    [tears][eyes]
This directed acyclic graph (DAG) formulation allows for:
Path analysis to trace semantic flow
Subgraph matching for idiom detection
Dynamic topology updates in dialog-based LLMs
B. Systemic Notation Using Lightweight Tensors
To generalize computational implementation, we define a simple Interaction Tensor I capturing:
i, j: Indexes of word pairs
k: Dimension representing interaction attributes
Let:
I = weight (w [2, +2])
I = stability (s [0, 1])
I = probability (p [0, 1])
Thus, for a phrase of 3 words, the interaction tensor would have shape [3, 3, 3], where the diagonal can be reserved for self-reflection metrics (i.e., lexical salience).
Example Tensor (Simplified):
For tokens: [0]: tears, [1]: eyes, [2]: crocodile
This tensor can serve as input to a differentiable module within LLM pipelines that modulates prediction paths or attention weights based on semantic resonance, not just token frequency.
Advantages of This Mathematical Formalism
Interpretability: Graph edges and tensor elements are human-readable, supporting explainable AI.
Computational Tractability: Sparse tensors and shallow graphs enable efficient integration with current LLMs.
Extensibility: This structure scales to higher interaction levels (n > 3) and can be fused with self-attention mechanisms in transformer architectures.
By embedding interaction structure into formal representations, CAS-6 enables models to navigate meaning space as a dynamic, context-sensitive topology---bringing them closer to the cognitive adaptability of human semantics.
