The 174-Step Scalar Balance Sheet

This document serves as the formal mathematical audit for the Integrated Efficiency Model (IEM). It provides the complete 174-step "Balance Sheet" of the universe, tracing the scalar progression from the Planck Length (\bm{1.6163 \times 10^{-35}} m) to the Observable Universe Radius (\bm{4.4 \times 10^{26}} m).

The Audit Methodology

By applying the 1.22 Primal Invariant and the 18.03% Displacement Tax (the 0.22 connectivity tax) at every scalar transition, this balance sheet demonstrates that cosmic expansion is a precise thermodynamic account rather than a series of stochastic events.

Key Audit Benchmarks:

• Steps 0–10: High-energy subatomic density transitions.

• Step 100: The macro-scale threshold (~20.5 meters).

• Step 150: The galactic core stability limit (~1.47 \bm{10^{18}} m).

• Step 174: The Universal Horizon, where the expansion energy "cheque" is balanced.

Scientific Context & Priority

This audit acts as the primary empirical proof for the Integrated Efficiency Model (IEM). It resolves the Hubble Tension by demonstrating that the Early Universe baseline (67.4 km/s/Mpc) naturally evolves into the observed Late Universe reality (82.23 km/s/Mpc) via the 1.22 scaling law.

Registration & Priority

• Parent Project: https://doi.org/10.17605/OSF.IO/WBZDF

• Status: This document serves as the final evidentiary link for calculations registered on January 26–27, 2026.