CompProv Produces Machine Readable Graphs Encoding Microscopic Algebraic Provenance for Reproducible Computation

Abstract: The reliability of computational results in scientific research and financial modeling increasingly depends on verifiable traceability, not merely on trust in a reported output. Existing provenance systems operate at the granularity of files, datasets, or pipeline stages, leaving the internal sequence of algebraic transformations connecting an algorithm's inputs to its outputs unrecorded; a rounding error, an undocumented substitution, or a missing intermediate value can propagate to a final result with no recoverable trace. This work presents CompProv, a Java-based, audit-oriented provenance framework that captures lineage at the atomic level of individual algebraic operations by encapsulating numerical values in high-precision wrapper objects, producing a serializable Calculation Provenance Graph (CPG) that persists as a self-contained artifact rather than a discarded byproduct. The framework is evaluated through three heterogeneous case studies: a decentralized-finance NAV calculation, a reconstruction of an interferometric gauge-block calibration in metrology under explicitly documented input assumptions, and a hydrological model performance evaluation. Deterministic replay reproduced each result exactly in a fresh environment, and CPG-based input substitution supported sensitivity analysis without exposing the underlying source code. These results indicate that, provided the CompProv runtime and wrapper classes are available in the replay environment, a CPG allows numerical integrity to be audited without disclosing proprietary business logic, and that its self-contained structure supports temporal auditability once an execution environment has become deprecated. This framework establishes an operation-level foundation for auditable-by-design computational systems, with scaling to high-throughput computing identified as a direction for future work.