The scratch-pool lock is the guard's API rather than a convention, because one caller had skipped it

[Rafael-SOWNet]

FractionFreeDeterminantTest.EliminationAgreesWithLaplaceWhereverBothApply fails on master
whenever it happens to run beside MatrixConcurrencyTest, and it fails in the way #1219 was
filed for — the determinant of a matrix whose entries are integers and a, b, c comes back
containing sin(a), which is an entry of the other test's matrices:

[[-4, 3, -1], [-2, a, 0], [1, a, 3]]:
  -9 * a + 18   vs   (-4) * (a * 3 + -sin(a) * 2 * sin(a)) + 18 + -((-2) * a + -a)

Thirteen of the three hundred generated matrices disagreed. Reproducing it needs nothing but the
two classes together, since xUnit runs test classes in parallel:

dotnet test Sources/Tests/UnitTests/UnitTests.csproj -c Release \
  --filter "FullyQualifiedName~MatrixConcurrencyTest|FullyQualifiedName~FractionFreeDeterminantTest"

Failed: 1 on master. Each class on its own passes, which is why this has not been noticed.

Why the #1230 guard did not cover it

It covers all three of the library's callers. This one is in the test tree: it reaches
DeterminantLaplace directly, because comparing Laplace against the elimination is the whole
point of the test and Determinant would answer by elimination. One unguarded caller is enough
to break every guarded one — it writes into the shared scratch matrix while they are reading it,
and reads their minors back.

What this changes

Locking in the test would fix this instance. Instead the lock object becomes private and the
three pool operations — DeterminantLaplace, Adjoint, InvertMatrix — become the guard's whole
surface, so a caller can no longer reach GenericTensor without the lock. The library's three call
sites lose their lock statements and gain a method call; the test calls the same method.

Adjoint returns the Entity rather than the tensor deliberately. The lock has to cover reading
the elements out of the tensor, and Entity.Matrix's constructor is where they are read, so a
GenTensor-returning signature would put that read on the far side of the lock. That is the
bracket the previous code had, kept.

No public API moves, and no answer changes on a single thread.

Measured

Three runs of the failing command with this change: Failed: 0 each time.

suite
UnitTests (!~Calculus)	8514 passed
UnitTests (~Calculus)	1508 passed
FSharpWrapperUnitTests	134 passed
InteractiveWrapperUnitTests	18 passed
TerminalUnitTests	41 passed

AotSmokeTest was left to CI — this change adds no reflection or generic instantiation, and
CPPWrapperUnitTests is a .bat.

Part of #1219, which was closed by #1230 and turns out to have had one caller left.

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https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura