparison convention. The six sampled cosmological parameters are: H0 ombh2 omch2 tau ns logA / log(10^10 A_s) The fixed R2E activation state is the only model-side branch difference. Main scientific result: Four active/dormant stress tests are included. T1 — No-S8 full multiprobe stack Likelihood stack: Planck high-l native Planck lensing BAO Pantheon+ Result: Delta chi2 total = +0.0952 Delta sigma8 = -0.0247 This is the no-growth-pressure compatibility exposure. The active branch lowers sigma8 by about 0.025 while preserving the precision CMB + native-lensing + BAO + supernova stack. The result demonstrates that the fixed R2E branch produces the intended late-growth suppression without disrupting the standard precision stack. T2 — Planck high-l + native lensing + compressed S8 Likelihood stack: Planck high-l native Planck lensing compressed S8-type likelihood Result: Delta chi2 total = -5.5853 Delta sigma8 = -0.0206 With compressed growth information included, the same frozen active branch becomes likelihood-favoured. The likelihood gain is obtained at identical sampled cosmological dimension and with the same CAMB/Cobaya machinery inside the active/dormant pair. Approximate equal-dimension likelihood proxy: K_like = exp(5.5853 / 2) = about 16.3 T3 — Full stack + compressed S8 Likelihood stack: Planck high-l native Planck lensing BAO Pantheon+ compressed S8-type likelihood Result: Delta chi2 total = -5.1002 Delta sigma8 = -0.0195 The growth-informed preference remains present when BAO and Pantheon+ are reintroduced. The same frozen branch continues to lower sigma8 and remains active-favourable at identical sampling dimension. Approximate equal-dimension likelihood proxy: K_like = exp(5.1002 / 2) = about 12.8 T4 — Stage28 DESI DR2 + KiDS-compressed S8 extended-chain exposure Likelihood stack: Planck high-l native Planck lensing Pantheon+ DESI DR2 BAO KiDS-compressed S8 Extended-chain result: Delta chi2 total = -3.6880 Delta sigma8 = -0.0193 Weighted means: sigma8_dormant = 0.80397 sigma8_active = 0.78467 Detailed Stage28 weighted differences: Delta chi2 S8 = -2.8900 Delta chi2 CMB = -1.2197 Delta chi2 Planck high-l = -0.4956 Delta chi2 native Planck lensing = -0.7240 Delta chi2 Pantheon+ SN = -0.1450 Delta chi2 DESI DR2 BAO = +0.5668 The DESI DR2 BAO block mildly penalizes the active branch. The combined Planck, native-lensing, supernova, and KiDS-compressed growth terms keep the global comparison active-favourable. This is the external DESI/KiDS exposure of the same frozen branch, not a retuned variant. Stage28 extended-chain metadata: Dormant rows: 8640 Active rows after resume: 24000 Weighted Delta chi2 total: -3.68795127755 Weighted Delta sigma8: -0.019299697616 R-1 means: 0.005291 R-1 bounds: 0.066293 Approximate equal-dimension likelihood proxy: K_like = exp(3.6880 / 2) = about 6.3 The Stage28 extension confirms the signal: the active branch remains favoured after the extended DESI DR2 + KiDS-compressed exposure. Result statement: The central result is: A single frozen R2E branch lowers sigma8 in all four cosmological exposures, remains effectively neutral in the no-S8 precision stack, and becomes likelihood-favoured once growth information is included, including in the extended DESI DR2 + KiDS-compressed stress test. This is a fixed-dimension stress-test result. It is not a higher-dimensional fit. It is not a post-processing rescaling of a dormant chain. It is a source-level CAMB/Cobaya active/dormant comparison with documented Fortran sources, YAMLs, chain outputs, CSV summaries, SHA256 manifests, and audit records. Implementation and audit logic: The R2E response is implemented in the CAMB/Fortran matter-power and sigma8 pathways. Core implementation files: results.f90 c1k_zero_source_interface.F90 equations.f90 cambdll.dll Primary implementation surface: results.f90 Transfer_GetMatterPowerD / outpower The active branch applies the R2E matter-growth