This work proposes a reader-friendly, implementation-oriented core for reasoning across networks of human and LLM intelligences without fixing a single evaluative basis. The vision is a portable “comparative mathematics” layer: results are stated once and reused across cost, probability, and relational models by making all assumptions explicit and minimal. Technically, the paper adopts a right-written composition convention and separates assumptions into two tiers: (W) homwise pointed ω-cpos with only the declared small joins (plus a Fubini-style exchange assumption), and (S) Sup-enriched/quantaloid structure with composition preserving all small joins. On arrays (“matrices”), it defines a right-written convolution ⋆\star⋆ and shows that the Kleene path closure Path=⋁n≥1A⋆n\mathsf{Path}=\bigvee_{n\ge1}\mathsf{A}^{\star n}Path=⋁n≥1A⋆n equals the least fixed point of X↦A∨(X⋆A)X\mapsto \mathsf{A}\vee(X\star\mathsf{A})X↦A∨(X⋆A) under (W). A weighted Čech local-to-global lower bound is proved on a minimal promonoidal equipment, while a mask principle provides sound upper bounds and—under ω-algebraic, finite-support conditions—threshold completeness. The paper further develops transport under base change: with lax/oplax monoidal functors one gets transport inequalities F(Path)⋛Path′F(\mathsf{Path})\gtreqless \mathsf{Path}'F(Path)⋛Path′; with strong monoidal, equality. Nuclei are packaged as reflective subquantaloids, enabling clean residuation for sequent-style thresholds. For evolving bases, the path construction is Scott lower semicontinuous in time. The manuscript includes a formalization guide and a compact dependency table mapping every result to the exact joins/axioms it uses, supporting proof reuse and mechanization (Lean/Coq/Agda). Three minimal sanity-check models—Lawvere cost, [0,1] probability/similarity, and Boolean/Rel—instantiate the theory. The result is a portable, safety-aware foundation for multi-agent / multi-model reasoning, robust enough for alignment and planning pipelines yet light enough to adopt incrementally. Keywords quantaloid; quantale; Sup-enriched category; right-written composition; convolution; Kleene fixed point; ω-cpo; dcpo; declared joins; Fubini exchange; promonoidal equipment; weighted Kan extension; Čech bound; mask bound; threshold completeness; base change; lax/oplax/strong monoidal functor; transport inequality; equality transport; nucleus; reflective subquantaloid; residuation; Scott lower semicontinuity; Lawvere metric/quantale; probability/similarity; Boolean relations; domain theory; multi-agent systems; LLM alignment; comparative universes; proof reuse; formal verification.