OT-GKSL
Published May 17, 2026 | Version v21
Preprint Open

A Source-Audited Production-Track CAMB/Cobaya Stress Test of a Frozen Einstein-Locked GKSL Late-Growth Branch: R8B Planck-Lensing Post-Processing and R9A/R9C Full Lensing MCMC

Authors/Creators

Description

Update:  Optmal-transport /GKSL framework: Stress-Test against Planck, BAO, Supernova, KiDS-S8 and DESI DR2

Framework: Foundations

This record provides the manuscript and reproducibility material for a source-audited CAMB/Cobaya stress test of a frozen late-growth readout branch. The branch is compared against a dormant identity branch under matched Cobaya likelihood configurations. Native Planck 2018 lensing is tested in two ways: first by post-processing completed active/dormant chains, and then by full MCMC inclusion from the beginning of the sampled Planck-primary-plus-lensing likelihood.

The release is organized around an executable active/dormant branch pair, not around an after-the-fact rescaling of published chains. The tested object is a frozen CAMB source-level readout state, implemented through a compiled active/dormant late-growth response in CAMB and then evaluated through matched Cobaya likelihood runs. The audit material includes CAMB source records, active and dormant branch controls, Cobaya YAML configurations, chain outputs, effective-sample diagnostics, native Planck-lensing post-processing records, full-MCMC Planck-primary-plus-lensing runs, likelihood-isolation diagnostics, and SHA-locked traceability artefacts.

The production branch acts at the CAMB matter-power and growth-amplitude readout level. The dormant branch returns the identity readout. In the active branch, the fixed transmission is

    P_active(k,z) = Gamma_eff P_dormant(k,z),

and

    sigma8_active = sqrt(Gamma_eff) sigma8_dormant,

with

    Gamma_eff = 0.9407576577720417

and

    sqrt(Gamma_eff) = 0.9699266249423416.

The operative source-level implementation is tied to the CAMB Fortran record `fortran/results.f90`, through the module `c1k_stage25_late_growth_response`. The source audit verifies the active/dormant ratios for both P(k) and sigma8 before any likelihood-level interpretation. This is therefore not a posterior scalar-amplitude adjustment in Cobaya.

The likelihood-facing sequence has three main stages. First, a production-track Planck NPIPE/CamSpec high-ell TTTEEE plus compressed-S8 MCMC compares the active branch to the dormant identity branch and recovers the intended lower-growth displacement. Second, R8B adds the native Planck 2018 lensing likelihood, `planck_2018_lensing.native`, by Cobaya post-processing on the completed active and dormant chains. Third, R9A/R9C includes the same native Planck-lensing likelihood from the beginning of both MCMC runs, giving the full sampled Planck-primary-plus-native-lensing confrontation of the same frozen branch.

The completed R9A/R9C full-MCMC comparison contains 12000 chain rows per branch. The reported effective-sample fractions are:

    f_ESS,dormant = 0.5760618629

and

    f_ESS,active = 0.5844448656.

On the sampled active/dormant comparison, the active branch remains lower:

    Delta chi2_total = -4.946277664,

    Delta chi2_lens = -0.6871262924,

    Delta(-log P) = -2.473136239.

The corresponding growth-coordinate shifts are

    Delta sigma8 = -0.02055920864

and

    Delta S8_recon = -0.01668570298.

As a likelihood-isolation diagnostic on the completed R9A/R9C chain support, the compressed S8-like contribution is removed from the reported chi-square decomposition. The active branch remains lower on the Planck high-ell plus native-lensing combination alone:

    Delta chi2_high-ell+lensing,no-S8 = -1.3668761177,

with separate contributions

    Delta chi2_high-ell = -0.6797459397

and

    Delta chi2_lens = -0.6871262924.

This diagnostic shows that the reported full-MCMC active-over-dormant direction is not carried only by the compressed S8-like term.

The scope of the record is explicit. This deposit does not claim a first-principles validation of the full upstream OT--GKSL framework. It does not introduce a sampled scalar-field sector, a primitive dark-fluid sector, or a sampled curvature-prefactor function G_eff(z,k). It also does not claim that the upstream certification burden has been independently derived here. The present production branch is a downstream late-growth readout implementation tested in CAMB/Cobaya. The result is a conditional, source-audited, likelihood-facing stress test of one frozen executable branch.

