A Better Score Cannot Buy Permission
09 November 2026
Decision-theory technical note

Abstract
Creative optimization often combines several objectives into a single score. CalcuArt v2.3 draws a boundary around that convenience: failed hard constraints must not be traded for higher aesthetic scores. This note examines the decision structure implied by that rule. It concerns admissibility and preference, not the convergence of a particular optimizer. The distinction matters whenever visual quality, resource limits and source requirements coexist. [1, original pp. 6–7]

Two questions, not one
First ask whether a candidate is allowed. Only then ask which allowed candidate is preferable. A budget limit, an identity constraint or a testable world-law bound can define membership in a feasible set. Composition, expression and stylistic fit can rank candidates within it. If a required condition is unknown, the source does not permit certification merely because the remaining attributes look strong. [1, pp. 6–7]

This ordering prevents compensation across incompatible categories. Imagine two hypothetical render plans: one stays inside a declared memory budget, while another exceeds it but receives a higher visual-quality rating. A weighted sum may select the second if quality carries enough weight. A hard budget gate rejects it before ranking. Neither calculation is inherently mysterious; they answer different questions. Calling the weighted result feasible would conceal the change of contract.

Normalization is a choice
The source permits a documented weighted sum of normalized objectives or a multiobjective comparison. Normalization makes numerical combination possible, but does not make the choice neutral. A feature measured over a narrow reference range can acquire greater influence than the same feature normalized over a broad range. The scale, evaluator and uncertainty therefore belong beside the score. [1, p. 7]

Weights encode priorities. They do not discover priorities from arithmetic alone. An evaluation should state whether a weight expresses a user preference, a resource price or a provisional modeling assumption. Changing that weight can legitimately change the selected candidate without showing that the earlier mathematics was wrong. What would be wrong is presenting the new selection as if the decision criteria had stayed fixed.

The frontier instead of a winner
For objectives to be minimized, one feasible candidate dominates another when it is no worse on every objective and better on at least one. A Pareto comparison retains candidates that are not dominated. It exposes tradeoffs rather than forcing all of them into one number. The source names this approach as an alternative, without claiming that it resolves subjective choice automatically. [1, p. 7]

Consider an illustrative pair of normalized cost vectors, (1,4) and (3,2). Neither dominates the other. Selecting between them requires an additional preference or constraint. A third vector, (4,5), is dominated by both. These numbers are a constructed explanation, not measurements of generated images. Their usefulness lies in making the decision logic inspectable before it is applied to a complex system.

A product can hide a veto
CalcuArt retains its older multiplicative art expression only as an optional calibrated heuristic and notes that a zero factor annihilates the product. This makes a product behave differently from a sum. A zero may represent genuine absence, a low rating or unavailable data; those meanings must not be collapsed. Missing measurements cannot safely be entered as zeros and then interpreted as evidence of total failure. [1, p. 7]

A product also depends on the chosen scales and signs. It may be appropriate for a declared heuristic, but it is not a universal unit of artistic value. Before adopting one, the designer should test how small changes or missing fields alter decisions. That sensitivity analysis is part of specifying the rule, not a cosmetic appendix after selection.

Proposed audit
Build a small, fixed candidate table with separate columns for hard constraints, measured objectives, judgment-based objectives and unknown values. Compare a gated weighted sum, a Pareto display and any proposed product heuristic. Include an attractive infeasible candidate, an incomplete candidate and a pair with a genuine tradeoff. Record which candidates each rule admits and selects. No such audit was executed for this note.

Then hold out an independent evaluation rather than optimizing and judging against the same reward model. The source explicitly warns that empirical judges may be biased or optimized against. A higher training score can reflect exploitation of an evaluator rather than improvement in the intended work. A simple baseline helps reveal whether added decision machinery contributes anything. [1, p. 7]

Conclusion
A score is a tool for comparison inside a declared decision problem. It cannot silently change that problem's boundaries. Separating permission, feasibility, uncertainty and preference makes creative optimization more honest, even when the final choice remains qualitative.

Reference
[1] CalcuArt v2.3, Calculus Only, 7 November 2026, original PDF pp. 6–7, hard constraints and multiobjective evaluation discussion. Only these scientific pages are supplied. Numerical examples and the audit protocol are original explanatory proposals, not observed production results.
