Where do physical structures come from?
One of the central questions of Cosmochrony is how physical structures such as mass, particles, or hierarchy emerge from a deeper relational substrate.
Instead of assuming these structures from the start, the programme asks a different question: what appears when the underlying relational system is progressively unfolded?
At each stage of this unfolding, new configurations become accessible. But not all of them represent genuinely new structure. Many are redundant, reflecting constraints that were already present at earlier stages.
Measuring genuine novelty
The key quantity is therefore not how many configurations exist, but how many of them bring new independent structure.
This is what we call projective capacity: the amount of new information that cannot be reconstructed from what was already available.
In practice, this is measured step by step, by comparing what each new layer adds beyond the structure already built.
A progressive loss of independence
Earlier results in the programme revealed a surprising phenomenon: as the system unfolds, new configurations become increasingly constrained.
Even though more and more configurations are accessible, they bring less and less new independent structure. The system becomes progressively organized rather than chaotic.
Why this was difficult to observe
Two obstacles prevented this effect from being measured clearly.
- Geometric obstruction: in some models, the unfolding is so fast that the relevant regime is compressed and becomes unobservable.
- Representation mismatch: even when the geometry is correct, the tools used to describe configurations may fail to capture their true structure.
By the time of O10, the geometry had been fixed, but the representation was still inadequate.
What O11 achieves
O11 introduces a representation better aligned with the internal structure of the system.
This makes it possible to measure, for the first time, how much genuinely new structure appears at each stage of the unfolding.
The result is clear: the contribution of each new layer follows a simple law.
new structure ∼ n−δ
This means that each new stage contributes less independent structure than the previous one.
A quantitative signature of emergence
The exponent δ measures how fast new structure becomes redundant.
Numerically, it stabilizes near a value around 3.4 in the current approximation.
This is the first time such a quantity can be measured reliably within the programme.
Why it matters
This result suggests that physical structure does not emerge from unlimited complexity, but from a progressive reduction of independent possibilities.
In other words, what we perceive as stable structures may correspond to regions where redundancy dominates and new degrees of freedom become constrained.
Next step
The current result relies on an approximate representation. The next step is to replace it with an exact mathematical construction, which should confirm the value of the exponent and connect it directly to the underlying theory.