The remaining validation frontiers are separate: a response-conserved Boltzmann-sector implementation, real multi-probe LSS likelihoods with full covariance and nuisance treatment, and independent calibration or derivation of the upstream certification burden. These are not folded into the present claim.

The purpose of this deposit is reproducibility and evidence separation. Source-level implementation, dormant identity controls, active readout probes, matched active/dormant Cobaya configurations, R8B native-lensing post-processing, R9A/R9C native-lensing full MCMC, R9F likelihood-isolation diagnostics, and SHA-based audit artefacts are kept as distinct evidence layers. This structure prevents the completed numerical stress test from being confused either with a full fundamental-theory validation or with a notebook-level scalar rescaling.

 With this interpretation fixed, the numerical results below quantify how the tested branch behaves under progressively stronger observational stress: production-track Planck high-ell plus compressed growth, R8B native-lensing post-processing, R9A/R9C native-lensing full MCMC, and likelihood-isolation diagnostics.

Framework-level meaning and falsification content of the test:

This release stress-tests the cosmology-facing consequence of a broader OT--GKSL Source/Readout  Foundations programme.  The upstream framework is
formulated as a low-energy Einstein-locked source/readout architecture: 
The gravitational kinetic sector is kept fixed, while readable state-dependence is carried by certified source/readout branches.  Its main validation domain is broader than cosmology and includes laboratory-facing protocols such as material-dependent source response, cold-atom and clock readout, condensate and superfluid platforms, cryogenic control regimes, and branch-discriminating lock-in or differential protocols. 

The CAMB/Cobaya analysis tests the part of this programme that becomes observable in late-growth cosmology.  The tested object is the cosmology-facing projection of a source/readout branch: a frozen late-growth fingerprint, implemented as a matched active/dormant CAMB/Cobaya branch pair, and exposed to likelihood blocks that can
falsify that projection.  This tested intersection is not decorative. It is a framework-committed downstream consequence: the branch predicts a specific active readout displacement in growth observables while keeping the Einstein--Hilbert kinetic sector fixed and without introducing a sampled scalar-field sector, primitive dark-fluid sector, or sampled curvature-prefactor function G_m eff(z,k).

The constraining power of the test comes from the fact that the same frozen active branch must survive several non-equivalent observational directions.  Planck high-elm tests the primary-CMB fit quality. Native Planck lensing tests the integrated growth-and-geometry response, which is the natural failure channel for a late-growth suppression branch.  The compressed growth diagnostic tests the intended low-growth direction.  BAO/SN extensions test low-redshift geometry.  These blocks
do not merely repeat the same observable; they probe different ways in which the source/readout projection could fail.

The release therefore addresses the following decision-level risk:

    H_null:
    the cosmology-facing OT--GKSL source/readout branch becomes     incompatible with Planck primary-CMB, native Planck-lensing,
    late-growth, or low-redshift geometry constraints once it is     implemented as an executable CAMB/Cobaya object.

against the branch hypothesis:

    H_branch:
    the same frozen source/readout fingerprint can be implemented as a     matched active/dormant CAMB/Cobaya branch pair and can survive those
    likelihood constraints without being sampled, retuned, or converted     into a free phenomenological amplitude.

A strong failure of the active branch against Planck high-ell, native Planck lensing, or BAO/SN geometry would have directly weakened the viability of the cosmology-facing projection of the OT--GKSL source/readout framework.  Conversely, the completed R8B/R9A--R9C sequence reduces the risk that this branch is observationally  incompatible, a post-hoc scalar rescaling, or an artefact of adding lensing only after sampling.

The tested signature is not asserted to be mathematically unique among all possible effective cosmological mechanisms: other mechanisms can also lower late-time growth.  The distinctive content here is the constrained combination of framework placement and implementation requirements: 
Einstein-locked kinetic sector, source/readout response, active/dormant branch logic, frozen upstream amplitude, source-level CAMB implementation, matched Cobaya likelihood exposure, and native Planck-lensing confrontation.  This combination makes the test informative for the OT--GKSL source/readout programme even though it is a branch-level test rather than a complete validation of the full native OT--GKSL dynamics.

