What it does
The Changes-Sieve constructs a KMotif-regulated data object, a compact representation of an evolving graph or simulation that emphasizes structural change over raw state.
Rather than storing every edge equally, the sieve records persistent topological events:
- revisited paths
- seam formations
- branching singularities
- regulated motif transitions
These measurements are summarized through the RSP scalar,
[ \mathrm{RSP}(G)= \left(R,S,P\right), ]
where
- (R) measures revisitation complexity,
- (S) measures seam continuity,
- (P) measures branching ("plus-sign") structure.
Derived quantities such as
[ \tau=f(R,S,P) ]
and
[ \rho=\frac{S}{P+S} ]
provide scale-independent descriptors of structural organization.
The resulting object serves as a geometry-aware intermediate representation for simulation, reinforcement learning, and language-model reasoning. A path is a commonly used term in computational language already, and this is merely extending that commonality into a heuristic that is workable.
KMotif regulation
Central to the representation is the family of KMotifs,
[ |3n-2|{-2,5}, ]
which defines a regulated motif grammar governing admissible structural growth.
Rather than treating paths as arbitrary walks, KMotifs constrain evolution into recursively compatible local configurations that remain stable under repeated transformations.
The Changes-Sieve therefore records regulated change, not merely graph connectivity.
Mathematically, each regulated object may be viewed as
[
\mathcal{K}
\left( V,E, R,S,P, \mathcal{M}, \Phi \right), ]
where
- (V,E) are the underlying graph,
- (R,S,P) are the structural invariants,
- (\mathcal M) is the motif hierarchy,
- (\Phi) denotes the regulation operators that preserve admissible evolution.
This allows downstream AI systems to reason over persistent structural features rather than raw transitions.
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