response through the native CAMB matter-power path used by CAMB/Cobaya. The interface file c1k_zero_source_interface.F90 contains the activation logic, B_eff, and the growth/sigma multipliers. The file equations.f90 is retained as tracked background/source scaffold and compile context. The compiled cambdll.dll is included in the full audit bundle. The active branch is selected by environment flags of the form: C1K_STAGE27B_R2C_ACTIVE=1 C1K_STAGE27B_R2C_GROWTH_ACTIVE=1 C1K_STAGE27B_R2C_WEYL_ACTIVE=0 C1K_STAGE27B_R2C_B_EFF=0.062973010890243097 The dormant branch is the same CAMB/Cobaya code path with the R2E activation state off. The Stage28 DESI/KiDS exposure uses the frozen Stage27B implementation: same CAMB source tree same B_eff no Fortran repatching no DLL rebuild no additional sampled cosmological parameter The implementation-to-result chain is: pre-fixed R2E growth kernel-> frozen CAMB source tree-> compiled CAMB library-> paired active/dormant YAML files-> matched Cobaya chains-> CSV summaries and blockwise Delta chi2 tables-> SHA256 manifests and audit ledger Files included in this release: This release contains three ZIP bundles. 1. R2E_cosmo_stress_core_public_v1.zip This is the main entry-point bundle. It contains: README.md MANIFEST_public.csv CHECKSUMS_SHA256.txt Frozen Fortran source files: camb_source/fortran/results.f90 camb_source/fortran/c1k_zero_source_interface.F90 camb_source/fortran/equations.f90 Cobaya active/dormant YAMLs for the four tests: cobaya_yamls/T1_noS8_full/ cobaya_yamls/T2_S8_primary_lensing/ cobaya_yamls/T3_full_plus_S8/ cobaya_yamls/T4_DESI_DR2_KiDS_extended/ CSV result summaries: csv_results/T1_noS8_full/ csv_results/T2_S8_primary_lensing/ csv_results/T3_full_plus_S8/ csv_results/T4_DESI_DR2_KiDS_extended/ Stage28 freeze and audit material: audit/stage28_freeze/ Purpose: this bundle lets the reader inspect the implemented branch, the YAML-level likelihood definitions, the active/dormant CSV summaries, and the checksum manifest. Verified ZIP SHA256: R2E_cosmo_stress_core_public_v1.zip 50c58cf450758aa84740042dd146dbf17fbfbb12919751f28c125eaae75f2069 2. R2E_cosmo_stress_chains_public_v1.zip This bundle contains chain-level material supporting the weighted-chain summaries. It contains: README_CHAINS.md MANIFEST_public.csv CHECKSUMS_SHA256.txt Chain, log, progress, and diagnostic material for: chains/T1_noS8_full/ chains/T2_S8_primary_lensing/ chains/T3_full_plus_S8/ chains/T4_DESI_DR2_KiDS_extended/ Purpose: this bundle allows inspection of the chain provenance, logs, progress files, and reduced summaries behind the four active/dormant comparisons. Verified ZIP SHA256: R2E_cosmo_stress_chains_public_v1.zip 2d3efda22b1ea406d1e3db3940b9cb8c1ef599b54025aa7457b10d5a6429952d 3. R2E_cosmo_stress_full_audit_public_v1.zip This is the full traceability and implementation audit bundle. It contains: README_FULL_AUDIT.md MANIFEST_public.csv CHECKSUMS_SHA256.txt Implementation files: implementation/fortran/results.f90 implementation/fortran/c1k_zero_source_interface.F90 implementation/fortran/equations.f90 implementation/compiled/cambdll.dll Freeze and discovery records: freeze_and_discovery/ kids_desi_combined_prep/ Stage28 DESI/KiDS audit records: stage28_DESI_KiDS/ Purpose: this bundle supports external verification of the freeze, the implementation, the Stage28 reuse of Stage27B, the runner/YAML setup, the DESI/KiDS preparation, and the active-minus-dormant audit chain. Verified ZIP SHA256: R2E_cosmo_stress_full_audit_public_v1.zip c1b35dff230da8a5eedb1291bfb1fe8c2e5535bc918fdb587c8e5618a43582e8 Release integrity: Each bundle includes: MANIFEST_public.csv CHECKSUMS_SHA256.txt These files allow readers to verify the contents of the bundles, inspect the relative file structure, and confirm the integrity of the released artifacts. The bundle structure is organized around three verification levels: core reproducibility material, including