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A Mathematical Framework for Legacy, Governance, and Decision Integrity in Enterprise AI

Shorab Sarker

arXiv:2609.00572v1cs.CYcs.AI

TL;DR

Enterprise AI governance lacks an integrated operational framework for preserving sound judgment as institutional conditions change. This paper develops mathematical, architectural, and computational artifacts for that purpose; its synthetic demonstration tests non-compensation and governance-aware routing under explicit assumptions, not field effectiveness.

  • Problem

    Enterprise AI quality requires preserving authority, human accountability, correction mechanisms, and lawful operation as conditions change, while existing governance principles do not by themselves provide an integrated operational framework.

    Source: §1 · p. 1, §16 · p. 18

  • Method

    The paper combines a penalized Legacy Score with confidence, risk, authority-aware retrieval, organizational memory, regulatory review, and federated knowledge-graph artifacts.

    Source: §16 · p. 18, §17 · p. 19

  • Results

    The synthetic demonstration showed how non-compensation and governance-aware routing can be tested under explicit assumptions.

    Source: §17 · p. 19

  • Takeaways & Limitations

    Institutional AI quality is longitudinal: organizations must preserve source authority, human accountability, correction mechanisms, and lawful operation when conditions change.

    Source: §16 · p. 18

    The framework has not been field-validated, and the synthetic simulation establishes neither external validity nor causal effectiveness or optimal thresholds.

    Source: §15 · p. 18

Abstract

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Enterprise artificial intelligence is increasingly embedded in decisions that must remain lawful, explainable, adaptable, and accountable despite personnel turnover, model replacement, regulatory change, and shifting organizational incentives. Existing governance frameworks provide important principles but do not by themselves supply a compact mathematical language for evaluating whether an institution can preserve sound judgment over time. This paper develops a design-science framework for institutional legacy: the durable capacity of a decision system to continue producing beneficial, lawful, explainable, and adaptable outcomes after its original designers have stepped away. The framework contributes: (i) a normalized Legacy Score based on a penalized geometric mean of knowledge retention, governance, human oversight, adaptability, feedback learning, and jurisdictional fidelity; (ii) Decision Confidence and Decision Risk models separating evidentiary confidence from consequence; (iii) authority-aware retrieval and calibrated abstention; (iv) Decision Memory for governed organizational learning; (v) Regulatory Change Velocity mapping change exposure to review intervals; and (vi) a federated regulatory knowledge-graph architecture preserving provenance and legal hierarchy. The paper also proposes eight AI Decision Integrity Rules, an evaluation protocol, and a reproducible computational demonstration. The demonstration combines a deterministic stress test with 200 Monte Carlo replications of 10,000 synthetic decisions each, illustrating Legacy Score non-compensation and comparing consequence- and authority-aware routing with a matched-coverage confidence-only baseline. The contribution remains conceptual rather than field-validated; the simulation tests internal behavior, not production performance, and all parameters require context-specific calibration.

1 Introduction

Enterprise AI decisions require more than predictive performance: institutions must preserve authority, evidence, human accountability, and lawful operation through change. The paper proposes an integrated framework for measuring and governing that longitudinal capacity.

1 Introduction

  • Decision quality must persist through changes in personnel, technology, markets, laws, and leadership, not rely on predictive performance alone.The proposed legacy concept treats continued beneficial, lawful, explainable, and adaptable outcomes as a measurable property of a decision system.Source: §1 · pp. 1–2

1.1 Contributions

  • The framework defines a Legacy Score, separates confidence from consequence, and formalizes authority-aware retrieval, Decision Memory, regulatory review intervals, and governance controls.It also proposes an operational architecture, eight AI Decision Integrity Rules, and a validation protocol.Source: §1.1 · p. 2
  • A reproducible synthetic demonstration stress-tests the score and compares routing policies at matched automation coverage; the framework is a design artifact, not a validated universal law.The authors make governance assumptions explicit, testable, and calibratable.Source: §1.1 · p. 2

