implications
plain-language theorem explainer
The definition enumerates four consequences of the 8-tick phase rotation for the imaginary unit and quantum mechanics. A researcher deriving complex structure from discrete time would reference it to link phase steps to i, waves, unitarity, and fermion statistics. The body is a direct list of statements extracted from the phase definition.
Claim. The 8-tick phase structure yields: $i^2 = -1$ because four ticks equal a rotation by $π$; oscillatory waves arise from continuous accumulation of phase; unitarity of evolution follows from phase conservation; a fermion acquires a minus sign under a $2π$ rotation, which equals eight ticks.
background
The module MATH-001 derives the imaginary unit from the eight-tick octave. The fundamental time quantum is the tick, defined as the constant 1 in RS-native units. The phase map assigns to each integer k in 0..7 the angle kπ/4, producing the cyclic group of eighth roots of unity. Upstream results supply the tick constant and the phase function; the eight-tick structure itself is the period-8 rotation generator.
proof idea
This is a definition that enumerates the four listed implications. No lemmas are applied; the body simply records the physical readings already obtained from the phase map and the rotation identifications (two ticks = π/2, four ticks = π).
why it matters
The entry closes the explanatory gap between the eight-tick octave (T7) and the appearance of i in the Schrödinger equation and Euler formula. It supplies the concrete list that later siblings (schrodinger_i_from_8tick, euler_from_8tick) presuppose. The declaration therefore anchors the claim that complex numbers are forced by the discrete phase circle rather than postulated.
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