Jump Epistemics: Topology, Pathology, and Dynamics for Finite Embedded Epistemic Agents

Jump Epistemics develops a meta-epistemology of knowledge generation for finite embedded epistemic agents. It represents epistemic activity as a forward-growing chain of costly loops and introduces five basic elements—memory–computation, distinction, record, index, and presupposition—together with derived judgments of evidence, reliability, qualification, and grounding. On this basis, the paper distinguishes legitimate local closure from final closure, recorded forward openness from backward and endless opening, and classifies pathologies of closure, openness, configuration, and order. A configurational account of inquiry and targeting shows why qualification depends on actual generative conditions rather than on the name or numerical value of an output. From this account the paper derives a strict form of Goodhart’s law: targeting can preserve an indicator’s symbolic identity while destroying its referential identity relative to the assertions it supports (support equivalence). A proposition on identity follows: sameness of name is not self-certifying, since the loss of referential identity cannot be registered by the records of the identically named indicator itself; identity is supplied by generative history, which cannot be recovered from the value. Applications include quotient formation, fraction reduction, diachronic reconstruction, numerical approximation, and the logical form of quantum-measurement puzzles. JE is operational and non-exempt: it takes no position on the first-order content of the domains it reviews, each of its reviews is an executed computation, and its own assertions fall under the same review. The framework permits conditional, corrigible knowledge without self-grounding, while specifying the additional evidence, declared restrictions, weakened targets, or derivations required for legitimate epistemic promotion.