The target is one retained source dynamics whose independently defined geometric, clock, and matter readouts converge to a compatible cosmology. Background agreement is a first benchmark; shared perturbation and normalization predictions provide stronger tests.
State the physical output before choosing the mechanism
The proposed output is an approximately homogeneous and isotropic geometry, a family of material clocks, propagating matter, and a conserved effective stress tensor. From these objects one should calculate expansion and light propagation. A further layer describes deviations from homogeneity and their growth.
This is more specific than asking for a temporal interpretation of a known scale factor. SMM supplies the ambition of a common origin; DTT should state how nested formation and outer completion restrict the outputs. A useful theorem would show that independently measured quantities agree because of the update, rather than because the same symbol was assigned to them.
Specify the source and its retained resources
Start with a state space S, retained memory, initial-state rule, autonomous update U, admissible local operations, and completion map Π. Define geometric comparisons and clock readings as separate observables of completed records. Explain which degrees of freedom are retained when a new spatial configuration becomes available.
The six inner roles must appear as nested dependencies in the actual operations or subspaces. The seventh completion role exposes a public record, not a new independent coordinate axis. Finite memory, control schedules, and preparation resources belong in the state description; leaving them outside can make a structured universe appear to emerge from an unstructured point without cost.
Recover a metric with an independent clock
A first finite model could produce record graphs with calibrated edge comparisons and stable local neighborhoods. Measure volume growth, diffusion, signal support, and material-clock response independently. A rank-three algebraic readout is useful, but it does not alone establish Euclidean distance or a universal causal cone.
Next compare persistent markers across completions to define a scale factor. Keep refinement of resolution separate from enlargement of physical distances. Show that different observers recover compatible large-scale geometry and that the same lapse converts the source parameter into the durations used by matter propagation and cosmological expansion.
Derive the effective dynamics and its conservation
State an effective action or equations for the retained geometric and matter variables. If Einstein gravity is recovered, identify the normalization of G, the vacuum term, and the stress tensor in one convention. The contracted geometric identities require compatible covariant stress conservation; an arbitrary new expansion term cannot be added without checking that consistency.
In a homogeneous sector the simplest check is ε̇+3H(ε+p)=0 for each separately conserved component. If source completion transfers energy between sectors, write explicit exchange terms whose sum vanishes in the total balance. This turns an informal claim of continual creation into a definite dynamical accounting rule.
Worked benchmark: radiation and matter together
Consider a flat standard-gravity benchmark with conserved radiation and pressureless matter, no Lambda, and a=1 at the reference epoch. Let their reference density fractions be Ωr and Ωm, with sum one. Conservation fixes the background relation H²/H*²=Ωra−4+Ωma−3.
Equality occurs at aeq=Ωr/Ωm. For the purely illustrative choice Ωr=0.1 and Ωm=0.9, equality is at a=1/9. A numerical source model should reproduce both limiting power laws and the crossover under one fixed clock and normalization. These chosen fractions are a test case, not measured cosmological parameters.
Go beyond fitting the background
A background expansion curve does not determine structure growth. In the pressureless, subhorizon Newtonian limit of standard gravity, the density contrast obeys δ̈+2Hδ̇−4πGρmδ=0, with ρm a mass density. For a flat matter-only background, H=2/(3t) and ρm=1/(6πGt²).
Trying δ proportional to tq gives q²+q/3−2/3=0. The modes are t2/3 and t−1, so the growing mode follows a(t). This is a precise conditional benchmark connecting background and perturbations. Pressure, radiation, horizon-scale effects, or modified gravity require a different equation rather than reuse of this result.
Seek a relation that survives calibration
Fix the source specification and the quantities used for calibration before computing reserved outputs. If an expansion function and an independent fluctuation function remain freely adjustable, fitting both does not establish a shared origin. A stronger result fixes a relation among their coefficients or predicts a finite-resolution departure with a definite scale dependence.
The Planck analysis illustrates why background parameters and primordial perturbation assumptions must both be declared. A new source model should be translated into comparable observables rather than compared only through similar-looking diagrams. Standard baselines, approximation errors, and any additional predicted contribution should remain separately identifiable.
A concrete sequence of success criteria
First establish finite, reproducible readouts and exact limiting checks. Then show a controlled large-scale regime with a common clock, approximately isotropic geometry, and conserved dynamics. Next calculate background expansion and at least one linked perturbation or propagation observable without introducing a separate normalization for it.
Finally, identify the source-imposed relation that alternatives could violate. A result fixing the response of geometry and matter together would be meaningful even before a complete cosmic history is derived. This sequence gives SMM/DTT a tractable cosmological program in which each new theorem closes a stated dependency rather than broadening an unconstrained interpretation.
Continue with the articles
- Summary of Modern Theories of Cosmology
Modern cosmology connects gravitation, expansion and the formation of structure. These established questions provide concrete targets for an SMM/DTT account of generated space and physical clocks.
- Prediction after calibration
Calibration produces a prediction only when the proposed output is fixed across the remaining admissible models, or constrained to a stated range. This criterion distinguishes cross-sector consequences from reuse of a fitted target.
- Why normalized response misses absolute vacuum offsets
Normalized responses erase source-independent offsets even when those offsets matter to an absolute functional. The exact obstruction explains why stiffnesses, spectral ratios, and temporal averaging do not alone determine gravitating vacuum energy.
- Why one clock model does not prove universality
Protected and ungated clocks can coexist with the same record geometry while assigning different readings to it. This countermodel shows why constructing one desired clock does not establish a universal material-clock law.
- From record refinement to a joint clock–band relation
Independent count, scale, phase, clock, and band measurements can satisfy a joint refinement relation under the supplied interfaces. The ungated-clock alternative identifies why the protected-clock premise remains essential.
- Why local geometry can be statistically rare
Lattice-like signed operation tables are rare in the stated permutation ensemble, with an entropy penalty of order N log N. Bounded selection costs cannot overcome that asymptotic disadvantage under the theorem's assumptions.
- The information cost of preparing locality
Preparing a geometric memory with appreciable probability requires relative entropy when geometry is rare in the reference ensemble. The bound quantifies information resources without automatically identifying them with work or elapsed time.
- Counting records to recover volume
Normalized archive counts recover four-volume under a supplied sampling law. Grid and Poisson examples show why mean density, count fluctuations, and autonomous preparation require separate physical explanations.
- Designing an overconstrained atomic test
An overconstrained atomic test compares independent residual directions with a declared set of source and nuisance coefficients. Covariance weighting and singular-value analysis reveal whether the chosen observables can actually distinguish the proposed mechanism.