The evidence gain should therefore be read as branch-level risk reduction.  The release tests whether the current cosmology-facing source/readout branch is executable, auditable, active/dormant controlled, and compatible with the principal Planck high-ell, native-lensing, and growth-facing constraints.  The remaining validation
layers are then sharply identified: a freshly sampled no-S_8-like MCMC, BAO/SN and later real-LSS likelihoods with full nuisance and covariance treatment, independent calibration or derivation of the upstream certification burden, laboratory-facing source-side tests, and a response-conserved Boltzmann-sector implementation in which the
source/readout response is propagated through perturbation and lensing sectors rather than applied only at the final matter-power and sigma_8 readout level.

  • Bibliography:

    • GKSL / Lindblad — foundational open-system framework for completely positive quantum dynamical semigroups.
    • Carlen–Maas — bridge between quantum Markov semigroups, entropy production, and optimal transport geometry.
    • Lovelock + Donoghue — Einstein-lock consistency and low-energy effective field theory (EFT) interpretation of gravity.
    • Jacobson + Sakharov — gravity interpreted as an equation of state or induced/emergent phenomenon.
    • Vassilevich / Seeley–DeWitt — spectral bridge from microscopic operators to geometry and effective actions.
    • Bekenstein–Hawking–Wald — black-hole horizons, entropy, and Noether-charge formulations of gravitational thermodynamics.
    • Wilson / Gross–Wilczek–Politzer — QCD, gauge structure, confinement, and asymptotic freedom.
    • Kasevich–Chu / Peters–Chu / Rosi–Tino — atom-interferometric gravimetry and precision low-energy gravitational testing.
    • Blais–Girvin–Oliver — transmon qubits and circuit-QED architectures relevant to CLCP/QBIT implementations.

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Other

Source--Geometry Equivalence and the OT--GKSL Readout introduction ( Foundations):

The starting point is not a technical modification of general relativity, but a deeper question about the ontological status of geometry in physics.

With special relativity, Einstein removed space, time, and simultaneity from the status of absolute structures. Lengths, durations, synchronizations, and reference frames are no longer properties of a pre-given geometric theatre. They are tied to operational procedures: clocks, rods, signals, observers, and physical protocols capable of comparing measurements. Geometric invariants remain extraordinarily powerful, but they are already reconstructed objects. They organize and reconcile operational measurements that, taken separately, depend on the physical conditions under which they are made.

Geometry therefore does not disappear. Its status changes. It ceases to be an absolute container and becomes a structure of invariance reconstructed from physical measurements. This is one of the deepest lessons of relativity: geometric objectivity survives, but no longer as the objectivity of a pre-existing background independent of measurement. It becomes the objectivity of a coherent reconstruction across observers and protocols.

Quantum theory intensifies this shift. It shows that an experimental protocol does not merely reveal a pre-existing classical property; it helps define which observable is being measured. Interference, polarization, which-path information, delayed-choice logic, and basis-dependent readout all show that one cannot naively separate the measured object, the measuring protocol, and the information extracted. Physics no longer describes only classical objects carrying definite properties. It describes states, correlations, amplitudes, observables, and readout operations.

This is where the tension with general relativity becomes deeper. Einstein’s equations are usually read as an interaction between two poles: geometry tells matter how to move, and matter tells geometry how to curve. Under this interpretation, if matter sources are quantum, it appears natural to quantize geometry itself. Geometry is then promoted to an object of the same ontological category as quantum fields, and one searches for gravitons, a quantum metric, spacetime foam, or some fundamentally quantized geometric structure.

But this conclusion is not forced. It depends on the prior assumption that geometry is the fundamental object to be quantized. Relativity itself had already weakened that assumption. Geometry is what makes operational measurements coherent; it need not be the primitive substance from which physics begins.