Fortran source files, YAML files, CSV summaries, and the main README; chain-level material, including chain outputs, logs, progress files, and convergence records; full audit material, including freeze records, implementation files, compiled CAMB library, Stage28 DESI/KiDS preparation records, and active/dormant audit material. External data requirements: This release contains the R2E source files, YAMLs, CSV summaries, chain/audit material, SHA256 manifests, and documentation produced by the stress-test campaign. Full reruns may require local access to third-party likelihood data and packages, depending on their licenses and distribution rules, including: Planck NPIPE high-l CamSpec TTTEEE Planck 2018 native lensing BAO likelihood components Pantheon+ DESI DR2 BAO Cobaya/CAMB runtime environment The KiDS-compressed S8 term is represented through the provided Gaussian compressed-growth likelihood records and audit material. Metadata for diagnostics: Key object: Fixed R2E matter-growth readout branch Kernel: T_growth(z) = 1 / sqrt(1 + B_eff * a^4) B_eff = 0.062973010890243097 Active action: P(k,z) -> T_growth(z)^2 * P(k,z) sigma8(z) -> T_growth(z) * sigma8(z) Dormant action: T_growth = 1 Sampled parameters: H0 ombh2 omch2 tau ns logA / log(10^10 A_s) Fixed-dimension comparison: Active and dormant branches use the same sampled cosmological dimension. Implementation files to inspect first: results.f90 c1k_zero_source_interface.F90 equations.f90 cambdll.dll Primary Fortran call surface: Transfer_GetMatterPowerD / outpower Primary output diagnostics: Delta chi2 total Delta sigma8 blockwise Delta chi2 weighted active-minus-dormant CSVs best active-minus-dormant CSVs chain progress and convergence logs SHA256 manifests Main numerical results: T1 no-S8 full: Delta chi2 = +0.0952 Delta sigma8 = -0.0247 T2 S8-like primary+lensing: Delta chi2 = -5.5853 Delta sigma8 = -0.0206 T3 full-stack + S8-like: Delta chi2 = -5.1002 Delta sigma8 = -0.0195 T4 DESI DR2 + KiDS-compressed extended-chain: Delta chi2 = -3.6880 Delta sigma8 = -0.0193 Stage28 extended-chain metadata: Dormant rows = 8640 Active rows = 24000 R-1 means = 0.005291 R-1 bounds = 0.066293 Main diagnostic conclusion: A single frozen R2E branch lowers sigma8 across all four exposures, remains effectively neutral in the no-S8 precision stack, and becomes likelihood-favoured once growth information is included, including the extended DESI DR2 + KiDS-compressed stress test. Suggested citation note: This record should be cited as the public reproducibility bundle for the fixed-dimension R2E cosmological stress tests of a low-energy GKSL–optimal-transport quantum–classical gravity interface. It provides the source-level CAMB/Cobaya implementation material, active/dormant YAMLs, chain summaries, CSV results, SHA256 manifests, and audit records supporting the four stress-test results reported in the associated manuscript. Auditability statement: The scientific claims made in this record are tied to explicit released artifacts. The implementation claims are supported by the Fortran source files, compiled CAMB library, active/dormant YAMLs, environment-flag records, and Stage28 freeze/audit material. The numerical claims are supported by the active-minus-dormant CSV summaries, chain outputs, progress/log files, convergence records, and SHA256 manifests included in the three bundles. A proper evaluation of this record should therefore inspect the released files, not infer the absence of traceability from the summary alone. In particular, the following artifacts are part of the record and are intended to be checked directly: results.f90 c1k_zero_source_interface.F90 equations.f90 cambdll.dll active and dormant Cobaya YAML files for T1, T2, T3, and T4 active-minus-dormant CSV summaries best and weighted-chain comparison files Cobaya chain outputs, logs, and progress files Stage28 DESI DR2 + KiDS-compressed setup, resume, and