Foundations of Mathematics: An Introduction to Generative History Theory (GHT)

Generative History Theory (GHT) moves foundational inquiry one step upstream from already constituted mathematical objects and asks how objects, relations, identity, comparison, composition, invariance, and scale acquire stable mathematical admissibility. The paper uses “This sentence has ended” to distinguish the non-mathematizable boundary of bare occurrence from the expressible first shadow layer. Re-addressable trace and re-entry lead to the Generative History Law N → N+n and to the Generative History Structure (GHS). On this basis, the paper develops seven mathematical primitives—distinction, equivalence, object, relation, composition, invariant, and scale—together with object–relation unity, Name–Relation duality, the one-way identity-to-evaluation principle, mature manifestation, mature presence, provenance continuity, operation-type discipline, and a Preserved/Hidden/Destroyed (P/H/D) ledger. It then provides foundational interfaces for natural numbers, addition, multiplication, Prime, logic, set theory, algebra, category theory, topology, analysis, measure, probability, geometry, operator theory, and spectral theory. The paper serves as Paper I of the GHT Foundations of Mathematics Series and supplies the minimal foundational interfaces used by Paper II.