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A completed autonomous operation need not leave its apparatus in a state admittedby the next operation. We construct a second service from the actual terminal record of a specifiedsource-refresh preparation, rather than replacing that record by an ideal ready state. A preinstalled,initially inactive twenty-four-coordinate supply augments the twenty-coordinate parent. Its routerarchives the old outputs, and a clock-driven mechanical exchange transfers the old carrier infor-mation into physical histories. The exact decoded scaling product differs from one: the realizedlaunch is close to, but not equal to, the stored mechanical reference. Both clock reactions andthe cost of activating the history energy are retained. A conserved internal norm excludes everyrecovered historical receiver box for the chosen new payload family; a separate functional receivingclass admits the actual continuation without deleting passive records. For every independentlysupplied four-dimensional payload of norm at most one half, a connected source-valid route reachesthe originally prescribed second readout. Its joint loading-and-processing error is below 0.000409,against the declared tolerance 0.01. Later interactions need no additional near-ideal angle conditionbecause their realized orthogonal operators fix the ideal zero-register target. All forty-four coordi-nates, old output archives, mechanical histories, and signed source-value events remain available.The result is conditional on the published first-terminal membership and supplied source, prepa-ration, and record identities. It is functional reuse with finite preinstalled resources, not exactreset, autonomous creation of supplies, a uniform first-use theorem, unlimited repeatability, or alaboratory demonstration. This manuscript consolidates analytic and finite-computation evidence,accompanied by a newly executed connected reproduction from the trusted first-terminal records.A dedicated Lean support package checks exact algebra, certificate arithmetic, and conditionalerror transport; physical instantiation of its hypotheses and full formalization of the cumulativetheorem remain outside its scope.
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Qingchun Zhang (2026) studied this question.
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