Theory · Predictions
Falsifiable predictions and the evidence each one requires
A hypothesis with no kill shot is not a hypothesis. Each entry below names the result that would end it.
Under the toy transform, effective separation is monotone non-increasing in every individual coupling, and strictly decreasing only for couplings on the active geodesic.
Evidence required
Sweep every edge across its range on multiple topologies and seeds; record any violation.
What would falsify it
A single reproducible case where increasing R_ij increases D falsifies our implementation or our transform.
Relational structure admits regimes where ‖δR‖ is small and |δD| is large — path-switch thresholds are the simplest example.
Evidence required
A search that finds leverage |δD| / ‖δR‖ far above the null-model distribution, reproducibly across seeds.
What would falsify it
If leverage never exceeds the shuffled null model, there is no nonlinear structure to speak of.
Distances built from information-theoretic couplings satisfy the metric axioms on a non-trivial class of states.
Evidence required
Metric audit passing on synthetic mutual-information matrices without shortest-path closure doing all the work.
What would falsify it
Systematic triangle-inequality violation before closure means the construction is not a distance and must be discarded.
Relational states of a given class reconstruct low-distortion embeddings into a smooth manifold, rather than arbitrary graph metrics.
Evidence required
Embedding distortion that falls with system size for structured states and does not for random ones.
What would falsify it
If structured and random states embed equally badly, emergence of geometry is not happening here.
Any adjacency change consistent with the model respects a causal ordering — no relational operation produces a spacelike-shortcut signal.
Evidence required
A Lorentzian extension in which the light-cone structure of the emergent geometry is computed and checked against the operation cost.
What would falsify it
If the framework can only be made to work by permitting signalling, the framework is wrong, not physics.
Adjacency change of a given magnitude carries a lower bound in energy or negative-energy resources.
Evidence required
A derived or estimated stress-energy correspondence with explicit energy-condition accounting.
What would falsify it
An unbounded-below cost or an unphysical resource requirement ends the engineering branch of the programme.
There exists an observable distinguishing relational-distance dynamics from a conventional geometric account.
Evidence required
A quantitative signature with a stated experimental regime and error budget.
What would falsify it
No distinguishing observable means the hypothesis is not science yet, whatever else it is.
Standing rule