With a slope and friction a marble can roll down and lose energy. Without friction it can keep moving; exact equilibrium is also possible. Driving can sustain a cycle. Noise changes the observed distribution. If motion reshapes the hill, the process changes its own future possibilities. These cases need different laws.
The four questions are: what is allowed, what does it require, how much weight does it carry, and how does it actually proceed? A photograph of where the marble is does not reveal the whole process.
Possibility says what is allowed. Weight says how strongly it counts. Consistency says whether parts can coexist. Two maps may each work but use different scales; comparison first needs the right conversion. If they then contradict each other for the same place under the same conditions, the whole does not yet fit.
Removing a hidden shared cause can leave the remaining parts coupled. In a static model this can appear as a four-way interaction. In a dynamic model past influences can return as memory, and fluctuations can be correlated in time. The model determines which terms are required; not every case produces all of them.
Within the weighting model, ε controls how sharply differences in cost matter. At finite ε multiple possibilities contribute. As it tends to zero, the lowest costs dominate, but tied minima can remain. The limit does not prove a unique universe.
The exact examples →Suppose you want to compare possible configurations. First specify what a configuration is and which variations are allowed. That is your space of alternatives. Saying “all possibilities” does not yet provide a usable list or measure.
Assign each configuration a non-negative resistance value. Fair comparison requires the same rule of measurement. A model might use description length, for example, but must then specify its language and precision.
This rule is a choice that needs justification. The words “least resistance” do not choose it for you.
Next assume that weight depends only on resistance. Also assume that independent composition adds resistances and multiplies weights. The formal theorem requires this rule for all non-negative resistance values.
With a positive weight no greater than one, an exponential rule follows. The same increase in resistance always multiplies weight by the same factor. If weight decreases anywhere, it decreases everywhere according to that rule. A rule that weights everything equally must be excluded separately.
Weights express relative amounts. Give two options weights 1 and ½. Dividing by their sum produces probabilities ⅔ and ⅓. With infinitely many options, first check that the sum is finite. With a continuous space, also specify how to integrate over the options.
Many individually light options can carry substantial weight together. The most probable individual configuration is not automatically the most probable entire class.
The calculation tells us what follows from the chosen model. It does not tell us that reality uses this model. A weighting distribution does not by itself set anything in motion either. A connection to physical states and dynamics is needed.
A landscape is a useful image: height represents resistance and the amount of mist represents weight. But the landscape's shape, the sizes of its regions and the weighting rule must already be known. The mist does not explain their origin.
According to EEML, the model itself should also be describable without unnecessary assumptions. That motivates comparison with alternatives. A short description does not make a model true. To prevail it must also account for phenomena and pass distinguishing checks.
The open task is to define resistance so that it excludes something in advance, without adapting it to the observation afterwards. The idea can then become a testable model. The zero point alone does not supply that definition.
Read the exact theorem →Open How do driving, resistance and history jointly determine a process? Consistency connects descriptions. K3 and α remain conditional research routes.
Reverse engineering through glue →The weight rule holds when you choose its assumptions. That theorem has now also passed the proof checker again. Two equally low valleys need not receive equal probability: a broad valley contains more possibilities than a narrow one. The calculated example divides probability roughly 63.4% versus 36.6%.
For K3, 24 is a calculable geometric quantity. Starting from a degree-four surface, it follows as 6×4. There is real mathematics to build on. The step from that geometry to measured α remains open. An error in an old numerical step invalidates that step, but does not prove the final aim impossible.
The K3 calculation step by step →v0.26 · 28 September 2026