Mises connects expected purchasing power with recent experience and ends the regression before the first monetary use. This is a theorem within his theoretical system, not statistical regression.
Demand for money depends on expectations about what it can obtain. Mises distinguishes the purchasing power being explained from the past purchasing power people start from. They are not the same magnitude at the same moment. [Mises — Human Action, XVII.4 and XVII.9]
Our illustration: bread cost 10 units yesterday and 12 today. Knowing 10 provides orientation but does not guarantee its preservation. New supply, demand and expectations change the outcome; the theorem does not determine the size of the change. [Mises — Human Action, XVII.4 and XVII.9]
Before a good’s first use as a medium of exchange, Mises assumes exchange value from nonmonetary use in consumption or production. This claim belongs to his argument; it does not itself establish the date or motive of a particular first exchange. [Mises — Human Action, XVII.4 and XVII.9]
Menger describes accepting a more saleable good even when its holder need not consume it. This facilitates obtaining desired things. Our distinction: this mechanism spreading indirect exchange is different from the continuity of valuation addressed by Regression Theorem. [Menger — The Nature and Origin of Money]
In The Theory of Money and Credit, Mises distinguishes commodity, credit and fiat money. In his account, an official designation alone cannot ensure that people actually use an object as a medium of exchange. Compare participants’ conduct, not just a token’s material or inscription. [Mises — Commodity Money, Credit Money, and Fiat Money]
Mises allows continued monetary use after a redemption claim is lost and distinguishes fiat money without industrial use. Do not confuse Regression Theorem’s initial condition with a requirement that every present unit remain redeemable for a commodity. [Mises — Human Action, XVII.4 and XVII.9]
Nakamoto describes signatures, transaction history and Proof of Work to address double spending. This technical design alone does not document participants’ motives in the first BTC exchange or its rate. Transfer functionality and the emergence of valuation are separate questions. [Nakamoto — Bitcoin: A Peer-to-Peer Electronic Cash System]
Our approach to applying Regression Theorem to Bitcoin: distinguish network launch, transfer between addresses, a quoted rate and a completed exchange. For an alleged nonmonetary use, document who valued what and when. Today’s price or mining cost alone cannot replace that historical evidence. [Nakamoto — Bitcoin: A Peer-to-Peer Electronic Cash System] [Mises — Human Action, XVII.4 and XVII.9]
For the clearest picture, read this entry together with Fiduciary Media, Fiat money, Medium of exchange, Ludwig von Mises, Bitcoin. The reverse links also lead from Commodity Money, Ludwig von Mises, Medium of exchange.