Falsifiability and observational hooks
Predictions
This page organizes the main falsifiable predictions of the Sobolev–Ozok Lattice (SOL) framework across cosmology, galaxies, black holes, and continuum behavior.
The goal is not only to describe what SOL proposes, but to show where its claims can be challenged by data, constrained by observation, or distinguished from standard expectations.
What this page does
Groups SOL predictions by domain so readers can quickly see where the framework becomes testable.
Why it matters
A framework becomes more serious when it makes concrete claims that can succeed or fail against observation.
How to use it
Jump to the domain you care about, then open the linked manuscript for the supporting derivation.
Cosmology
Supporting manuscript: “From Pre-Geometric Coherence to the Present Universe…” (Zenodo: 16890398)
In the cosmology branch, SOL proposes that discrete step-count structure can leave observable traces in large-scale behavior and propagation phenomena.
Discrete step-count signatures
These are examples of places where a discrete coherence history could leave structured observational effects.
- CMB large-scale anomalies, including suppressed low-ℓ power and possible large-scale alignment effects.
- BAO phase behavior with small coherent offsets tied to discrete step-count structure.
- FRB propagation with small frequency-independent, achromatic delay components distinguishable from ordinary plasma dispersion.
- Standard sirens showing possible GW–EM luminosity-distance mismatch if the two channels couple differently to the lattice structure.
Why this matters
These claims matter because they move SOL beyond conceptual cosmology and into possible observational discrimination.
Galaxies
Supporting manuscript: “SOL and the BTFR…” (Zenodo: 16884010)
At galaxy scale, SOL aims to recover regularities normally associated with dark-matter phenomenology through coherence structure rather than per-galaxy fitting.
BTFR without per-galaxy tuning
The main galaxy-scale claim is that the baryonic Tully–Fisher relation can emerge from the internal structure of the framework.
- A BTFR slope near 4 emerging from k = 2 coherence scaling, without introducing a separate tuned parameter for each galaxy.
- Rotation-curve behavior compatible with an asymptotically flat regime from the same structural logic.
Why this matters
This is one of the strongest applied hooks in the framework because it connects SOL directly to a major astrophysical scaling relation.
Black holes
Supporting manuscript: “Black Holes from SOL: Derivation, Galaxy Occupation Thresholds, and Quasi-Black-Hole Signatures” (Zenodo: 16889440)
The black-hole branch focuses on threshold behavior and possible quasi-black-hole deviations that could distinguish SOL from standard compact-object expectations.
QBH discovery relation
A strong falsifiability target is a structured relation between shadow deviation and ISCO shift.
- A linear relation of the form δsh = s(q) · δISCO with discrete slopes s(q) = 3, 6, 12 for q = 1, 2, 3.
- Systems closer to the occupation threshold, corresponding to lower σ/σmin, should display larger deviations than high-dispersion systems.
Why this matters
This is valuable because it creates a sharp observational target: a structured relation rather than a vague qualitative difference.
Continuum & spectral stability
Supporting manuscript: “Spectral Stability and Continuum Limit of the SOL Model” (Zenodo: 17924486)
This branch focuses on mathematical consistency targets, especially how discrete models behave as resolution changes and whether continuum-like limits remain stable.
Continuum-limit consistency
These predictions are less observational in the astrophysical sense, but they are still falsifiable within the mathematical behavior of the model.
- Eigenmodes should approach stable values across increasing lattice resolutions, providing a continuum-limit consistency test.
- There should be identifiable spectral-stability windows that help validate or reject discretization choices.
Why this matters
A discrete theory must not only fit ideas at large scale; it must also behave coherently under refinement and numerical testing.