Search for the tie vertex stride: 64 where one exists, none for 62%

The 16-byte reading was retracted without a replacement. This searches for one -- every tie vertex region, strides 4, 8, ... up to len/16, keeping any stride where some byte offset is constant across every unit: regions examined 1,844 no stride found at all 1,139 (61.7%) stride 64 491 stride 56 120 stride 72 49 stride 48 12 stride 16 3 64 where a stride is detectable, not 16. And for 1,139 regions there is no stride in range producing a single constant byte -- those are genuinely variable, or the element is larger than region/16, which is the same statement. THE CONTROL THAT CHANGED THE ANSWER The first run reported 1,561 regions at stride 64. Wrong, and wrong in a way worth recording: a large stride divides a region into fewer units, and fewer units makes an accidental constant more likely. Region length is fixed across candidates, so the widest stride always has the fewest units and the best chance of constancy by luck alone. The search was reporting its own sampling. Requiring every candidate stride to cover the SAME minimum of 16 units, and preferring the SMALLER stride on ties, drops it to 491 and promotes 56 and 72 into view, which were invisible before. This is rule 3a's sampling failure in its purest form -- an aggregate over candidates with different denominators, where the largest denominator wins for a reason unconnected to the data. The first number was not imprecise; it WAS the artefact. Worth noting that without the control I would have reported "64" with confidence and been right by accident, three times the observed figure. What this does not settle: 64 is the stride where one is detectable, which is not the same as the stride. The 1,139 regions with no constant byte at any tested stride leave the element genuinely unknown. But 16 is now excluded quantitatively -- 3 of 1,844 regions show a constant byte there -- which is the retraction's content, as a measurement, and a third independent check now agreeing with it.
2026-10-14 03:54:32 +02:00
parent 7b6de36958
commit b3b4d47d97
1 changed files with 46 additions and 0 deletions
@@ -3383,3 +3383,49 @@ That gap is the artifact, and naming both denominators is the most useful thing
 this section can do about it. A percentage over vertices and a percentage over
 distinct values answer different questions, and only one of them was ever asked
 about.
+
+
+## The tie vertex stride, searched properly: 64 where one exists, none for 62%
+
+The 16-byte reading was retracted without a replacement. Searching for one: for
+every tie vertex region, try strides 4, 8, ... up to `len / 16` and keep any where
+some byte offset is constant across every unit.
+
+    regions examined                1,844
+    no stride found at all            1,139   (61.7%)
+    stride 64                           491
+    stride 56                           120
+    stride 72                            49
+    stride 48                            12
+    stride 16                             3
+
+**64 bytes, not 16, wherever a stride is detectable** -- and for more than three in
+five regions there is no stride in range that produces a single constant byte.
+Those regions are genuinely variable, or the element is larger than the region
+divided by sixteen units, which is the same statement.
+
+### The control that changed the answer
+
+The first run of this search reported **1,561** regions at stride 64. It was
+wrong, and wrong in a way worth recording: a large stride divides a region into
+fewer units, and fewer units makes an accidental constant more likely. Length is
+fixed across strides, so the widest candidate always has the fewest units and the
+best chance of constancy by luck alone.
+
+Requiring every candidate stride to cover the **same** minimum of 16 units, and
+preferring the **smaller** stride when hit counts tie, drops it to 491 and
+promotes 56 and 72 into view -- which were invisible before.
+
+That is rule 3a's sampling failure in its purest form: an aggregate over
+candidates with different denominators, where the largest denominator wins for a
+reason that has nothing to do with the data. The first number was not merely
+imprecise, it was reporting the artefact.
+
+### What this does not settle
+
+64 is the stride where one is detectable, which is not the same as the stride.
+For the 1,139 regions with no constant byte under any tested stride, the element
+is still unknown, and the tie vertex layout remains open. What is settled is that
+**16 is not it** -- only 3 of 1,844 regions show a constant byte at 16 -- which is
+the quantitative version of the retraction, and a third independent measurement
+now agreeing with it.