Run the real algebra · families · twelve operations · the bridge
Not a paraphrase — the actual eight-rung modality ladder, executing.
A Value is a product of monoids across families; combine merges, chain composes along phases (and refuses a backward step), promote/reconcile/deliberate repair. A Score lives in a semiring. The bridge gates the gradient on the floor: a vetoed option becomes 0̲ and can never be selected. A third rung — norms — adds obligation, permission, and prohibition; govern stacks all three with the precedence alethic ▸ deontic ▸ axiological. A fourth rung lifts the algebra to trajectories: LTL monitor/supervise — safety as a runtime shield, liveness as a horizon obligation. A fifth lets the policy revise itself — revise/entrench, with a constitutional core it can tighten but never weaken. Three more rungs — epistemic (knowledge & graded belief), strategic (coalitional ability), and resource (the economy the ladder runs on) — complete the eight. Everything below runs client-side, importing the same .mjs modules that ship in the package.
1 · The laws hold
the cross-layer sandbox — all eight rungs & their bridges (all 97 laws): invariant · heuristic · bridge · deontic · temporal · reflexive · epistemic · strategic · resource. The exact suite node test/laws.mjs runs.
The proof it's the real algebra and not a story: each law checked against random values. Switch the semiring in the top bar and re-run — idempotence (H6) holds only on the tropical dioid.
2 · Composition catches a contradiction
the RAG pipeline · multi-family
Two sources are combined, an answer chained forward, then reused as its own context — a self-citation loop. No single family catches it; composed, consume refuses and names which families. Then the endomorphisms repair the value.
3 · The bridge: a strong action, vetoed
floor-then-gradient · OWASP LLM06
Three candidate actions, each a full Value plus a heuristic utility. The highest-utility one loops on itself (κ) and has no authority — consume vetoes it, 0̲ annihilates it, the gradient picks the best feasible action.