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# Argument selection for T595
The policy read for this run is archived in
`agents/runs/20261029T002659Z-build-skills/manifest.json`. Both valid local and
live copies have SHA-256
`28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199`.
The copy of that manifest in `skill-evidence.json` records the full path.
The mathematical object is the zeta-regularized determinant of the nonnegative
scalar Laplace–Beltrami operator on the radius-one round sphere, excluding the
constant eigenfunction. Cunha and Freitas, arXiv:2404.12114v1, Introduction and
Section 2.1, explicitly specify this geometry, spectrum and regularization.
Their Theorems 2.7 and 2.8 treat the dimension-dependent family.
## Dimension: discrete_index
`d` is the integer dimension of the sphere, with domain d >= 1, not a continuous
argument disguised as an index. We choose every dimension 1 through 20.
This is a practical, noncanonical prefix of an established geometric family.
It covers ten dimensions of each parity, the elementary circle and the
low-dimensional closed forms, and higher-dimensional values governed by both
parity formulas. These are plausible targets when identifying functional
determinants from spectral geometry. We do not assert a distinct application
for each dimension. The source itself treats all dimensions and gives a
hundred-row numerical comparison; copying that full range is unnecessary.
Breadth was reviewed before depth: both parity branches and every intermediate
dimension are retained, rather than extending one parity or keeping only the
famous first few dimensions. Different radii, shifted operators, masses,
curvature couplings, hemispheres and projective spaces describe other families
and are outside this definition. They are not silently varied free parameters.
Forty roughly hundred-digit values remain readable. The cutoff is a coverage
choice, not a size-limit target; numerical evidence reports actual lengths.
## Convention: intrinsic
`convention` exhausts exactly `det` and `logdet`, enumerated in that order after
each increasing d. They are D_d > 0 and its real natural logarithm L_d, related
by D_d = exp(L_d). Either determines the other, conversion is inexpensive and
the ranges coincide. Thus the skill's invertible-convention exception applies.
This is not a choice among different operators or geometric quantities.
Cunha and Freitas, equation (1.2) and Theorems 2.7 and 2.8, explicitly relate
these two representations.
There are no exploratory reference samples, mixed roles, continuous grids,
parameter couplings, or campaign-excluded statistical quantities. The
completeness note and generator enumerate the same 40 ordered identities.
This is a build justification, not independent argument-review acceptance.
A separate critic must assess it and produce the controller's sidecar.