Glossary

Technical terms used throughout this repository, organized by domain.

Accounting Standards

IFRS (International Financial Reporting Standards)

Global accounting standards issued by the International Accounting Standards Board (IASB). Used in 140+ countries including EU, UK, Canada, Australia.

Key Standards Referenced: - IAS 1: Presentation of Financial Statements (equity reconciliation §106-107) - IAS 19: Employee Benefits (actuarial gains/losses through OCI §93) - IAS 21: The Effects of Changes in Foreign Exchange Rates (translation adjustments §52) - IAS 32: Financial Instruments: Presentation (treasury stock classification §33) - IFRS 3: Business Combinations (acquisition method, goodwill) - IFRS 9: Financial Instruments (FVOCI classification §5.7.1) - IFRS 10: Consolidated Financial Statements (NCI requirements) - IFRS 13: Fair Value Measurement (Level 1/2/3 hierarchy) - IFRS 16: Leases (right-of-use assets) - IFRS 17: Insurance Contracts (contractual service margin)

US GAAP (Generally Accepted Accounting Principles)

Accounting standards used in the United States, codified in the FASB Accounting Standards Codification (ASC).

Key Topics Referenced: - ASC 220: Comprehensive Income - ASC 260: Earnings Per Share - ASC 505: Equity - ASC 810: Consolidation - ASC 842: Leases - ASC 944: Financial Services - Insurance

XBRL (eXtensible Business Reporting Language)

XML-based standard for machine-readable financial reports. Required by SEC for public company filings since 2009.

Example Tags: - us-gaap:NetIncomeLoss - Net income - us-gaap:OtherComprehensiveIncomeForeignCurrencyTranslationAdjustmentNetOfTax - FX translation OCI - ifrs-full:NonControllingInterest - NCI in consolidated statements

OCI (Other Comprehensive Income)

Items that bypass the income statement but affect equity. Examples: FX translation, FVOCI fair value changes, actuarial gains/losses on pensions.

IFRS Standard: IAS 1.7 defines OCI as “items of income and expense that are not recognized in profit or loss as required or permitted by other IFRSs.”

NCI (Non-Controlling Interest)

Equity in a subsidiary not attributable to the parent company. Previously called “minority interest.”

IFRS Standard: IFRS 10.22 requires NCI to be presented in consolidated equity separately from parent equity.

Mathematical Concepts

Conservation Law

Principle stating that a quantity remains constant (conserved) within a closed system over time, unless added/removed by sources/sinks.

Examples: - Physics: Mass conservation (dm/dt = sources) - Accounting: Equity conservation (dE/dt = income + contributions - distributions)

Key Distinction: Physics conservation is empirical (mass cannot be created). Accounting conservation is definitional (equity defined as A - L).

Graph Theory

Branch of mathematics studying networks (nodes connected by edges).

Application to Accounting: - Nodes = Account balances (Assets, Liabilities, Equity components) - Edges = Journal entries (debits/credits) - Balance Sheet = Snapshot of graph state at time t

Foundation: Ellerman (1982) showed double-entry satisfies Kirchhoff’s Current Law (flow conservation).

Kirchhoff’s Current Law (KCL)

In electrical circuits: Sum of currents into a node = Sum of currents out of node.

Accounting Analog: Sum of debits to an account = Sum of credits (flow conservation).

Discrete Continuity Equation

Discrete-time analog of the continuity equation from fluid mechanics:

Continuous Form: ∂ρ/∂t + ∇·J = s (density change = negative divergence of flux + source)

Discrete Form: x_{t+1} = x_t + flows + sources (balance tomorrow = balance today + changes)

Reynolds Transport Theorem (RTT)

Theorem relating time derivative inside a moving control volume to time derivative of the control volume itself.

Standard Form:

d/dt ∫(CV) ρ dV = ∫(CV) ∂ρ/∂t dV + ∫(∂CV) ρ(v·n) dA
              rate inside     boundary flux

Accounting Application: M&A as entities crossing consolidation boundary (∂CV)

Incidence Matrix

Matrix P where rows = accounts, columns = transactions. Entry P[i,j] = ±1 if account i is affected by transaction j.

Property: For valid double-entry, P·a = 0 where a = transaction amounts vector.

