neutralityScore_succ
plain-language theorem explainer
The lemma establishes that the neutrality score at t0+1 equals the sum of the next eight consecutive values of the weight function w. Researchers adjusting time origins in 8-tick flight schedules cite this shift property to realign control windows without recomputing the full sum. The proof is a direct reflexivity step that follows immediately from the definition of the score as an 8-window summation.
Claim. For a weight function $w : ℕ → ℝ$ and initial index $t_0 ∈ ℕ$, the neutrality score satisfies neutralityScore$(w, t_0 + 1) = ∑_{k=0}^7 w(t_0 + 1 + k)$.
background
The neutrality score is defined in SpiralField as the sum of eight consecutive values of w starting at a given index t0. This module re-exports the definition for 8-tick flight scheduling, where control sequences operate under periodic 8-phase windows drawn from the eight-tick structure. Upstream results supply the explicit summation formula (Finset.range 8).sum (fun k => w (t0 + k)) together with phase definitions for the 8-tick cycle.
proof idea
The proof is a one-line reflexivity step that matches the left-hand side directly to the expanded sum in the definition of neutralityScore.
why it matters
This shift lemma supports index manipulation in 8-tick control schedules. It aligns with the eight-tick octave (T7) in the forcing chain, allowing neutrality diagnostics to be applied consistently across shifted periods. No downstream theorems are recorded yet, so its role in larger schedule proofs remains open for future closure.
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