2.1 AI risk management and documentation

  • Model cards, datasheets, and risk-management frameworks support transparency and accountability, but do not fully capture downstream decisions, overrides, regulatory change, or persistent organizational knowledge.Decision Memory extends static documentation into a governed learning substrate.Source: §2.1 · p. 3

2.2 Selective prediction, abstention, and interpretability

  • The proposed routing policy extends selective prediction by incorporating authority sufficiency, jurisdiction match, impact severity, and human validation.Human review is treated as an authority-bearing control, not ceremonial approval.Source: §2.2 · p. 3

2.3 Retrieval, provenance, and knowledge graphs

  • The federated regulatory knowledge graph preserves provenance and distinctions among legal and institutional source types because semantic relevance does not establish authority.Retrieved sources are evaluated for jurisdiction, effective date, source type, subsequent treatment, and supersession.Source: §2.3 · p. 3

2.4 Design-science methodology

  • The design-science study constructs formal artifacts, demonstrates their use, evaluates mathematical properties, and specifies criteria for future empirical work.The artifacts include equations, data structures, routing rules, and an enterprise architecture.Source: §2.4 · p. 3

2.5 Regulatory context

  • The framework complements regulatory resources with operational models while distinguishing current obligations from emerging expectations as change exposure increases.It is an operational model, not a statement of law.Source: §2.5 · pp. 3–4

3 Research Method

The method constructs formal governance artifacts and evaluates their behavior analytically and computationally under disclosed assumptions. Its Legacy Score makes institutional capabilities and unresolved risk explicit, including non-compensation and the possibility of deterioration despite capability gains.

3 Research Method

  • The design-science method identifies fragmented enterprise governance, constructs connecting artifacts, demonstrates them in representative patterns, and specifies future field evaluation.A deterministic stress test and fixed-seed Monte Carlo experiment examine behavior under a disclosed synthetic process; coefficients and thresholds are not claimed to be universally optimal.Source: §3 · p. 4

4.1 Dimensions

  • The Legacy Score is defined over six normalized dimensions and unresolved risk, with an unweighted formulation preferred as the default.The dimensions include jurisdictional fidelity, while unresolved risk includes stale rules, undocumented overrides, known harms, control deficiencies, technical debt, and unremediated model risk.Source: §4.1 · pp. 4–5
  • A zero essential dimension collapses the geometric mean, so strong performance in other dimensions cannot compensate for absent governance or jurisdictional mismatch.The same non-compensation applies to extensive documentation when meaningful human authority is absent.Source: §4.1 · p. 5

4.2 Sensitivity and trajectory

  • Several capabilities may improve while legacy deteriorates if unresolved risk grows faster than those capabilities.The sensitivity analysis also states that the marginal value of improving a weak dimension is high relative to its current level.Source: §4.2 · p. 5

4.3 Illustrative calculation

  • The illustrative calculation uses hypothetical inputs and supports longitudinal comparison and scenario analysis, but its value is not a rating standard.Calibration should use observable indicators, confidence intervals, and governance-approved scoring rubrics.Source: §4.3 · p. 6

5 A Constrained Public-Value Objective

The section frames high-impact AI as constrained public value and develops routing that distinguishes evidentiary confidence, consequence, and authority. Generation requires adequate authority and expected benefit above the cost of qualified review; otherwise the system reviews, escalates, or abstains.

5 A Constrained Public-Value Objective

  • The objective balances client, sustainable economic, and human benefits against expected harm, subject to law, rights, safety, fiduciary duty, and institutional policy.Efficiency alone is not a sufficient objective for high-impact AI.Source: §5 · p. 6

6.1 Separating confidence from impact

  • Separating evidentiary confidence from impact means equal confidence need not lead to the same treatment for low- and high-consequence tasks.The confidence model includes factors such as source authority, data quality and freshness, jurisdiction match, and human validation.Source: §6.1 · pp. 6–7

6.2 Authority sufficiency

  • Authority sufficiency measures whether retrieved evidence meets the task’s minimum authority requirement, which semantic similarity cannot offset in high-impact legal or regulatory decisions.Authority may reflect source type and hierarchy, jurisdiction, effective date, supersession, provenance, and consistency among controlling authorities.Source: §6.2 · p. 7

6.3 Routing policy

  • The representative policy escalates or abstains when authority, jurisdiction match, or risk breaches a threshold and reviews cases with intermediate evidence or impact.The thresholds are described as automation thresholds.Source: §6.3 · p. 7

6.4 Risk-calibrated generation

  • Generation requires adequate authority and expected benefit above qualified-review cost; otherwise the system should review, escalate, or abstain.Confidence without adequate authority is not treated as a high-confidence decision.Source: §6.4 · p. 7

7 Authority-Aware Retrieval

Authority-aware retrieval filters sources for legal and temporal applicability before ranking them semantically. If no feasible source remains or top authorities materially conflict, the system returns a structured insufficient-basis response.

7 Authority-Aware Retrieval

  • The retrieval score considers semantic similarity, source authority, jurisdiction match, freshness, provenance completeness, and known conflict or adverse treatment.The score is defined for a candidate document, query, target jurisdiction, and decision time.Source: §7 · p. 8
  • Hard filters can require that a document apply in the target jurisdiction and time, remain valid and unsuperseded, and meet the minimum source class.The framework says these filters may be required for legal and regulatory tasks.Source: §7 · p. 8
  • If no source passes the filters or the highest-ranked authorities materially conflict, retrieval returns a structured insufficient-basis response rather than a ranked answer.Semantic ranking occurs only within the feasible set.Source: §7 · p. 8

8 Decision Memory and Constrained Organizational Learning

Decision Memory turns organizational learning into governed, versioned records, while Bayesian updating prioritizes investigation and review only within interpretations compatible with binding law and policy.

8.1 Decision Memory object

  • A Decision Memory record can capture case inputs, recommendations, override reasons, supporting sources and provenance, and model, prompt, policy, and workflow versions.The tuple also includes an accountable human reviewer and owner.Source: §8.1 · p. 9
  • Decision Memory converts overrides, near misses, complaints, control failures, and lessons into governed data, with access, retention, privacy, and quality controls because the records can themselves create bias or leak confidential data.The record is a versioned tuple that can include case context, model recommendation, override reason, supporting sources, versions, and accountable reviewer.Source: §8.1 · p. 9

8.2 Bayesian learning under legal constraints

  • Bayesian updating can prioritize investigation and allocate review, but the posterior is normalized only over interpretations compatible with binding law and policy.Controlling statutes, regulations, or judicial holdings operate as hard constraints, not merely weighted observations.Source: §8.2 · p. 9

9 Regulatory Change Velocity

Regulatory Change Velocity links change exposure and uncertainty to review timing, with faster review as specified change factors increase. The federated knowledge architecture connects regulatory evidence while preserving distinctions among authority types and the substantive authority of its contributors.

9 Regulatory Change Velocity

  • The model uses material-change rate and interpretive, legal, or jurisdictional uncertainty to distinguish review schedules across sources or domains.The repository should not assign every source the same review schedule.Source: §9 · p. 10
  • Holding other variables fixed, the recommended review interval decreases as the rate of material change, impact, dependency, or uncertainty increases.The model treats change velocity as an input and review interval as an output; its parameters should be calibrated against stale-rule incidents, missed updates, review costs, and false alarms.Source: §9 · p. 10

10 Federated Regulatory Knowledge Architecture

  • The knowledge architecture preserves distinctions among authority types rather than placing statutes, proposed and final rules, settlements, opinions, policies, and commentary into one undifferentiated context.Figure 3 describes a federated evidence layer linking law, policy, controls, and AI decisions while preserving provenance and authority.Source: §10 · p. 10, Figure 3 · p. 11
  • The graph is federated: legislative, executive, judicial, and institutional actors retain substantive authority while publishing interoperable metadata and resolvable identifiers.Graph nodes carry authority, jurisdiction, effective date, status, provenance, owner, and confidence metadata.Source: §10 · p. 10

11 Illustrative Enterprise Patterns

The section presents workflow-first and governed-knowledge patterns as illustrations, not endorsements or rankings. The patterns govern different parts of enterprise AI work: how work is performed, and the evidence, models, tools, and policies used within it.

11.1 Workflow-first design

  • Workflow-first design considers which steps are deterministic or probabilistic, require human authority, need retained evidence, and feed exceptions, overrides, and outcomes into future design.Source: §11.1 · p. 11
  • A Regulatory Change Impact and Implementation Tracker illustrates workflow-first design, from ingesting regulatory changes through human validation, implementation coordination, evidence preservation, and outcome capture.The proposed extensions include a Decision Confidence schema with configurable routing thresholds.Source: §11.1 · p. 11
  • Its proposed workflow artifacts include reusable Decision Memory, dependency and silo graphs, a longitudinal Legacy Score dashboard, and an exportable evidence trace from authority to control and final decision.Source: §11.1 · pp. 11–12

11.2 Governed-knowledge and agent execution

  • Governed-knowledge systems emphasize authority-weighted retrieval and calibrated abstention, alongside regulatory freshness clocks, reviewer-learning workflows, and cross-jurisdiction knowledge partitions.Source: §11.2 · p. 12
  • The two patterns are complementary: workflow-first design governs how work is performed, while governed-knowledge execution governs the evidence, models, tools, and policies used within that work.Source: §11.2 · p. 12

12 AI Decision Integrity Rules

The section presents eight proposed AI Decision Integrity Rules and a synthetic computational demonstration of selected framework behaviors. The demonstration reports matched-coverage routing results and differentiated review schedules, while explicitly distinguishing implementation evidence from field validation.

12 AI Decision Integrity Rules

  • The eight proposed rules cover provenance and authority, calibrated abstention, regulatory freshness, contestability, Decision Memory, third-party accountability, interoperability, and substantiated AI claims.They are original policy and design proposals, not statements of current law or adopted rules.Source: §12 · pp. 12–13

13 Worked Computational Demonstration

  • The reproducible demonstration uses a deterministic stress test and Monte Carlo simulation to test framework behavior under transparent synthetic assumptions, not to establish real-world effectiveness or vendor performance.The fixed-seed implementation and generated result files are supplied with the submission.Source: §13 · p. 13

13.1 Stress test of the Legacy Score

  • When human oversight H is zero, the geometric Legacy Score is zero while the arithmetic comparator remains 0.675, illustrating non-compensation for a failed essential dimension.Both scores equal 0.81 when all six dimensions equal 0.9.Source: §13.1 · p. 13, Figure 4 · p. 14

13.2 Monte Carlo routing experiment

  • At equal mean automation coverage, governance-aware routing reduces automated error by 3.51 percentage points, high-impact automated errors by approximately 79.2%, and consequence-weighted expected harm by approximately 38.5%.The error-rate reduction is approximately 28.5% relative to the confidence-only baseline; authority-deficient automation is zero by construction under the hard authority filter.Source: §13.2 · p. 14, Figure 5 · p. 15, Table 2 · p. 15

13.3 Regulatory review scheduling illustration

  • Four hypothetical regulatory profiles receive differentiated review schedules, with unstable, material, highly connected, and legally uncertain sources assigned shorter intervals than stable, low-dependency sources.The examples use normalized design assumptions rather than estimates of any actual regulator or legal domain.Source: §13.3 · p. 15, Table 3 · p. 16

13.4 Interpretive boundary

  • The demonstration verifies implementability and makes assumptions inspectable, but does not establish external validity, causal effectiveness, or optimal thresholds; production use requires validation.The stipulated error process, error-free synthetic authority variables, and unmodeled human-review outcomes limit the demonstration.Source: §13.2 · pp. 14–15, §13.4 · pp. 15–16

14 Evaluation Protocol

The evaluation protocol proposes operational measurement and testable hypotheses for framework components, then outlines designs for future field evaluation. It calls for reporting uncertainty, subgroup performance, review burden, and failure costs rather than treating abstention as inherently beneficial.

