Computational Layer of Fiscal Geometry: The ITI–gITI–IDI Dual-Index Architecture for XY-Based Institutional Analysis

Computational Layer of Fiscal Geometry The ITI–gITI–IDI Dual-Index System for XY-Based Institutional Analysis Author： Jim Y. Huang*1 Abstract This white paper presents the computational layer of Fiscal Geometry. Built on the Two-Axis Fiscal Framework—where the X-axis traces cross-border fiscal flows and the Y-axis captures intergenerational post-tax capacity—the ITI–gITI–IDI system provides the first quantitative method for extracting institutional tension and structural distortion from XYbased fiscal event geometry. The framework introduces a dual-index architecture for mapping institutional strain: (1) the Institutional Tension Index (ITI), an arithmetic estimator derived from weighted econometric combinations of representative fiscal-event series; and (2) the Institutional Distortion Index (IDI), generated from geometric projections of fiscalevent clusters on the XY fiscal plane. While the ITI measures rule-side tension encoded in institutional design, the gITI captures movement-side tension arising from lived fiscal behavior. The IDI quantifies the divergence between these two forms of tension, isolating the structural misalignment within an institutional field. Together, the ITI–gITI–IDI system provides a coherent, unified analytic language for understanding cross-jurisdictional capital movement and intergenerational transmission cycles. 1. Introduction Institutions generate tension when rules interact with two fundamental fiscal movements: • X-axis: cross-jurisdictional shifts of pre-tax public capital and post-tax private capital, * Doctoral Researcher , University of Toronto (OISE). Chartered Professional Accountant (CPA, Canada), Cer�fied Prac�sing Accountant (CPA, Australia), and Trust and Estate Prac��oner (TEP). Research focuses on fiscal architecture, cross-border capital movement, intergenera�onal post-tax capacity, and ins�tu�onal inequality. Contact email : jimy.huan[email protected]oronto.ca • Y-axis: downward intergenerational transmission of post-tax capacity. The Institutional Tension Index (ITI) quantifies the rule-based pressure produced by these movements using arithmetic combinations extracted from representative public datasets. The newly introduced Institutional Distortion Index (IDI) measures the gap between arithmetic tension and geometric tension, revealing the structural distortion generated when fiscal movement patterns deviate from rule-defined expectations. 2. The Arithmetic Institutional Tension Index (ITI) 2.1 Concept The arithmetic ITI is constructed through econometric estimation, using a fixed panel of highly representative data series (e.g., tax revenue patterns, migration flows, household transmission indicators, regulatory signals). 2.2 Structure • Input: A vector of 𝑛𝑛representative fiscal-event data series. • Method: Econometric estimation (e.g., linear model, regression weights, normalized coefficients). • Output: A value in [0,1]representing composite institutional tension. 2.3 Interpretation The ITI expresses rule-induced pressure. This is “policy-side tension.” 3. The Geometric Institutional Tension Index (gITI) 3.1 Concept The geometric ITI (gITI) is generated directly from the shape of fiscal-event clusters plotted on the XY fiscal plane. No weights. No modeling assumptions. Pure data-driven shape geometry. 3.2 Structure • Input: The same 𝑛𝑛representative data series used in the ITI. • Method: o Convert each event series into point clouds on the XY fiscal plane. o Compute density fields, shadow projections, and cluster envelopes. • Output: A normalized geometric tension score in [0,1]. 3.3 Interpretation gITI expresses movement-side tension. This is “behavior-side tension.” 4. Computational Structure: The ITI and IDI Dual System This section translates the geometric and field-based foundations of Fiscal Geometry (FG) into a computable structure, establishing the dual-index architecture composed of the Institutional Tension Index (ITI) and the Institutional Distortion Index (IDI). 4.1 Data Foundation and Coding Reproducibility The computation of both the ITI and the gITI relies on a fixed set of representative fiscal-event series (typically 15–20 indicators). These series are drawn exclusively from publicly accessible administrative or statistical sources. The selection and extraction of these data series follow transparent, rule-based coding criteria. Any researcher applying the same extraction criteria can fully reproduce the underlying dataset without discretion or calibration by the author. This mechanism ensures that the dual-index architecture satisfies the core requirements of socialscience measurement: transparency, replicability, and methodological consistency across applications and jurisdictions. 4.2 Institutional Tension Index (ITI): Arithmetic-Side and Movement-Side Tension The measurement of institutional tension is separated into two analytically distinct components—rule-side tension and movement-side tension—in order to address the longstanding issue of weight subjectivity in social-science index construction. (1) Arithmetic ITI • Concept: Constructed through econometric estimation using model-derived weights. • Interpretation: Captures the pressure generated by institutional rules, i.e., policy-side tension. • Input / Method: A vector of 𝑛𝑛representative fiscal-event series (an ordered set of indicators), estimated via regression-based weights or normalized coefficients. • Output: A composite institutional-tension value normalized to the interval [0,1]. (2) Geometric ITI (gITI) • Concept: Derived directly from the geometric structure of fiscal-event point clouds on the XY fiscal plane, without weights or modeling assumptions. • Interpretation: Represents the tension emerging from actual capital movements, i.e., behavior-side tension. • Method: Convert each fiscal-event series into point clouds on the XY plane; construct density fields; compute shadow projections and cluster envelopes; extract the corresponding geometric tension score. 4.3 Institutional Distortion Index (IDI) : Structural Misalignement The IDI measures the structural gap between rule-side and movement-side tension, isolating the distortion zone within the institutional field. (1) Definition and Formula The IDI is defined as the absolute structural deviation between arithmetic tension and geometric tension: IDI =∣ITI −gITI ∣ (2) Interpretation • IDI ≈0: Rule-side expectations and actual fiscal movements are closely aligned. • Increasing IDI: Indicates growing divergence between institutional rules and lived fiscal behavior. The IDI isolates and quantifies the structural mismatch between what rules expect and what capital actually does. To date, no existing social-science index explicitly captures this form of misalignment; the IDI provides the first dedicated structural framework for doing so. 5. Why the ITI–IDI Dual System Is a Breakthrough 5.1 It solves the weighting problem Social scientists have struggled for decades with the subjectivity of weights. Here: • ITI uses model-derived weights. • gITI uses no weights, pure geometry. The difference is not noise—it is institutional distortion itself. 5.2 It provides a fiscal coordinate language The XY fiscal plane is minimal and generative: • two capitals • two directions • one reclassification mechanism • one going-concern condition Everything else is derived. 5.3 It creates a universal dual-index toolkit Any domain that has: • cross-boundary movement, and • intergenerational transfer can now be mapped. Education, health care, migration, housing, social welfare, taxation. 6. Conclusion The ITI–IDI system provides a structural language for institutions. • ITI captures rule-side tension. • gITI maps movement-side tension. • IDI measures the distortion between the two. Together they form a coherent, closed, generative framework. This white paper establishes the conceptual basis for subsequent technical documents detailing the formal algorithms, proofs, and computational implementations. 7. Suggested Keywords • Fiscal Geometry • Institutional Tension Index • Institutional Distortion Index • XY Fiscal Plane • Cross-Jurisdictional Capital Movement • Intergenerational Transmission • Structural Distortion • Data Geometry • Econometric Estimation