Bounded Judgment: A Conceptual Course Through the Identity-Persistence Program

Abstract Bounded Judgment is a thirteen-lecture conceptual course through the Identity-Persistence Program, a formal research program on the structural preconditions of coherent judgment by bounded observers. Its generative question is: what licenses sameness through change? The course asks what must already be fixed before an evaluator can meaningfully determine that something is the same, has changed, remains admissible, follows from evidence, or has been verified. The lectures develop the program’s dependency architecture in pedagogical form. A sufficiently declared regime determines the distinctions relevant to a judgment; those distinctions induce identity conditions and quotient structure; identity makes admissible transformation and persistence meaningful; observable distinctions and retained evidence determine what can be derived; and, where the available resolution is insufficient, the exact obstruction, minimal informational repair, realizability question, and declaration boundary can be separated. Consequence and verification occur only after these upstream conditions are in place. The course emphasizes recurring non-collapses: state is not object-as-judged; representation is not identity; evidence accumulation is not unique identification; mathematical sufficiency is not realization; realization is not authorization; declaration is not derivation; and verification under a declared regime is not final ontology. A bounded evaluator can produce judgments that another bounded evaluator can verify exactly, up to the capacity of the declared channels, without thereby certifying the governing regime as reality’s final constitution. The same discipline applies to every application of theory. Each application operates through a regime of questions, distinctions, access conditions, inference rules, and resolution, whether that index is explicit or partly tacit. Making the index visible neither demotes a theory nor grants it special privilege. Equal treatment does not imply equal merit: applications remain distinguishable by empirical reach, predictive accuracy, robustness, resolution, reproducibility, and practical success. The course also develops the dual problem of lawful forgetting: distinctions may be retired when remaining licensed demands no longer require them, without erasing their historical provenance. Worked finite examples make the principal operations explicit, including equivalence classes, quotients, admissible transitions, demand refinement, evidence collapse, factorization, minimal repair, declaration, and retirement. A final lecture runs the architecture longitudinally through a single consequential judgment, while the appendices provide claim-status discipline, proof ownership, a controlled glossary, and a finite problem laboratory. The course claims no new theorem ownership. Its purpose is to make the corpus’s dependency structure intelligible, operational, and teachable while preserving the exact scopes, claim types, and boundaries of the underlying formal results.