Audit & Validation

Leverage Identity

Fundamental accounting identity: A = L + E (Assets = Liabilities + Equity)

Ratio Form: A/E - L/E = 1 (used for validation with tolerance)

Framework Test: Pass if |A/E - L/E - 1| < 0.05 (5% tolerance)

Equity Bridge

Reconciliation of equity from one period to the next:

E₁ = E₀ + Net Income + OCI + Owner Contributions - Dividends - Buybacks ± NCI Changes

Framework Test: Pass if |computed E₁ - reported E₁| < 0.03 × avg(E₀, E₁)

Source Term

Component contributing to equity change. Framework decomposes into: 1. Profit/Loss (IAS 1.106) 2. OCI (7 components per IFRS 9, IAS 21, IAS 19, etc.) 3. Owner Transactions (dividends, buybacks, contributions) 4. Boundary Flux (M&A, NCI changes) 5. Measurement (revaluations, impairments)

Pass Rate

Percentage of filings where validation test passes (within tolerance).

Example Results: - Leverage identity: 72.9% (means 72.9% of 2,000 filings have A ≈ L + E within 5% tolerance) - Equity bridge: 54.9% (means 54.9% have complete reconciliation within 3% tolerance)

Interpretation: Failures often indicate XBRL data quality issues, not accounting fraud.

Wilson Score Interval

Statistical method for computing confidence intervals for proportions. More accurate than normal approximation when sample size is small or proportion near 0/1.

Formula: Uses quadratic equation based on binomial distribution.

Why We Use It: Pass rates are proportions (e.g., 72.9% ± CI). Wilson gives correct confidence intervals.

AUC (Area Under Curve)

Metric for binary classification models. Measures area under ROC curve (true positive rate vs. false positive rate).

Interpretation: - AUC = 0.5: Random guessing - AUC = 0.7: Acceptable - AUC = 0.9: Excellent - AUC = 0.949: Our ML audit risk model

Meaning: 94.9% probability that model ranks a randomly chosen high-risk filing higher than a randomly chosen low-risk filing.

Technical Implementation

Poetry

Python dependency management tool. Alternative to pip + requirements.txt.

Key Files: - pyproject.toml: Dependency specifications - poetry.lock: Exact versions installed (reproducibility)

Commands:

poetry install  # Install dependencies
poetry run pytest  # Run tests in virtual environment

Pandera

DataFrame schema validation library for pandas/polars.

Example:

import pandera as pa

schema = pa.DataFrameSchema({
    "ticker": pa.Column(str, nullable=False),
    "equity": pa.Column(float, pa.Check.ge(0))
})
validated_df = schema.validate(df)

JSON Schema

Standard for validating JSON structure. Used for metrics.json validation.

Example:

{
  "type": "object",
  "properties": {
    "pass_rate": {"type": "number", "minimum": 0, "maximum": 1}
  },
  "required": ["pass_rate"]
}

Pre-commit Hooks

Automated checks run before git commits. Our hooks: - black: Python code formatting - ruff: Python linting - mypy: Static type checking - YAML validation: Syntax checking for .yml files

GitHub Actions

CI/CD platform running automated workflows. Our workflows: - test.yml: Run pytest on every push - security.yml: Bandit, pip-audit, Semgrep, Gitleaks - pages-preview.yml: Deploy preview to GitHub Pages (PR branches) - pages-release.yml: Deploy production site (main branch)

Mermaid

Markdown-based diagramming language. Renders in GitHub/GitLab.

Example:

flowchart LR
    A[Start] --> B[Process]
    B --> C[End]

Dataset & Data Quality

SEC EDGAR

Electronic Data Gathering, Analysis, and Retrieval system. Public database of company filings.

API Endpoints: - companyfacts: /api/xbrl/companyfacts/CIK{CIK}.json - Rate limit: 10 requests/second

CIK (Central Index Key)

Unique identifier for companies in SEC EDGAR. 10-digit number (with leading zeros).

Example: Apple Inc. = CIK 0000320193

Ticker Symbol

Stock market abbreviation (e.g., AAPL for Apple). Not unique (can change over time).

Framework: Uses CIK internally, accepts ticker as input (resolves via mapping).

S&P 500

Stock market index of 500 large US companies. Our validation dataset.

Selection Criteria: Large-cap, liquid, representative of US economy.

Why We Use It: High-quality XBRL data, diverse sectors, public interest.

Fiscal Period

Company’s accounting period (not necessarily calendar year).

Formats: - Annual: 2024-FY (fiscal year ending in 2024) - Quarterly: 2024-Q3 (third quarter of fiscal 2024)

Complication: Apple’s fiscal year ends September (FY 2024 = Sept 2023 to Sept 2024).

