Residual Representation Revision and Counterexample-Driven Conceptual Expansion: A Technical Companion to Residual Boundary Theory

Abstract

This technical companion integrates the representation-revision and conceptual-expansion modules of Residual Boundary Theory. Part I distinguishes reweighting, reservoir recruitment, nonlinear construction, coordinate-only change, and fixed-capacity replacement under matched information and resource budgets. Part II distinguishes local counterexample repair, reusable condition repair, and transferable representational expansion, while requiring a completeness argument for universal claims and a declared sampling contract for population claims. The integration does not claim that error-driven feature learning, counterexample-guided repair, predicate invention, or constructive learning are new primitives. Its candidate contribution is a common source-history contract: unresolved discrepancies retain source, event, map version, failed repair, and provenance; later discrepancies may make subsets jointly relevant; proposed changes are evaluated for function-level gain, protected-case preservation, validation appropriate to the claim, and transfer when claimed. Conditional results quantify when weak single features can form a useful block, how exact protection consumes rank, what a finite audit can certify, and how failure information changes proof allocation. Coverage and full-budget outcomes constrain repair evaluation. These results and finite diagnostics remain conditional or local. No consciousness validation is claimed. Publication role. Companion A (about 26,300 words, dated 19 September 2026) develops the representation and conceptual-repair branches of the integrated flagship of Residual Boundary Theory, which is archived separately. Companion B develops the governed agentic architecture, and a separate protocol sets out the prospective empirical programme. Numbered source papers refer to archived technical modules; the archived pre-integration manuscript is not the current flagship. Trained-agent and human studies remain prospective. The accompanying supplement archive holds the companion diagnostics (part-level checks, audit power, repair and representation extensions with their reference outputs), the preserved technical-module material for Modules 2 and 4 including their external evidence ledgers, and a README, MANIFEST.json and SHA-256 checksums (31 files). The diagnostics check the stated mathematical models; they are not independent empirical confirmations.