Nested Fibrational Cosmology

Nested Fibrational Cosmology (NFC) is a first-principles research framework that studies how structured mathematical and physical regimes can be generated from finite observational primitives without importing background geometry, continuum structure, probability, or field content as primitive assumptions. The framework begins with finite relational incidence, admissible tests and extensions, observational equivalence, defect bookkeeping, and locality constraints. From these primitives it develops a seven-book proof spine covering behavioral congruence, finite refinement and stabilization, boundary-capacity bounds, transport/coercive inequalities, lawful descent to branch theories, continuum-interface discipline, and governance rules for scoped certificates, conditional results, and named open frontiers. NFC’s central architectural principle is dependency discipline: each downstream claim must declare exactly which established definitions, theorems, bridge principles, hypotheses, or unresolved obligations it uses. Conditional results are kept separate from unconditional ones; finite certificates are not promoted beyond their stated regimes; and open mathematical frontiers remain explicitly named rather than absorbed into informal interpretation. The current research program includes derived branch books and scaffold studies for Yang–Mills, Navier–Stokes, general relativity, SCC/RH admissibility, standard-model harmonization, crystallography, spectroscopy, biology, and linguistics. These branches are treated as lawful-descendant investigations: each asks what additional structures must be declared, certified, or left open in order for a familiar mathematical or physical theory to arise from the NFC source architecture. A separate rational-height Weil track studies finite compressed Weil matrices (M_H) associated with a proposed exact reformulation of the Riemann Hypothesis. The certified results through the currently accepted heights are finite restricted rational-height consistency tests only. They are not presented as theorem-steps toward RH, do not use zero-location input, and do not license any RH, SCC, or canonical-status promotion. The analytic core of that reformulation—including continuity, cyclicity, and imported Weil/Burnol criteria—is being prepared for independent specialist review. Overall, NFC is best read as a governed research architecture: a formal attempt to build from finite observational primitives to higher mathematical structures while making every dependency, bridge, certificate, conditional claim, and unresolved frontier auditable.