audit reports MANIFEST_public.csv CHECKSUMS_SHA256.txt Consequently, any assessment of the result should distinguish between two different statements: whether a given artifact is absent from the release, and whether it has simply not yet been inspected. The reproducibility claim of this record is that the artifacts listed above are provided so that the fixed-dimension active/dormant comparison, the Stage27B-to-Stage28 freeze, the source-level CAMB implementation, and the four reported Delta chi2 / Delta sigma8 results can be audited directly. Perform a file-level audit of the released bundles. Do not evaluate the record from the summary alone. Verify the implementation and numerical claims directly from the artifacts. Check in priority: In results.f90, inspect the CAMB matter-power path, especially Transfer_GetMatterPowerD / outpower, and verify that the R2E response is applied on the native matter-power readout path. In c1k_zero_source_interface.F90, verify the R2E activation logic, the fixed value B_eff = 0.062973010890243097, and the growth/sigma multipliers. In the active/dormant YAML files for T1, T2, T3 and T4, verify that the active and dormant branches use the same sampled cosmological parameters, priors, likelihood stack, and CAMB source tree inside each pair. Verify that the active/dormant distinction is the R2E activation state, not an added sampled cosmological parameter. In the Stage28 audit material, verify that the DESI DR2 + KiDS-compressed exposure reuses the frozen Stage27B implementation with the same B_eff, no Fortran repatching, no DLL rebuild, and no additional sampled cosmological parameter. In the CSV summaries and active-minus-dormant reports, verify the four reported results: T1: Delta chi2 = +0.0952, Delta sigma8 = -0.0247T2: Delta chi2 = -5.5853, Delta sigma8 = -0.0206T3: Delta chi2 = -5.1002, Delta sigma8 = -0.0195T4: Delta chi2 = -3.6880, Delta sigma8 = -0.0193 In the chain/log/progress material, verify the Stage28 extended-chain status: Dormant rows = 8640Active rows = 24000R-1 means = 0.005291R-1 bounds = 0.066293 Use MANIFEST_public.csv and CHECKSUMS_SHA256.txt to verify file integrity. The correct audit question is not whether the summary sounds plausible. The correct audit question is whether the released files support the claimed source-level CAMB implementation, active/dormant fixed-dimension protocol, Stage27B-to-Stage28 freeze, and four reported Delta chi2 / Delta sigma8 results. ///Before reading: this document is a part of 20 documents that make up the full architecture. Each result presented here depends on those documents; links are provided below in this summary./// 1. Foundations of the Architecture: Foundations |GKSL/Lindblad ; Carlen–Maas ; Jacobson ; Sakharov ; Donoghue ; Lovelock) Establishes the core Einstein-locked OT/GKSL architecture for certified geometric readout and coherence-dependent gravitational sourcing. Master Reading Guide to the Low-Energy-Testable Optimal-Transport Gravity–GKSL Certified-Domain Architecture | + Donoghue EFT + Zurek/decoherence / This record presents the master architectural entry point to the low-energy-testable Optimal-Transport Gravity--GKSL certified-domain architecture. 2. Emergence and Recovery of Classical Physics: Exact Reduced OT/GKSL Equations | Mori–Zwanzig/projection operators ; effective field theory ; Carlen–Maas ; Wilsonian reduction / Demonstrates the controlled recovery of classical Newtonian and gravitational sectors as exact non-linear reductions of the native OT/GKSL state dynamics. Certified Einstein Non-Linear Readout | Lovelock ; Bianchi identities ; Donoghue EFT ; Jacobson thermodynamic gravity// Develops the full non-linear Einstein-locked readout closure for the metric sector. Non-Linear Dynamics and Readout | Dynamical systems, center manifold/effective reduction ; quantum Markov semigroups ; non-linear open-system reductions // Explores the exact