Re-verify the 368 stride with a control matched to its data
The sky autocorrelation turned out to be inflated by a control that did not match the data, so the 368 result was re-checked the same way rather than being left on the evidence I now know to be weak. Range measured: each level's post-shrub region start, first 65536 bytes. Method: as before, but the control is the same bytes shuffled rather than uniform random. Shuffling preserves the value distribution and destroys only the ordering, which is what a control for this statistic needs to do. Level 0's region is evenly distributed -- 256 distinct byte values, most common only 15.6% -- so uniform random was the appropriate control here, and the shuffled control independently confirms it, reading 0.0000 at strides 340, 368 and 4 against the real data's 0.1110 at 368. Recomputed across all levels with matched controls: 24 of 24 peak at exactly 368, every one with excess above 0.05. So the 368 period stands, now with a control appropriate to its data. The contrast is the useful part: the same statistic, asked the same question of two regions, gave a real answer in one and an inflated one in the other, and the only thing that separated them was whether the control matched the byte distribution.
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@@ -292,3 +292,30 @@ do not: an earlier "256x236" is wrong and should not be used.
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So the sky region is not one thing. Its first ~60 KB is an image; the rest is
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So the sky region is not one thing. Its first ~60 KB is an image; the rest is
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whatever the layer offsets address. Both halves still need work, and the
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whatever the layer offsets address. Both halves still need work, and the
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image is the tractable one.
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image is the tractable one.
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## Re-verified: the 368 stride, against a matched control
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The sky autocorrelation was found to be inflated by a control that did not
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match the data, so the 368 result was re-checked the same way.
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**Range measured:** each level's post-shrub region start, first 65,536 bytes.
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**Method:** as before, but the control is the same bytes shuffled rather than
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uniform random bytes. Shuffling preserves the value distribution and destroys
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only the ordering, which is exactly what the control needs to do.
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**Result:**
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- Level 0's region is evenly distributed: 256 distinct byte values, most
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common only 15.6%. Uniform random was therefore the *appropriate* control
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here, and the shuffled control independently confirms it, reading **0.0000**
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at strides 340, 368 and 4.
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- Level 0 peak remains 368 at 0.1110, against 0.0000 for the matched control.
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- Recomputed across all levels with matched controls: **24 of 24 peak at
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exactly 368, every one with excess above 0.05.**
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So the 368-byte period stands, now with a control appropriate to its data.
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The contrast with sky is the point: the same statistic on the same kind of
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question gave a real answer in one region and an inflated one in the other,
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and the only thing that told them apart was whether the control matched the
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byte distribution.
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