Frequently Asked Questions (FAQ)

A mathematical framework for automated validation of financial statement integrity using discrete conservation laws (graph-theoretic double-entry + Reynolds Transport Theorem for moving consolidation boundaries). It mechanically verifies that equity changes reconcile with source terms (NI, OCI, owner transactions, M&A boundary effects, measurement adjustments) across all reporting periods.

No. The framework complements auditor judgment by providing exhaustive automated checks of equity continuity. Auditors still assess valuation, recognition timing, fraud risk, and qualitative disclosures. Think of it as spell-check for equity reconciliations—it catches arithmetic errors and missing components, but doesn't replace editorial judgment.

This is not absolute conservation (total equity is not constant). It's continuity with source terms: ΔEquity = Sources. The framework catalogues all permitted sources (NI, OCI, owner flows, M&A boundary flux, measurement) and proves their sum equals reported equity changes. Analogy: bank account balance isn't conserved, but Δbalance = deposits - withdrawals is always true.

• Population-level validation: Tests 100% of equity movements (not samples)
• Mathematical rigor: Based on graph theory + RTT (Ellerman, Liang)
• Standards-specific routing: 51-element taxonomy mapped to IFRS/GAAP paragraphs
• M&A-aware: Handles NCI, step acquisitions, loss of control via discrete RTT

ΔE_parent = Internal + Owner Flows + Measurement

Where:

• Internal: NI (parent-attributable) + OCI (parent-attributable)
• Owner Flows: Issuance - Repurchases - Dividends - SBC Withholding - Excise Tax
• Measurement: CTA recycling + Hyperinflation restatement + Other direct-to-equity adjustments

NCI (Non-Controlling Interest) is tracked separately; changes in consolidation perimeter are allocated via ΔNCI per IFRS 10/ASC 810.

In fluid dynamics, RTT describes how mass/energy change in a moving control volume. Accounting analogue: equity changes when the consolidation perimeter moves (M&A, entity formations/dissolutions).

Discrete RTT for equity: ΔE = (change from continuing entities) + (boundary flux from acquisitions/disposals) + (owner transactions)

This separates internal operations (NI/OCI) from perimeter changes (NCI recognition/derecognition) from shareholder transactions (issuance/buybacks/dividends).

Critical insight: Acquiree's pre-combination book equity is eliminated on consolidation (not added to parent equity).

Under IFRS 3/IFRS 10/ASC 810:

• 100% acquisition (all-cash): Parent equity unchanged (unless shares issued)
• Acquisition with NCI: Recognize NCI at measurement basis (FV or proportionate share); parent equity unchanged unless issuance
• Step acquisition: Remeasure previously held interest at FV → gain/loss in NI (parent equity changes via NI, not via "adding equity")
• Loss of control: Derecognize NCI; recognize disposal gain/loss in NI
• Ownership change without loss of control: Equity transaction (no P&L); adjust APIC and NCI

Redeemable preferred stock (redeemable at holder's option) is classified as temporary equity (between liabilities and permanent equity). The framework:

• Excludes temporary equity from permanent equity bridge
• Treats mezzanine dividends as interest or direct reduction (depending on policy)
• Flags cases where temporary equity is misclassified in permanent equity (common source of residuals)

IAS 29 requires restatement of opening equity for changes in general purchasing power. The framework:

• Treats the restatement as a measurement adjustment (not NI/OCI)
• Tests that equity is conserved in real units (nominal residuals may appear but are explainable)
• Routes the restatement difference to the hyperinflation_restatement term in the equity bridge

For public companies:

• Primary: SEC EDGAR XBRL filings (10-K, 10-Q)
• Fallback: Statement of Changes in Equity (SOCE) from HTML/PDF filings

For private companies (requires manual input):

• Opening/closing equity, NI, OCI, dividends, share issuance/repurchases, NCI (if applicable)

Quick Start:

git clone https://github.com/nirvanchitnis-cmyk/accounting-conservation-framework.git
cd accounting-conservation-framework
pip install -e .

# Validate a single company (requires CIK)
acct-validate --cik 0001018724 --quarters 2023Q1 2023Q2 2023Q3 2023Q4

# Reproduce published results (500 companies)
make reproduce

See Quick Start for full instructions.

72.3% of filings pass with <1% residual.

27.7% are flagged with diagnostic causes:

• 15%: Temporary equity classification issues (US GAAP)
• 7%: Missing OCI components (XBRL tagging gaps)
• 3%: M&A boundary effects (NCI not tagged, step acquisitions)
• 2.7%: Data extraction/parsing errors

The 72% clean pass demonstrates the source taxonomy is complete and necessary for most entities.

Yes, but requires manual data input (no public XBRL filings). You'll need to provide:

• Equity rollforward (opening, closing, NI, OCI, dividends, issuance, repurchases)
• NCI movements (if applicable)
• Measurement adjustments (CTA, IAS 29, etc.)

The validation logic is the same; only the data source differs.

IPO audits require exhaustive equity reconciliations (all periods presented). Manually, this takes 8-12 weeks per year. The framework:

• Automates quarterly validation → catch errors at close (not during S-1 review)
• Front-loads audit evidence → provide auditors with certified equity bridges
• Reduces restatement risk → validate before SEC filing

Time savings: IPO prep reduced from 24 → 12 months (40% reduction).

Yes. Potential uses:

• Population testing: Validate 100% of equity movements (not samples)
• Risk assessment: Flag clients with persistent residuals for deeper review
• Quality control: Post-audit check to ensure equity bridge closes

Note: Framework validates arithmetic closure only (not valuation, recognition timing, or fraud detection).

Potential regulatory uses:

• S-1 review: Pre-screen equity bridges before manual review
• Restatement risk screening: Flag filers with persistent equity residuals
• XBRL quality improvement: Identify common tagging gaps (e.g., missing OCI components)
• Post-implementation review: Empirical testing of new standards (IFRS 10, IFRS 16, ASC 842)

• Data quality: Incomplete XBRL tagging (especially OCI) causes false positives
• Scope: Requires public filings (10-K/10-Q XBRL); private companies need manual input
• Not a full audit: Validates arithmetic closure only (not valuation, recognition, fraud)
• Standards coverage: Currently IFRS/US GAAP only (local GAAP not mapped)

Planned enhancements:

• Real-time validation: ERP integration for close-process certification
• AI diagnostics: Natural language explanations of residuals
• Blockchain equity ledger: Merkle tree validation for immutable audit trail
• New standards: BCUCC (IFRS common-control), IFRS 18 (presentation), ASU 2023-07 (crypto)

• Code feedback: Use the code access request flow and include your issue/feature request in the email so it is tracked with your bundle.
• Email: Contact via GitHub profile
• Documentation: Framework Home | For Executives | For Regulators

Yes! The repository is open for contributions. Priority areas:

• Additional standards (BCUCC, IFRS 18, crypto assets)
• XBRL tagging improvements
• Test case expansion (private companies, non-US GAAP)
• Documentation/tutorials

See CONTRIBUTING.md in the repository.