14 Evaluation Protocol

  • A credible field evaluation should compare baseline and framework-enabled workflows across multiple use cases, institutions, and time periods because the synthetic demonstration is not empirical validation.Source: §14 · p. 16

14.2 Testable hypotheses

  • Five hypotheses propose testing routing, authority-aware retrieval, Decision Memory, Regulatory Change Velocity, and the geometric Legacy Score against specified alternatives or outcomes.The hypotheses address unsupported automated decisions, jurisdiction and supersession errors, repeated control failures, stale-source incidents, and detection of weak dimensions.Source: §14.2 · pp. 16–17

14.3 Experimental designs

  • Proposed designs include retrospective simulation, shadow-mode deployment, stepped-wedge rollout, randomized retrieval review, interrupted time-series analysis, and expert elicitation.Source: §14.3 · p. 17
  • Evaluation should report uncertainty, subgroup performance, review burden, and failure costs; abstention must be assessed against error reduction, human capacity, latency, and delay consequences.Source: §14.3 · p. 17

15 Limitations

The framework remains a context-dependent design proposal: its measures and governance choices require operationalization, and its synthetic demonstration does not establish field validity. The discussion and conclusion frame institutional AI quality as the capacity to preserve accountability and lawful operation as conditions change.

15 Limitations

  • The Legacy Score’s dimensions and measurements need context-specific operationalization, since poorly chosen indicators may create false precision or encourage gaming.Source: §15 · p. 18
  • Thresholds, weights, authority classes, and consequence scales remain governance choices; making them explicit does not make them apolitical.Source: §15 · p. 18
  • Decision Memory data may be incomplete, biased, confidential, or causally ambiguous, and human overrides require review before being treated as ground truth.Source: §15 · p. 18
  • Legal hierarchy varies by jurisdiction, so the feasible-set approach requires qualified legal interpretation and reliable metadata.Source: §15 · p. 18
  • The enterprise patterns are illustrative and based on public materials; product features can change, and vendor adoption of the proposed extensions is not claimed.Source: §15 · p. 18
  • The framework is not field-validated, and its stipulated synthetic simulation establishes neither external validity, causal effectiveness, nor optimal thresholds.Future work should test predictive validity, inter-rater reliability, cost-effectiveness, reviewer capacity, measurement error, and susceptibility to strategic manipulation.Source: §15 · p. 18

16 Discussion

  • Institutional AI quality is longitudinal: organizations must preserve source authority, human accountability, correction mechanisms, and lawful operation as conditions change.The discussion contrasts this capacity with a model’s predictive performance at a single point in time.Source: §16 · p. 18

17 Conclusion

  • The conclusion presents the framework as a research program whose value depends on transparent operationalization, empirical validation, qualified oversight, and treating governance as part of system design.Source: §17 · p. 19

A Operational Definitions and Example Indicators

The appendices define example indicators for the framework’s constructs, outline Decision Memory fields and a governance-calibration procedure, and identify files and requirements for reproducing the computational demonstration.

A Operational Definitions and Example Indicators

  • Example indicators operationalize institutional dimensions such as knowledge retention, governance, human oversight, adaptability, feedback learning, and jurisdictional fidelity, alongside unresolved risk and decision confidence.The appendix also defines impact severity, decision risk, regulatory change velocity, and review interval.Source: A Operational Definitions and Example… · p. 21

B Example Decision Memory Schema

  • A minimal Decision Memory schema records decision and workflow identifiers, jurisdiction and authority sources, model and policy versions, recommendations, routing, human review, rationale, outcomes, corrective actions, and retention information.Source: B Example Decision Memory Schema · pp. 21–22

C Example Governance Calibration Procedure

D Computational Reproducibility Files

  • The reproducibility bundle includes a simulation script, result and input-value files, and three generated vector PDF figures; compatible NumPy random-number generation yields deterministic seeded numerical outputs.Figure rendering may vary slightly across library versions.Source: D Computational Reproducibility Files · pp. 22–23
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