Zero Boundary Algebra (ZBA) is a new typed algebraic specification for directional boundary states, signed zero, polarity, mirror involution, reset projection, recursive evidence, and tamper-evident provenance. I define ten axioms and five proved propositions, give operational semantics and conformance levels, and provide an executable Python reference model, JSON Schema, test vectors, property checks, and mutation tests. The finite verifier evaluates 144 states, confirms the stated mirror/reset properties over that domain, accepts a valid six-record evidence chain, and detects all 14 supplied mutation and topology faults. The accompanying encryption-profile audit identifies at least seven author-created protected-data constructions, formats, or application integrations plus Matrix end-to-end encryption, while explicitly attributing confidentiality to established cryptographic primitives rather than claiming invention of those primitives. This is a public formalisation and reproducibility release, not peer review, security certification, or a claim of quantum-computing execution. Source and version history: https://github.com/ResearchForumOnline/research/releases/tag/zba-v1.1.0