Research · Convergence Programming · The paper
Convergence Programming
Iterative, World-Grounded Alignment of Lossy Human Intent with Executable Behavior
Abstract
AI-assisted workflows, from "vibe coding" to tool-using agents, now turn lossy natural language into executable behavior. Yet behavior that looks correct under a demo, visible review, or task-completion score can still fail under hidden world states, scenario-dependent requirements, or operational constraints. We call this failure false convergence: the trajectory appears ready according to visible proxies while hidden requirements, critical blockers, or untested world outcomes remain unsafe, unsatisfied, or unmeasured.
We introduce Convergence Programming as a response to false convergence. Rather than treating AI-assisted creation as a prompt or final artifact, Convergence Programming treats it as a world-grounded trajectory: prompts, generated procedures, actions, observations, feedback, repairs, and act/ship/block decisions over time. The central claim is that AI-generated behavior fails not only because generation is weak, but because readiness is information-limited: a system cannot certify distinctions its trajectory has not extracted from the world. We recast a set of information-theoretic and probabilistic limits in a common convergence notation, organizing them into one account of when behavior can be certified as ready. As a scoped agentic extension, we compose autonomy accounting with a common-mode verifier model to derive a conditional action-window bound, implying that persistent autonomy must be receding-horizon rather than one indefinitely valid approval under stale evidence. We specify a preregisterable evaluation design centered on hidden-constraint discovery and calibrated permission to act, instantiated in a worked clinic-intake world.
The figures on this site illustrate the arguments. They do not report measured results or establish that this approach outperforms other development workflows.
Contributions
- A definition and theory of false convergence.The failure mode in which visible interaction, user acceptance, model confidence, known-ledger scores, or other observable proxies suggest readiness while hidden requirements, critical blockers, or untested world states remain unsafe or unmeasured, formalized as information-limited under bounded evidence.
- Convergence Programming as a response.AI-assisted creation defined as a world-grounded trajectory from lossy intent signals to executable behavior; as a scoped agentic extension, autonomy accounting and verifier correlation combine into a conditional action-window budget rather than a standalone certificate of long-running operation.
- Design criteria for convergence evaluation.Convergence Worlds: partially observable executable environments with hidden constraints, action surfaces, evidence envelopes, autonomy budgets, discoverability invariants and preregisterable metrics, instantiated in the clinic-intake world.
The named results, in plain statements
Formal statements and proofs are in the manuscript. Each result below is conditional on the paper's boundedness assumptions: scoped executable worlds, finite observation histories, evaluator ledgers, defined action surfaces, and evidence envelopes.
- Latent operational target and intent ledger
- The hidden target behavior is supposed to satisfy is represented for evaluation by a ledger of anchors with weights, severities, visibility status and satisfaction scores. Three residual gaps follow: full (all anchors), known (anchors revealed so far), unrevealed (the rest). The full ledger is an evaluator instrument, not available to the acting system.
- Specification debt
- A prompt is an information bottleneck. Constraints neither encoded in it nor revealed by later interaction are absent from the evidence, and no model capability turns unobserved world structure into evidence.
- No free readiness
- If two worlds produce the same observation history but demand different safety decisions, no rule that sees only that history can certify both. The distinguishing observation must be made, elicited, monitored, or carried as open risk.
- Proxy improvement is not full convergence
- A known-ledger or visible score can improve while full-ledger behavior does not. A large difference between known and full gaps is a false-convergence signature.
- Critical blockers are not averages
- One unresolved critical blocker changes the type of decision. Under any average-gap threshold, enough routine successes hide a single critical failure; readiness requires a lexicographic blocker gate.
- Autonomy spends evidence
- Every accepted action draws down a finite budget of residual uncertainty. Given an independently provenanced critical-risk bound and a common-mode verifier model, the number of actions a body of evidence licenses is bounded: the conditional action window. Persistent autonomy must be receding-horizon.
