Core Semiotic Universe

The interactive semioverse extends a semiotic universe. The base layer provides:

• a semantic domain H that is a complete Heyting algebra,
• a modal closure operator j,
• a trace comonad G,
• definable operators interpreted into H,
• fragments and a closure operator S.

This layer ensures that all semantic work is closed under logic, modality, and temporal trace before any thing-facing interaction is added.