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Show the sky sub-object shape holds across levels

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Range measured: sub-objects of the sky region on levels 0, 1, 3, 7, 13 and
26 -- 25 sub-objects, each over its whole length.

Method: correlation at lag against the byte sequence, as before.

  lag 8      +0.53 .. +0.79   positive on all 25
  lag 64     +0.16 .. +0.63   positive on all 25
  lag 512    -0.13 .. +0.42   not universal
  lag 1024   -0.05 .. +0.37   not universal

Lag 8 and lag 64 hold on every sub-object of every level tested. The longer
lags do not, so the second scale seen in level 0's first sub-object is a
property of that data rather than of the format.

The sky sub-objects are all the same kind of thing: 8-byte units strongly
related to their neighbours, with a further relation at 64 bytes. That is the
first result about sky that holds everywhere rather than on one level. The
8-byte unit is still unnamed and the values still unidentified.
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2026-10-11 03:55:06 +02:00
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@@ -429,3 +429,32 @@ computed per vertex.
**Still not decoded.** Nothing here names the values or the sampling. But the
structure is now characterised well enough that a decode attempt has a shape
to aim at rather than a field to hunt for.
### Sky sub-objects share one shape, across every level
**Range measured:** sub-objects of the sky region on levels 0, 1, 3, 7, 13
and 26 -- 25 sub-objects in total, each measured over its whole length.
**Method:** as above, correlation at lag against the byte sequence.
**Result:**
| quantity | range over 25 sub-objects |
|---|---|
| lag 8 | +0.53 .. +0.79 |
| lag 64 | +0.16 .. +0.63 |
| lag 512 | -0.13 .. +0.42 (not universal) |
| lag 1024 | -0.05 .. +0.37 (not universal) |
**Lag 8 and lag 64 are positive on every sub-object of every level tested.**
The longer lags are not, so the second scale seen in level 0's first
sub-object is a property of that data rather than of the format.
So the sky sub-objects are all the same kind of thing: 8-byte units, strongly
related to their neighbours, with a further relation at 64 bytes. That is a
consistent description across the format, and it is the first result about sky
that holds everywhere rather than on one level.
**Not decoded.** The 8-byte unit is still unnamed and the values are still not
identified, but "same kind of thing, 8-byte units, correlated at 8 and 64" is
now a statement about the format rather than about one level's data.