Entries against numbers stored, for sin of a sum on 6 points a side, as indices are added
At its defaults it draws entries against numbers stored, for sin of a sum on 6 points a side, as indices are added. The upper line is the tensor: 6^d entries, which is a straight line on a logarithmic axis and reaches 46,656 at d = 6. The lower one is the train, which for this family is 4n(d − 1) exactly — 24, 48, 72, 96, 120 — a straight line on a *linear* axis and therefore a logarithm on this one. Its fitted slope against d is 24.0, which is 4n. The two are the same object to within 1.39·10⁻¹⁵, so nothing has been given up: the ratio at d = 6 is 389, and it grows by a factor of n with every index added.
train-dimension is one function in lib/figures/ttrain.js —
the train — one rank per cut of the index list, and the iterate that must be cut back. Everything below came out of it during this build, at
arguments taken from the essays rather than invented for this page. A figure here is the
figure a reader meets in an essay, and if the generator changes, this page changes with it.
At its defaults
Drawn even though every essay passes arguments — which on this site is every essay, at 100% of placements since the standard pass. A default nothing exercises is a trap for the next essay to call this with none, and this is the page where a default that has drifted from the figures around it becomes visible.
The upper line is the tensor: 6^d entries, which is a straight line on a logarithmic axis and reaches 46,656 at d = 6. The lower one is the train, which for this family is 4n(d − 1) exactly — 24, 48, 72, 96, 120 — a straight line on a *linear* axis and therefore a logarithm on this one. Its fitted slope against d is 24.0, which is 4n. The two are the same object to within 1.39·10⁻¹⁵, so nothing has been given up: the ratio at d = 6 is 389, and it grows by a factor of n with every index added.
n: 4
The arguments are the ones A compression of 10¹⁴ that still does not fit passes. A value nobody placed would be a picture no essay asked for and no claim was ever checked against.
The upper line is the tensor: 4^d entries, which is a straight line on a logarithmic axis and reaches 4,096 at d = 6. The lower one is the train, which for this family is 4n(d − 1) exactly — 16, 32, 48, 64, 80 — a straight line on a *linear* axis and therefore a logarithm on this one. Its fitted slope against d is 16.0, which is 4n. The two are the same object to within 8.25·10⁻¹⁶, so nothing has been given up: the ratio at d = 6 is 51, and it grows by a factor of n with every index added.
n: 6
The arguments are the ones The format that does not notice the dimension passes. A value nobody placed would be a picture no essay asked for and no claim was ever checked against.
The upper line is the tensor: 6^d entries, which is a straight line on a logarithmic axis and reaches 46,656 at d = 6. The lower one is the train, which for this family is 4n(d − 1) exactly — 24, 48, 72, 96, 120 — a straight line on a *linear* axis and therefore a logarithm on this one. Its fitted slope against d is 24.0, which is 4n. The two are the same object to within 1.39·10⁻¹⁵, so nothing has been given up: the ratio at d = 6 is 389, and it grows by a factor of n with every index added.
n: 3
The arguments are the ones The format that does not notice the dimension passes. A value nobody placed would be a picture no essay asked for and no claim was ever checked against.
The upper line is the tensor: 3^d entries, which is a straight line on a logarithmic axis and reaches 729 at d = 6. The lower one is the train, which for this family is 4n(d − 1) exactly — 12, 24, 36, 48, 60 — a straight line on a *linear* axis and therefore a logarithm on this one. Its fitted slope against d is 12.0, which is 4n. The two are the same object to within 3.58·10⁻¹⁵, so nothing has been given up: the ratio at d = 6 is 12, and it grows by a factor of n with every index added.
What it checked while drawing
Every figure above checked its own claims on the way to being drawn, and a claim that failed
would have stopped the picture rather than shipped a wrong one. Those checks used to leave
no trace at all: a passing one returned true and the only evidence the figure had
checked anything was that nothing crashed. The list below is what they actually said, collected
by running this generator with an observer installed — not a description of
what it is believed to check.
8 distinct claims across 4 sets of arguments, grouped below by shape — because most of them are one sentence with a different number in it, and how many separate times that sentence was put to the test is the informative part.
every cut at d = 2 has rank two — checked 5 times
a grid the tensors can be formed at
and the storage is 4n(d − 1)
so the storage grows by 4n per index
Against the rule
The rule does not apply to it. It factorises nothing, so there is no residual it could be withholding. That is worth stating rather than leaving blank: a site that reported the rule as satisfied by every generator would be counting mostly generators the rule never reached.
Across the library: the rule bites on 217
of 397 generators —
199 print a residual and
18 are exempt with a published reason;
180 factorise nothing.
Read from lib/residual-rule.js, which is the same body the gate enforces from,
and the gate's last check fails the build if this page and it disagree about any generator.
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.
A compression of 10¹⁴ that still does not fit
A Tucker core of a twenty-index array at rank four is 1.1·10¹² numbers against the tensor's 1.05·10²⁶ — a compression by a factor of 9.5·10¹³ that is still nearly nine terabytes. The ratio is not the verdict. The verdict is a ceiling, and the ceiling is a number of indices.
When the index is a tupleThe format that does not notice the dimension
A Tucker core is r^d numbers, so the format that repaired the definition still cannot go past five indices. Cutting between the indices rather than across them gives d − 1 ranks instead of d, storage linear in the number of indices, and a family whose ranks are two everywhere by an addition formula.