10. Bounded on purpose · Convergence Programming

Convergence Programming is bounded not because it is small, but because bounded worlds make oversight measurable.

This is the epistemic contract, and we would rather state it plainly than have it discovered. Every boundary below is a place where the framework declines to claim something.

Boundary	What is assumed	Why it matters
Task	A scoped executable world, not the whole of human value.	Prevents overclaiming.
World	An environment that can be modeled, simulated, sampled or operationally scoped.	Makes grounding possible at all.
Ledger	A hidden but finite evaluator target.	Makes scoring possible.
Observation	Claims limited by what the history actually contains.	Gives the non-certification result its force.
Action	A defined action surface.	Lets risk scale with autonomy.
Budget	Oversight costs questions, scenarios, experts, tools, compute.	Connects to scalable supervision.
Envelope	Evidence valid only under stated conditions.	Handles drift and deployment shift.

What this is not: a theory of all human values, a replacement for formal methods, a claim that natural language is a sufficient specification, an assumption that every hidden constraint is discoverable, or an argument that long-running agents are impossible. The boundedness is not a retreat from the alignment problem. It is what turns abstract oversight failures into measurable trajectory failures you can run today.

Eight worlds in which to ask the question

The paper proposes these settings for evaluating discovery and evidence. Each illustration separates the visible task from one local constraint that changes what action is supported.

The eight proposed worlds are clinic intake, cold-chain logistics, restaurant compliance, school pickup, support escalation, finance approval, government permit, and field-service dispatch. Each pairs a request with a local rule, an observation that can reveal it, and a repair that needs rechecking. These are proposed evaluation designs, not released worlds or measured runs.

For researchers

The safety relevance sits in the weak-inspector, strong-generator gap: as action surfaces expand, the problem becomes scalable oversight in a bounded, executable form. The paper does not claim to solve superalignment; it makes several oversight failures measurable in artifact and agent worlds, and proposes an evaluation design (Convergence Worlds with hidden ledgers, action surfaces, evidence envelopes, autonomy budgets and a discoverability invariant) whose primary metrics are false-convergence rate, final full-ledger gap, critical-blocker-free action and decision calibration error. The benchmark is proposed, not released; no results are reported here.