Business & Strategy

Big 4

Four largest accounting/audit firms globally: 1. Deloitte 2. PwC (PricewaterhouseCoopers) 3. KPMG 4. EY (Ernst & Young)

Relevance: Collectively investing $4.4B in AI audit technology (our target market).

PCAOB (Public Company Accounting Oversight Board)

US regulator overseeing audits of public companies. Created by Sarbanes-Oxley Act (2002).

Function: Inspects audit firms, sets audit standards, enforces compliance.

Relevance: Potential adopter of framework for inspection procedures.

SEC (Securities and Exchange Commission)

US federal agency regulating securities markets and protecting investors.

Relevant Divisions: - Corporation Finance: Reviews company filings (10-K, 10-Q) - Enforcement: Investigates fraud

Relevance: Potential adopter for automated filing review.

AICPA (American Institute of CPAs)

US professional organization for certified public accountants.

Function: Sets professional standards (non-governmental), provides training/certification.

IASB/FASB

IASB (International Accounting Standards Board): Issues IFRS standards globally.

FASB (Financial Accounting Standards Board): Issues US GAAP standards.

Relationship: Working toward convergence (harmonizing IFRS/GAAP) since 2002 Norwalk Agreement.

Case Study Companies

Boeing (BA)

Aerospace manufacturer with negative parent equity (-$3.3B) but positive total equity ($14.2B).

Framework Finding: Structural (excessive buybacks), not fraudulent. Leverage identity validates.

Interactive Brokers (IBKR)

Brokerage with NCI exceeding parent equity (2.8× ratio).

Framework Finding: Partnership structure (broker-dealer model). Reconciliation validates.

Lowe’s (LOW)

Home improvement retailer with aggressive share buybacks reducing equity.

Framework Finding: Owner-driven negative equity, not operational failure.

Domino’s (DPZ)

Pizza franchisor with negative equity due to leveraged business model.

Framework Finding: Structural (high debt, franchising asset-light model). Not distress.

Ellerman (1982)

David Ellerman’s graph-theoretic formalization of double-entry.

Contribution: Showed accounting satisfies Kirchhoff’s law (flow conservation).

Our Extension: Added source terms + temporal dynamics + moving boundaries.

Liang (2001)

Pierre-Jin Liang’s computational graph dynamics for accounting.

Contribution: Graph algorithms for balance sheet construction.

Our Extension: Map to IFRS/GAAP standards with XBRL implementation.

Ijiri (1989)

Yuji Ijiri’s momentum accounting framework.

Contribution: Time derivatives (dA/dt), “force” analog to income.

Our Extension: Empirical validation (Ijiri was theoretical only).

Stock-Flow Consistent Models (Godley 2007)

Macroeconomic framework ensuring sectoral balances reconcile.

Difference: Godley = macro (government/household/firm sectors), Us = micro (single entity).

Not applicable: Different level of analysis.

Common Abbreviations

Terminology Clarifications

“Conservation” vs. “Conserved”

Conservation (noun): Mathematical property where a quantity is tracked with explicit accounting for sources/sinks.

Conserved (adjective): Property of a physical quantity that cannot be created/destroyed (e.g., mass in classical physics).

Our Usage: Accounting equity exhibits conservation (we track sources) but is NOT conserved (equity can be created via income, destroyed via distributions).

“Framework” vs. “Standard”

Framework: Conceptual structure with mathematical foundation (this repository).

Standard: Authoritative requirement issued by standards body (IFRS, US GAAP).

Our Framework ≠ Standard: We provide tools to validate compliance with standards, but are not ourselves a standard.

“Validation” vs. “Verification”

Validation: Checking if output meets requirements (did we build the right thing?).

Verification: Checking if implementation matches specification (did we build it right?).

Our Framework: Both. Validates financial statements against standards, verifies AI audit algorithms match math spec.

“Audit” vs. “Assurance”

Audit: Statutory examination of financial statements (opinion on fair presentation).

Assurance: Broader term including audits, reviews, agreed-upon procedures.

Our Framework: Supports audit procedures, not a complete audit solution (doesn’t replace professional judgment).

References

For detailed explanations and mathematical derivations: - index.html: Complete mathematical exposition - FOR_RESEARCHERS.md: Technical deep-dive - SOURCES.md: Full bibliography (20+ citations) - RELATED_WORK.md: Comparison to prior art

Last Updated: 2025-01-05