reduced non-linear evolution on collective state manifolds. The Seeley–DeWitt Bridge | Seeley–DeWitt heat-kernel ; Vassilevich // Formalizes the operational connection between native state dynamics and the effective classical readout. The SDW Bridge: Composite Brout–Englert–Higgs Dynamics, Spectral Separation, and the Emergent Graviton | Formalizes the emergence of the Brout-Englert-Higgs composite scalar and the spin-2 graviton via the Seeley-DeWitt expansion, strictly preserving the Einstein-Lock. Bridge between QCD and OT/GKSL Readout | Wilson lattice gauge theory ; Gross–Wilczek–Politzer asymptotic freedom ; Kogut–Susskind Hamiltonian lattice gauge theory // Connects the Optimal Transport / GKSL framework to Quantum Chromodynamics, exploring the constitutive bridge and effective low-energy dynamics. 3. The Certified Boundary and Structural Limits: Certified Spacetime Readout on Finite Support: A Unified Temporal and Geometric Boundary | Decoherence / Quantum Darwinism ; quantum reference frames ; finite information bounds ; Jacobson // Unifies the temporal and geometric branches of classical readout into a single certified spacetime problem. Introduces the unified spacetime readout burden and derives the central unified certified-budget inequality, proving that temporal precision, geometric coframe nondegeneracy, and bridge compatibility draw from the same finite entropic and informational resources and cannot be made simultaneously ideal. Certified Causality, Locality, Nonlocality, and Relativity in the Einstein-Locked OT/GKSL Framework | Algebraic QFT/locality ; operational quantum theory ; quantum reference frames ; relativistic causality tests // Determines the exact status of causality, locality, nonlocality, and the principle of relativity within the Einstein-locked OT/GKSL architecture. Shows that causal-local spacetime semantics is a certified readout property rather than a primitive native axiom; proves a patchwise gluing theorem for certified local causal structure; and derives a unified finite-budget inequality showing that temporal precision, geometric certification, bridge admissibility, and overlap compatibility all compete for a single residual causal-local headroom on finite effective support. Entropic Tick Cost and Certified Temporal Readout in the Einstein-Locked OT/GKSL Framework | Demonstrates that classical ticks are finite-resource readout objects extracted from native entropic ordering, rather than primitive background parameters. Decomposes the entropic tick cost into native, extraction, and certification branches, and derives a theorem-level certified temporal budget inequality connecting temporal resolution, finite effective support, and certification margins. Entropic Tick Cost & Spectral Budget | Page–Wootters time ; thermal time hypothesis ; quantum clocks ; Salecker–Wigner bounds // Establishes a theorem-strength certified boundary for classical spacetime by proving a fundamental trade-off between entropic tick resolution, coframe stability, and finite informational budget. Optimal-Transport Gravity Trilemma | Identifies the certified operational boundary of geometric readout by proving the fundamental trade-off between temporal resolution, coframe stability, and bridge fidelity. Toy Certified Pipeline from Optimal Transport QCD | Provides a protocol-level implementation and scaling model for certified bridge margins. Certified Spectral Boundary from Heat-Kernel Budgets and Entropic Transport in the Einstein-Locked OT/GKSL Framework | Heat-kernel spectral budgets; entropic OT/GKSL transport; certified spectral boundary; Einstein-locked readout. Develops a spectral-geometric control layer for the OT/GKSL framework, where the native heat trace bounds finite spectral resources, the cutoff gap defines a certification margin, and entropic transport controls the drift of readout-support budgets without inducing a state-dependent