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3263 bytes, as of the version from 2026-10-29 04:58 (current). Recorded here, not run.
# Argument selection for T600
This build follows the coordinated skill recorded in
`agents/runs/20261029T043345Z-build-skills/manifest.json`. Both the local and
live copies have SHA-256
`28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199`.
The attached `skill-evidence.json` records the manifest and both digests.
The named object is the zeta-regularized determinant of the nonnegative scalar
Laplacian on real projective space with the metric induced by the unit round
sphere. The constant zero mode is removed. The trivial line bundle, radius
one, and absence of a mass or curvature shift are fixed definitions, not
sampled inputs. Cunha and Freitas, arXiv:2404.12114v1, Section 3.2 and Theorem
3.3, and Spreafico, arXiv:math/0110175, Section 3, specify this family and
spectrum. These sources were read in this build.
## Dimension d: discrete_index
Every integer d >= 1 names a member of a standard geometric family. The
stored prefix contains every d from 1 through 20. It includes the circle and
projective plane, ten dimensions of each parity, and five representatives of
each residue class modulo four. The latter classes occur in the shifted
spectral-zeta recurrence in Cunha and Freitas, Section 3.2. Both the orientable
odd-dimensional cases and the nonorientable even-dimensional cases are
included; the scalar operator is defined in both.
The endpoint 20 is a noncanonical practical choice, not a theorem or a claim
that each dimension has a separate application. Breadth across the parity
cases and recurrence classes takes priority over carrying a single sequence
to the source's dimension 100. Polynomial multiplicities through degree 19
make a separate high-precision spectral continuation tractable. A contiguous
prefix avoids cherry-picking favorable digits or exceptional low-dimensional
closed forms. High dimensions add cancellation and depth without a new
operator or geometric construction. This is a discrete family, not a
continuous mesh disguised as an index, and not exploratory reference sampling.
## Convention: intrinsic
The two values are `det` (D_d) and `logdet` (L_d). They are exhaustive for the
specified pair of invertible conventions D_d = exp(L_d), L_d = log(D_d).
All determinants are strictly positive. Conversion is elementary, both forms
have the same dimension domain, and neither is a specialization of the other.
No other named quantity or operator is included. The header names both D_d and
L_d; symbolic labels describe the conventions, not a conversion formula.
## Enumeration and completeness
The generator's default enumeration is ascending d = 1,...,20, with `det`
then `logdet` for each d, for exactly 40 entries. The table parameter domain
remains d >= 1. The completeness note identifies this prefix, both conventions,
the quotient metric and the breadth/cost rationale. There are no independent
reference-input groups, arbitrary decimal grids, hidden couplings, or quantiles.
The build reassessed the family proposal against the current archived skill.
This explanation is not the required independent critique. The controller must
obtain the critique's parameter assessments, live selection fingerprint, and
hashes of every selection-relevant attachment before any offer for review.