ifc-0269
18.3 A candidate double geometry
The proposed double object has the following interpretation.
|
Base structure |
Local directions |
Finite realization |
|
|---|---|---|---|
|
Image side |
Noise-indexed image state |
Score or probability-flow vector fields |
Conditioned generative flow groupoid |
|
Language side |
Visual theory and semantic model |
Concept, relation, binding, or interface variations |
Visual-sketch extension and semantic transport |
|
Core |
Shared image–language grounding |
Mixed binding and relational directions |
Admitted correspondence between language construction and visual effect |
If both sides integrate and satisfy the required interchange laws, their square structure is a candidate double groupoid whose infinitesimal object should be compared with DIAL. That conclusion is a research target, not an assumption. In particular, the stochastic side may require a second-order or Markov-enriched generalization of involution algebroids.
The core is experimentally concrete. Image geometry can expose a direction in which pixels or latents change without saying what the change means. Language geometry can distinguish symbols without guaranteeing a controlled visual effect. Their mixed core contains grounded attribute binding, relational composition, viewpoint-dependent identity, part–whole structure, and other effects that are invisible from either side alone.