- Repair can be anti-convergent
- A repair that fixes the latest visible issue can corrupt prior anchors or optimize a proxy. The positive counterpart is conditional: if repair is contractive with respect to the latent residual gap, convergence is reachable at bounded oversight cost, with interactions logarithmic in the desired precision.
- Evidence must be independent, scoped, and horizon-bounded
- Verifier multiplicity is not independence: shared families, prompts, data and frames impose a common-mode risk floor. Self-reported evidence not bound to independent observation collapses evidence-gated readiness into self-report. Evidence certifies systems under conditions, not globally.
- True convergence may surface bad news
- Discovering a hidden anchor can reduce epistemic uncertainty while making the measured known-ledger gap temporarily worse. Non-monotonic known scores are not necessarily failures.
- The architecture rule
- If a design cannot distinguish critical hidden scenarios, preserve discovered anchors across repair, bind readiness claims to independent evidence, veto known critical blockers, or scope evidence to the deployment envelope, then there is a bounded world consistent with its observations in which it falsely converges.
Relation to existing approaches
Requirement discovery, iterative refinement, external feedback, and regression testing have established roles in software development. Convergence Programming proposes evaluating their connection across one recorded trajectory, including the evidence behind permission to act. The approaches below overlap; this comparison describes their focus and the proposed framing, not measured differences in performance.
| Approach | Focus | Feedback already available | Convergence Programming's proposed emphasis |
|---|---|---|---|
| Traditional development | Software built from an evolving understanding of the work | User collaboration, prototypes, tests, review, and operation | Evaluate the history of requirement discovery and preservation alongside the artifact and its tests. |
| End-user programming | Software created by the person who knows the work | Direct use, logic inspection, examples, and colleague feedback | Retain the requirements and evidence discovered during use, with their conditions of validity. |
| Programming by demonstration | Procedures inferred from demonstrations or examples | Additional examples, corrections, and interactive refinement | Connect demonstrations to a broader record of observations and the actions they support. |
| Program synthesis | A program satisfying formal, partial, or example-based requirements | Candidate checking and counterexample-guided refinement | Record how operational requirements enter the specification and where its guarantees apply. |
| Prompt to code | Applications created and revised through natural language | Follow-up questions, execution, testing, and review | Evaluate the whole build trajectory, including requirements discovered after the initial prompt. |
| Tool-using agents | Planning and acting through tools toward a goal | Tool results, environment observations, execution checks, and human feedback | Connect accumulated evidence and preserved requirements to scoped permission for subsequent actions. |
| Agent and code benchmarks | Performance measured under a defined evaluation protocol | Tests, held-out scenarios, environment outcomes, and trajectory checks | Measure hidden-requirement discovery, evidence sufficiency, critical blockers, and decisions to act or seek information. |
| Convergence Programming | The recorded path from partial intent to executable behavior in a scoped world | Active observation, requirement confirmation, repair, and regression checks | A proposed framework connecting discovery, preservation, evidence, and permission. Discovery may remain incomplete; comparative outcomes require measurement. |
The Agile principles explicitly welcome changing requirements and collaboration. Syntax-Guided Synthesis describes counterexample-guided refinement against a stated specification. Anthropic's Building effective agents describes grounding progress in tool results and code execution. These are foundations and neighbors of the proposed framework.
The epistemic contract
Convergence Programming is bounded not because it is small, but because bounded worlds make oversight measurable.
| Boundary | Meaning | Why it matters |
|---|---|---|
| Task | Scoped executable world, not all values | Prevents overclaiming superalignment |
| World | Environment modeled, simulated, sampled, or operationally scoped | Makes grounding possible |
| Ledger | Hidden but finite or sampled evaluator target | Makes scoring possible |
| Observation | Claims limited by observation history | Gives the non-certification theorem force |
| Action | 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 runtime drift and deployment shift |
Citing this work
Until the paper is released, cite the manuscript:
Pantasdo, K. D., & Wu, P. (2026). Convergence Programming: Iterative, World-Grounded Alignment of Lossy Human Intent with Executable Behavior. Manuscript in preparation. https://superalignment.inc/research/convergence-programming/