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
Map the conceptual transition toward modern cosmology, highlighting the roles of gravitation, observation, and cosmic evolution. Explain where SMM proposes a different starting point.
- Prediction after calibration
Present the calibration-fiber criterion for a conditional prediction. An additional observable must be fixed across the allowed calibrated models to avoid merely reusing its target value.
- Why normalized response misses absolute vacuum offsets
Explain the obstruction to inferring gravitating vacuum energy from normalized completion response. Adding an invisible offset exposes information that the response alone cannot determine.
- Why one clock model does not prove universality
Use the ungated-clock countermodel to show that a realizable clock law need not be physically universal. Explain the extra selection principle required for all material clocks to agree.
- From record refinement to a joint clock–band relation
Introduce the conditional relation connecting geometry, clock response, and matter transport. Explain why the interfaces and coefficients must be independently calibrated.
- Why local geometry can be statistically rare
Explain the entropy barrier to lattice-like relational memories in the stated permutation ensemble. The result concerns a specified preparation problem, not every possible mechanism for emergent space.
- The information cost of preparing locality
Introduce the relative-entropy lower bound on preparation resources. Explain how a geometric memory can require information scaling more strongly than the number of labels alone.
- Counting records to recover volume
Explore the archive and sampling assumptions used to connect normalized record counts with homogeneous four-volume. Compare a Poisson benchmark with the separately specified autonomous sampler.
- Designing an overconstrained atomic test
Turn the skeleton draft’s research direction into a practical analysis plan. Require more independent observables than fitted parameters and predeclare the cross-state prediction rules.