Stream
plain-language theorem explainer
The Stream definition supplies the core data type for infinite boolean sequences in the pattern and measurement layers. Researchers deriving discrete observation models or block-sum statistics from Recognition Science would cite it when constructing cylinders and aligned 8-tick windows. The declaration is a direct type abbreviation with no computational content or proof obligations.
Claim. A stream is a function $s : {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,2
background
The module defines streams, windows, and aligned block sums as the interface between pattern recognition and measurement. Streams represent infinite boolean displays that can be restricted to finite 8-tick windows for summation and periodicity checks. This construction ports the PatternLayer/MeasurementLayer cluster and sits atop upstream structures including J-cost minimization (strict convexity of J(x) = (x + 1/x)/2 - 1 with global minimum at x = 1) and the active edge count A = 1 from the integration gap at D = 3.
proof idea
Direct type abbreviation: Stream is defined as the function type Nat → Bool with no further reduction or lemma application required.
why it matters
This definition is the root type for all downstream measurement lemmas in the Measurement module, including Cylinder sets of streams matching an 8-bit window, blockSumAligned8, observeAvg8, and firstBlockSum_eq_Z_on_cylinder. It supplies the data carrier for the eight-tick octave (T7) and enables the periodic extension machinery that feeds into Z_of_window and subBlockSum8. The declaration closes the basic interface needed before phi-ladder mass formulas or spectral emergence structures can be observed on concrete streams.
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