interference_from_8tick
plain-language theorem explainer
Recognition Science asserts that double-slit interference arises from 8-tick phase accumulation along the two paths, with each tick advancing phase by π/4. A researcher building quantum results from the eight-tick octave would cite this to connect the fundamental time quantum to observed fringes. The proof is a one-line trivial assertion that the mechanism yields the pattern.
Claim. The 8-tick phase mechanism produces the double-slit interference pattern: phase difference $Δφ = φ_L - φ_R$ yields intensity proportional to $2 + 2 cos(Δφ)$, with constructive fringes at $Δφ = 2nπ$ and destructive at $(2n+1)π$.
background
The DoubleSlit module targets derivation of interference from the 8-tick structure. The tick is the fundamental RS time quantum, set to 1 in native units. The phase function returns kπ/4 for k = 0..7 and is periodic with period 2π. Upstream results from Constants establish the tick as base unit while EightTick supplies the discrete phase steps. The local setting is QF-012, where left and right paths accumulate phases that combine as complex amplitudes to give probability ∝ |e^{iφ_L} + e^{iφ_R}|^2.
proof idea
The proof is a term-mode trivial that directly asserts the claim. It relies on the prior definitions of tick and phase from Constants and EightTick to ground the 8-tick mechanism without further reduction steps.
why it matters
This declaration fills the QF-012 target, linking the eight-tick octave (T7) to the double-slit experiment. It supplies the bridge from the phase structure to quantum superposition effects. No downstream uses are recorded, leaving open explicit derivation of fringe spacing Δy = λL/d from the phi-ladder.
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