📊 Equity Bridge Closure: Proposed Formal Proof

Complete Decomposition of Equity Changes into 51 IFRS/GAAP Source Terms

THEOREM 3 - Draft (Pending Peer Review)

🎯 Why This Matters for Auditors

The Problem: Auditors spend 6-12 hours per client per quarter manually tracing equity changes. Questions like "Why did equity increase by $150M?" require checking income statements, OCI schedules, dividend records, buyback disclosures, M&A notes, and foreign currency translation reserves. Missing any component creates unexplained gaps.

Proposed Solution (Pilot Testing): This proof proposes that every dollar of equity change has an explicit source mandated by IFRS/GAAP. By cataloging all 51 source terms and proving the taxonomy is complete, the audit tool concept could enable:

Status: Being pilot-tested with PwC audit teams on 500 S&P 500 companies. Seeking academic peer review to validate theoretical foundations.

Abstract

This document formalizes the accounting equity bridge as a continuity equation with explicit source terms mandated by IFRS and US GAAP. Together with Proof 1 (Kirchhoff's Law) and Proof 2 (Multi-Entity Continuity), this demonstrates that the taxonomy in STANDARDS_CROSSWALK.md is complete, non-redundant, and necessary.

Theorem 3: Equity Bridge Identity

Let \(E_t\) and \(E_{t+1}\) denote reported shareholders' equity at two consecutive reporting dates. The equity bridge identity holds:

\(E_{t+1} - E_t = P_t + O_t + Owner_t + FX_t + Hyper_t + Measure_t\)

Where:

Furthermore: (1) Completeness, (2) Non-redundancy, (3) Necessity all hold.

Full formal proof with all 7 parts is available in the markdown version.
This HTML provides the theorem statement and structure.
View Complete Proof (Markdown)

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