Maximum Determinacy I: Foundations

Maximum determinacy (MD) begins with related quantities whose joint resolution isbounded: each pair has a floor K on the product of its widths, and one universal purenumber, the pace ceiling rmax, bounds how fast and how finely any member is determined.This paper develops what follows with no non-classical premise. Objects are families ofrelated pairs; split-invariance gives an exponential resolution law; directed record roles andthe area content of a cell give a symplectic form; the floor, the pace and an exchange ceilingdefine a critical cell and, for a position–time lock, a causal cone. The saturated cells of apair run along a hyperbola from the critical cell, the fine end, which is the narrowest a cellcan be, towards the vacuum, where energy and momentum are determinate and time andposition are not; sources, not records, break the vacuum into a lattice. Objects move byhops across joins, at most one join per pair per tick, so each coordinate moves at most c∗,as in 1+1, and light, which hops like any content, reaches c∗ without a separate premise.Given pace along the motion, the floor of the time pair and an energy balance, cells of anyaspect and Hamilton’s equations imply each other to first order in the cell’s size, and actionreads as a count of cells; these are equivalences under stated premises, not a derivationof dynamics from the floor alone. Depth is relative: a motion’s capacity is its extents infloors, μmax = log(UV/K), capped at 2 log rmax. The axioms have a classical model, sonothing here forces quantum behaviour; the one non-classical premise, that joins betweencells are dynamically real, and what it buys are the subject of Paper II. Every result carriesits grade and premises; the premises are collected in Paper VI.