Two Scoped Identifiability Theorems for Typed Algorithmic Pipelines: Intervention-Rank Stage Identifiability and Boundary-Block Identifiability

This independent research note formalizes two scoped identifiability results for typed algorithmic pipelines: (1) the Intervention-Rank Stage Identifiability Theorem and (2) the Boundary-Block Identifiability Theorem. The results concern pipelines decomposed into typed stages such as Support, Birth, Executability, Selection, Certification, Commit, and Feedback. They characterize when individual stage coefficients can be uniquely recovered from interventions and telemetry, and what remains identifiable when internal boundary measurements are missing. The record includes formal statements, proof sketches, executable synthetic benchmarks, observability certificates, claim ledgers, and reproducibility artifacts. Its mathematical spine uses linear algebra, rank and nullspace analysis, and structural identifiability. Therefore, this work does not claim a new universal mathematical primitive or verified worldwide priority. Its contribution is a domain-specific formulation for Algorithmic Dynamics and an auditable route from ontology to observability, diagnosis, and experimental design. This record is published as an open independent research milestone. Open problems for the wider research community include robust identification under noise and time variation, minimum-cost sensor and intervention design, independent reimplementation, external-engine telemetry, and field validation.