Appendix F: Mathematical Ledger — Status of Formal Claims

This appendix catalogues every numbered formal statement in the manuscript — definitions, axioms, theorems, propositions, lemmas, corollaries, and conventions — together with its epistemic status and dependencies. The purpose is transparency: a reader should be able to see at a glance what is assumed (as a modeling choice mapping ethical phenomena to mathematical structures), what is proved (given those assumptions), and what is conjectured or proposed for future investigation.

Five epistemic categories are used. Formal Definition: a standard mathematical construction carrying no ethical modeling claim (e.g., “topological manifold”). Modeling Axiom: a mathematical structure posited as a model of an ethical phenomenon; these are the bridge assumptions that connect the mathematics to moral reasoning, and they are the primary target of empirical and philosophical scrutiny. Conditional Theorem: a result that is mathematically proved given stated assumptions (listed in the Dependencies column); the theorem is as strong as its premises. Proved: a result that follows from standard mathematics alone, without ethical modeling assumptions. Conjecture/Proposal: a formally stated claim that is either unproved, depends on open problems, or represents a proposed extension not yet implemented. The table is organized by chapter. “TA” denotes the chapter’s Technical Appendix.