blockSumAligned8
plain-language theorem explainer
The aligned block sum counts the total number of true events across k successive 8-tick blocks of a boolean stream. Measurement-layer users cite it to obtain the raw count before averaging over instrument length T=8k. The declaration is realized as a one-line abbreviation that forwards the summation to the Streams.Blocks implementation.
Claim. For a boolean stream $s$ and natural number $k$, define the aligned block sum by $B(k,s) := 2^{k-1} + 2^{k-2} + 2^{k-3} + 2^{k-4} + 2^{k-5} + 2^{k-6} + 2^{k-7} + 2^{k-8} + 2^{k-9} + 2^{k-10} + 2^{k-11} + 2^{k-12} + 2^{k-13} + 2^{k-14} + 2^{k-15} + 2^{k-16} + 2^{k-17} + 2^{k-18} + 2^{k-19} + 2^{k-20} + 2^{k-21} + 2^{k-22} + 2^{k-23} + 2^{k-24} + 2^{k-25} + 2^{k-26} + 2^{k-27} + 2^{k-28} + 2^{k-29} + 2^{k-30} + 2^{k-31} + 2^{k-32} + 2^{k-33} + 2^{k-34} + 2^{k-35} + 2^{k-36} + 2^{k-37} + 2^{k-38} + 2^{k-39} + 2^{k-40} + 2^{k-41} + 2^{k-42} + 2^{k-43} + 2^{k-44} + 2^{k-45} + 2^{k-46} + 2^{k-47} + 2^{k-48} + 2^{k-49} + 2^{k-50} + 2^{k-51} + 2^{k-52} + 2^{k-53} + 2^{k-54} + 2^{k-55} + 2^{k-56} + 2^{k-57} + 2^{k-58} + 2^{k-59} + 2^{k-60} + 2^{k-61} + 2^{k-62} + 2^{k-63} + 2^{k-64} + 2^{k-65} + 2
background
A Stream is a function Nat → Bool, representing an infinite boolean sequence. The eight-tick window is the fundamental period fixed by the T7 step of the forcing chain. The present declaration re-exports the summation that adds the integer values of k successive aligned 8-tick blocks, where each block value is obtained by subBlockSum8. The module supplies the measurement-layer interface to these eight-tick invariants together with a lightweight CQ-score scaffold.
proof idea
One-line wrapper that applies the definition blockSumAligned8 from the Streams.Blocks layer, which expands directly to the sum over Fin k of subBlockSum8 s j.val.
why it matters
The definition supplies the raw count that blockSumAligned8_periodic converts into k · Z(w) for periodic extensions and that observeAvg8 normalizes to the per-window average. It therefore implements the T7 eight-tick octave inside the measurement layer and supports the DNARP equation relating averaged observations to the window integer Z. The re-export keeps the Measurement module free of direct dependence on the lower Blocks implementation.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.