Segal Coherence Interface Theory (SCIT)
Architecture Document Coherence Interface for Multi-Input Composition Purpose Build a coherence interface that makes “multi-input composition” usable without demanding strict syntactic associativity/interchange equations everywhere. Instead, composition is expressed as structured data + commuting comparison maps that guarantee the usual laws (associativity, unitality, whiskering/exchange) up to specified equivalence , and in a way that scales to bicategories / virtual equipments / Segal-style models. This is an interface architecture: it defines what data you must provide , what the system guarantees , and how you validate coherence . 1) Design goals G1 — Multi-input first-class Support composition of many inputs at once (strings, grids, pastings), not only binary composition. G2 — Coherence by structure, not by brute equations Replace fragile “prove 200 lemmas that diagrams commute” with a small number of universal commuting squares / naturality laws . G3 — Segal-like recover...