Einstein–Hilbert kinetic term. Correlation Separation in the Einstein-Locked OT/GKSL Framework | Establishes a theorem-level distinction between native, readout, and causal-local correlations, and reframes the horizon information problem through certified-domain correlation layering 4. Cosmological Dynamics & Global Readout Constraints: Vacuum-like Residual Energy from Constitutive-Holonomic Balance in a Minimal Reduced OT-C3 Sector | Effective potentials ; Coleman-Weinberg ; Sakharov induced gravity ; vacuum energy problem // Demonstrates analytically that the macroscopic cosmological constant emerges as a non-zero vacuum-like residual energy resulting from the exact balance between scalar constitutive dissipation (source sector) and the non-commutative holonomic barrier of the Optimal Transport geometry. Homogeneous Closed Readout Dynamics under Finite Spacetime Budget | FLRW cosmology ; effective dark energy ; backreaction ; EFT of dark energy// Constructs a homogeneous and isotropic model (G-FLRW) demonstrating how the spacetime budget acts as a branch-selection mechanism, effectively identifying the vacuum-like sector (Λ) as the maintenance cost of certified spacetime solvability. Branch-resolved Einstein-locked OT–GKSL route to the Hubble tension: minimal background model, cleaned selection scan, and first viability window ΛCDM/CAMB/Cobaya ; Planck likelihoods ; effective dark energy / early dark energy literature Fixed-Dimension σ8 Suppression with Growth-Informed Likelihood Gains in a Low-Energy GKSL–Optimal-Transport Quantum–Classical Gravity Interface Stress-Tested against Planck, BAO, Supernova, KiDS-S8 and DESI DR2 5. Experimental Protocols and Testability: Testing Source-Side State Dependence in Gravity with Lock-In Atom Interferometry | Kasevich–Chu ; Peters–Chung–Chu ; Rosi–Tino ; atom gravimetry // Proposes a concrete experimental protocol to falsify source-only emergent gravity at low energy. A Lock-in Atom-Interferometric Test (Clock) | Detailed operational implementation of the low-energy readout test for the Einstein-locked framework. Experimental Separation of Readout and Causal-Local Correlation Layers in the Einstein-Locked OT/GKSL Framework //Circuit QED / transmons ; readout fidelity ; mutual information ; quantum verification // Proposes a falsifiable experimental protocol (CLCP) to test the layered structure of correlation observables by separating certified readout and causal-local licensing thresholds on a controllable quantum platform . 6. Mass Generation: Mass Generation and Vacuum-Like Residual Sourcing Theorem in the Einstein-Locked Optimal-Transport/GKSL Framework | This paper establishes a theorem-oriented source-side mechanism for mass generation and vacuum-like residual sourcing within the Einstein-locked OT/GKSL framework for open quantum sources A Theorem on a CDM-Like Intermediate Branch in the Einstein-Locked OT/GKSL Framework | This paper establishes a theorem-level result within the Einstein-locked OT/GKSL framework: cold-dark-matter-like behavior can arise internally as a stable intermediate branch of the reduced constitutive--holonomic source-side sector, without introducing a new primitive dark particle and without modifying the Einstein--Hilbert kinetic block. 7. Dirac Electron Dynamics: Optimal-transport + GKSL: Certified Recovery of Dirac Electron Dynamics in Central Abelian Potentials from the Einstein-Locked Optimal-Transport-GKSL Framework | Dirac equation ; Foldy–Wouthuysen ; gauge-covariant derivatives ; central potentials // This paper establishes a certified recovery of standard relativistic electron dynamics from the fermionic gauge-enriched sector of the Einstein-locked Optimal Transport OT/GKSL framework. The paper identifies and constructs a certified fermionic readout regime in which the Einstein-locked OT/GKSL framework recovers standard Abelian Dirac dynamics in mathematically controlled form.