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The mathematics of Roth Conversions, written down carefully.

Most Roth-conversion advice rests on a shortcut: compare your tax rate today to your tax rate later. The shortcut hides components that materially change the answer. This site collects working research papers that decompose conversion value into the pieces that actually drive household wealth — and shows, in plain English, what each one is and why it matters.

Start here

New to this? The Practitioner Guide walks through the conversion decision from first principles, in plain prose. If you want the math, start with the Synthetic Roth Contribution paper.

Working draft · May 2026

The Synthetic Roth Contribution

When you pay Roth conversion tax from outside the retirement account, you've quietly made a Roth contribution equal to the tax — bypassing the IRS contribution limit. This paper proves it four ways.

Working draft · May 2026

Tax-Drag Shelter

The defining value of a retirement account isn't the tax-rate trade — it's the elimination of annual tax drag on savings. A Roth conversion accesses this benefit through two distinct channels, separately quantified here in PV and IRR.

Foundational paper · April 2025 · Published on SSRN June 2025

Roth Conversion Valuation & Mechanics

The paper that introduced the Synthetic Roth Contribution concept and decomposed conversion-tax payback into its components. The framework has been substantially extended in the two working drafts above.

See the research applied

RothGPT

The frameworks developed here are implemented in a working calculator: RothGPT.com. Enter your own numbers and see the Synthetic Roth Contribution, Tax-Drag Shelter alpha, time-weighted distribution rate, and break-even tax rate computed for your actual situation.