The difficulty becomes sharper when the sources themselves are genuinely non-classical. A quantum source is not a point-like body endowed with a definite position, trajectory, orientation, and proper time. It is described by a state, a density matrix, coherence, correlations, decoherence channels, and readout conditions. If a physical region is dominated by sources in condensate-like, collective, or strongly coherent states, it becomes operationally problematic to define the classical reference frames needed to construct an ordinary background geometry. Without classical position, orientation, and proper time for the sources, metric geometry cannot simply be assumed as a primitive object from the operational point of view.

This is the central displacement introduced by the OT--GKSL framework. The relation between source and geometry need not be understood as an interaction between two primitive objects of the same level. It can instead be understood as a non-naive equivalence: classical geometry is the stable readout form of source content once that content becomes classicalizable.

The analogy with E=mc2 is instructive. Mass and energy are not identical notions at the level of their original conceptual categories. Yet relativity reveals a deep equivalence between them. Similarly, geometry and source content should not be naively identified. But Einstein’s equations can be read as expressing a source--geometry equivalence: what we call geometry is the reconstructed, readable, certified form of source content within a classical operational window.

On this reading, geometry is not the object that must be directly quantized. Quantum complexity belongs first on the source side: states, coherence, entropy, density matrices, dissipative channels, gauge structure, holonomies, and classicalization. Geometry then appears as a certified projection of source content, as a readout condition, not as a primitive quantum substance.

This shift has a major consequence: the Einstein--Hilbert sector remains locked. The gravitational kinetic block is preserved. One does not place a state-dependent G(x), a free Geff(z,k), or a state-dependent prefactor in front of R[g]. The classical gravitational law remains Einstein-locked. What may depend on the state is not the way a classical source reads geometry, but the source/readout contribution through which a source, depending on its coherence and degree of classicalization, becomes gravitationally readable.

This simultaneously protects several structural requirements. It avoids a direct variation of G, preserves the weak equivalence principle inside the certified classical window, avoids conflict with the Bianchi identities, and bypasses pathologies associated with treating spacetime geometry as a primitive quantum object. The problem is not evaded; it is moved to the level where quantum physics naturally places it: the state of the sources and their transition toward classical readout.

The native level of the framework is therefore not a metric manifold. It is a state space. The central object is not gμν, but the density matrix and its open-system evolution. The natural mechanism for decoherence and dissipation is of GKSL type. But if metric geometry is not primitive, then metric time cannot be taken as the ultimate native parameter. At the fundamental level, evolution is better understood as a flow on state space, tied to entropy, information cost, dissipation, and quantum optimal transport geometry.

The link between GKSL dynamics and optimal-transport geometry provides the conceptual bridge. Dissipative evolution can be understood as an entropy-gradient flow on a state manifold equipped with a transport structure. Classical physical time appears within the certified readout window; the native parameter is closer to an entropic time, defined by the evolution of the state, the cost of information, decoherence, and classicalization.

From this native level, one can define moments, entropic energies, channels, holonomic branches, stiffnesses, mass terms, and structures analogous to non-Abelian gauge connections. QED, QCD, mass generation, effective dark-matter-like behaviour, effective dark-energy-like behaviour, and classical Einsteinian gravity are not introduced as independent ad hoc sectors. They are to be recovered as coherent branches, projections, or readouts of the same source--state--transport--geometry architecture.

Classical geometry thus becomes what a radical reading of relativity may have always suggested: not the quantum container of physics, but the readability condition of classicalized sources. It is objective because it is reconstructed stably inside a certified window, not because it is a primitive substance independent of sources, observers, and readout operations.

In this perspective, the current cosmological tests have a precise status. They are not a validation of the entire framework. They test a downstream projection of the source--geometry equivalence: a late-growth source/readout branch implemented in CAMB/Cobaya, modifying the growth contribution while preserving the Einstein--Hilbert block. If this projection were to fail against Planck high-ℓ\ellℓ, Planck lensing, or BAO/SN, it would genuinely weaken the cosmology-facing viability of the framework. If it survives, it reduces the risk that this source/readout interpretation is incompatible with cosmological constraints.

The programme is therefore not to build “one more quantum gravity” by quantizing the metric. It is to change the level of the question: how do open, coherent, quantum sources become classicalizable in such a way that a stable, Einstein-locked, geometrical readout emerges? This question, rather than the primitive quantization of geometry, is the core of the OT--GKSL framework.

 

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