Consolidated Axiomatic Knowledge Networks (CAKN): A Proven Write-Time Consistency Gate for Causally-Acyclic, Continually-Learned Knowledge Graphs

Contemporary frontier models excel on static benchmarks yet fail systematically on three capabilities widely treated as necessary (not sufficient) conditions for general intelligence: out-of-distribution generalization, multi-step causal reasoning, and stable continual learning without catastrophic forgetting. We argue that these failures share a common root: learned representations are ungrounded—they are not anchored to formally specified, revisable knowledge with explicit consistency constraints. We propose Consolidated Axiomatic Knowledge Networks (CAKN), an architecture that couples (i) a formally specified, versioned axiom system distilled from consolidated human knowledge, (ii) a typed knowledge graph whose edge insertions are validated against those axioms at write time, (iii) local neural plasticity gated so that synaptic change cannot violate consolidated structure — a layer we specify with a spiking/liquid substrate but evaluate here through a minimal real rate-based plasticity instance (Appendix O), where the consolidation gate eliminates catastrophic forgetting at an honest stability–plasticity cost, leaving the spiking substrate as future work, (iv) an explicit memory-consolidation process with full provenance, and (v) a controlled axiom-revision mechanism that lets the system refine its own constraints under evidence. The central design commitment is plasticity within constraints: the system learns continuously, but learning is bounded by axioms that are themselves revisable only through an auditable, evidence-gated pipeline. We give formal definitions, complexity characterizations, an engineering specification, an evaluation methodology with ablations, and an explicit account of limitations and threats to validity. We are explicit about scope: CAKN structures the formalizable fraction of knowledge and supplies an epistemic hygiene over it (auditability, revisability, calibrated uncertainty); it does not, and is not claimed to, produce wisdom, which we argue is a distinct category subject to the is–ought gap, the frame problem, tacit knowledge, and symbol grounding. CAKN is presented as a falsifiable research program rather than a finished system.