From Represented Complexity to Computational Economy: A Testable Theory of Cost Inversion in Autonomic Cognitive Architectures

Abstract

Abstract This paper develops a testable theory of computational cost inversion arising from the mathematical formalisation of the Orchard Cognitive Framework’s autonomic architecture. The companion paper Towards a Mathematics of Autonomic Cognitive Organisation ( https://doi.org/10.5281/zenodo.21862919 ) proposed six substrate-agnostic candidate primitives: typed distinction and non-collapse; conservative differentiation; conservative recursive composition; projection-preserving commutability; categorical admissibility with conditional alignment cost; and reciprocal unresolvedness–structure dynamics. The present work asks a different question: if those mechanics preserve lawful structure across time, representation and recursive depth, what computational economy might follow? Three staged pilot campaigns are reported. CE-PILOT-01 establishes the elementary amortisation mechanism: reusable higher-order form can transform repeated deep computation, while a hostile structured baseline shows that the gain is not Orchard-specific. CE-PILOT-02/02B removes explicit identity across surface representations and tests lawful cross-representational commutation. In the corrected one-shot challenge, hidden motifs were recovered across unseen surface forms in the noiseless toy ecology, but an equally capable conventional projection solver remained cheaper when given the same structural machinery without constitutional overhead. CE-PILOT-03 therefore isolates the specifically epistemic hypothesis: typed uncertainty, witness-bearing admission, HOLD/reappraisal and provenance may become computationally economical when false structural reuse produces recursively expensive downstream repair. The resulting candidate theory distinguishes represented complexity from effective unresolved dimensionality. Let Rₛ = d_eff / d_nom denote a structural resolution ratio and Γ(Ξ) = C_baseline(Ξ) / C_typed(Ξ) a cost-ratio field over complexity state Ξ. The central hypothesis is not that complexity becomes intrinsically cheap, but that accumulated lawful structure can reduce the fraction of nominal complexity requiring independent resolution. A cost-inversion boundary B = {Ξ : Γ(Ξ) = 1} then separates regimes in which constitutional structure is overhead from regimes in which it is computationally advantageous. CE-PILOT-03 produces the predicted qualitative geometry under explicitly synthetic laws, including positive dimensional and recursive gradients and a positive interaction term, but does not independently validate those laws. A Recursive Liminal Calibration (RLC) empirical programme is specified to prevent the theory from being tuned toward a desired curve. Candidate scaling families—including constant-factor, power-law, exponential, saturating and phase-transition models—must compete on held-out complexity bands. Residual structure, rather than apparent advantage, governs model revision. The paper concludes with an executable factorial programme designed to determine whether the predicted inversion, effective-dimensionality reduction and positive interaction curvature arise when costs are measured rather than prescribed. Keywords: computational economy; cognitive architecture; effective dimensionality; recursive calibration; AI safety; hallucination; typed uncertainty; pattern reuse; amortised computation; complexity scaling; alignment. 1. Introduction Cognitive architectures incur costs not only when they solve a problem, but when they decide what the problem is. A system that preserves provenance, distinguishes unknown from false, maintains relation history, witnesses structural transformations, refuses unsupported interpolation, and reappraises previously valid mappings after contextual change performs more work at ingestion than a system that simply collapses incoming information into an immediately usable representation. At first sight this appears computationally disadvantageous. The Orchard autonomic programme was not originally designed as a cost-optimisation scheme. Its first concern is lawful representation: uncertainty should remain uncertainty; provenance should survive transformation; recursive composition should not silently promote authority; alignment exclusions should not become tradeable rewards; and structural similarity should not be mistaken for identity. Yet these commitments imply a computational possibility. If sufficiently rich context mapping allows previously resolved structure to be reused across later problems, the initial representational cost may become an investment in future reduction of unresolved work. This paper formalises that possibility as a cost-inversion hypothesis. The conjecture is deliberately narrower than claims that “complexity becomes cheaper” or that an architecture defeats computational hardness. Intrinsic lower bounds remain lower bounds. The proposed mechanism instead concerns the difference between nominal complexity and complexity that still requires independent resolution after lawful prior structure is applied. represented complexity ↑ while effective unresolved dimensionality ↓ If that separation exists, increasing knowledge changes the geometry of subsequent problems. A new observation is no longer encountered only as an isolated payload. It arrives into a relational fabric containing typed distinctions, witnessed patterns, known commutations, admissibility boundaries, unresolved regions and acquisition pathways. Previously resolved relational form may therefore remove degrees of freedom from the next problem without deleting the underlying detail. The research question is consequently not whether cognition can cache answers. It is whether a context-mapped architecture can lawfully transform repeated discovery into reusable form across heterogeneous representations and recursive depths, while avoiding the potentially large cost of false reuse. The pilots reported here progressively make that question harder.