What Survives Measurement: Ordinal Identification and Cardinal Fragility in Heresthetic Collective Choice

The heresthetic framework represents language expansion by cardinal, within-voter utility increments, but an analyst observes only finite ordinal panels. This paper asks what those primitives can identify. An additive ordinal panel is rationalizable if and only if a finite homogeneous system of strict linear inequalities is feasible; its rationalizations form a relatively open convex polyhedral cone, and normalized sections of that cone deliver set-valued counterfactual predictions. Joint voterwise positive-affine changes of baseline utilities and all criterion responses preserve comparisons and, under affine-equivariant admissibility, preserve the induced transition graph, its strongly connected components, and graph-theoretic immunity. This is an invariance floor, not an invariance theorem for fixed-price strategic payoffs. The paper separates robust from possible transitions. Scalable sign-countervailing criteria alone do not make the unanimity-face connectivity of a corpus robust to every rationalization, and an explicit three-alternative counterexample defeats both arc isolation and set reachability; a uniform isolation-ratio condition restores the result under the quantifier order "for every rationalization and every required edge there exists an admission." Constructive conclusions are more fragile: two rationalizations of one ordinal panel can yield different unobserved Condorcet winners, spatial crossing thresholds, and route-specific blocking prices through different induced tournaments. Linear and linear-fractional functionals nonetheless have computable normalized bounds, and winner sets are computable by finite linear-program enumeration. Additive preference stability supplies the identifying exclusion. Without it, post-admission rankings can always be rationalized by language-specific reframing, so attribution and unobserved transitions are unidentified; with it, the polyhedral test applies and a new ordinal four-state restriction rules out checkerboard reversals. Quasilinearity fixes the money scale, but finite priced choices generally set-identify rather than point-identify utility differences, and exact reservation prices point-identify them only under stable-consequence and cross-context assumptions. Ledger affordability and technological security thresholds remain money-metric, while willingness, equilibrium implementation, and dynamic regime selection retain cardinal content. For finite public games whose primitives depend polynomially on the cardinal microfoundation, the identified polyhedron and the equilibrium-record recursion compose into exact first-order formulas for existential, robust-possible, and robust-universal implementation. Exact maximum-prefix capital formulas further distinguish working capital from total expenditure, and a solved three-voter economy carries these distinctions through explicit inequalities and verified bounds.