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6028 bytes, as of the version from 2026-10-29 06:33 (current). Recorded here, not run.
# Argument selection for T602
This build uses the coordinated canonical skill archived in
`agents/runs/20261029T055510Z-build-skills/manifest.json` (attached as
`skill-manifest.json`). Both local and live copies have SHA-256
`28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199`.
The following is the builder's justification, not the independent critic's
acceptance. The controller must commission that independent review.
The object is T(D)=integral_D u, where -Delta u=1 with zero Dirichlet values
on every boundary component and bank of a cut. This is the normalization of
van den Berg, Buttazzo and Pratelli, equation (1.1). Scaling in dimension two
is T(cD)=c^4 T(D), by their (1.5). The material modulus is not a parameter.
## Domain: mixed, with four disjoint exhaustive groups
1. **Intrinsic symmetric controls:** `disk`, `rectangle-1-1`,
`equilateral-triangle`. The circle and these regular polygons provide smooth
and cornered symmetric benchmark domains. Their Poisson problems admit
quadratic, separated-variable, and cubic solutions, respectively. This is a
selected benchmark group; it does not claim completeness over regular
polygons. Sources checked: Love §225(a), §225(c); Comer–McDonald Proposition
2.1; the exact cubic solution verified in checks.py and derivations.md.
2. **Documented applications:** `right-isosceles-triangle`, `half-disk`,
`slit-disk`. OEIS A180314, A180310 and A180311 explicitly identify the
corresponding shaft torsion constants. Their engineering normalization is
J=4T. These add a different triangle, a mixed straight/curved boundary, and
a cut with two zero-Dirichlet banks. Their conventions and formulas were
checked against the named sources and independent PDE calculations.
3. **Rectangular reference sample:** `rectangle-4-3`, `rectangle-3-2`,
`rectangle-5-3`, `rectangle-2-1`, `rectangle-5-2`, `rectangle-3-1`,
`rectangle-4-1`, `rectangle-5-1`, `rectangle-6-1`.
Purpose: recognition of separated-variable Poisson integrals and
rectangular section constants with simple exact side ratios.
Bounds: together with the square, every reduced r=p/q>=1 with p<=6 and
q<=3, for the rectangle (0,r)x(0,1). Coverage: moderately asymmetric
through elongated rectangles, with several intermediate ratios because
the non-elementary separation sum has a plausible reference role beyond
the symmetric controls. These are noncanonical exploratory choices,
independent of decimal notation, not an arithmetic theorem and not a
claimed application at each ratio. Source checked: Comer–McDonald
Proposition 2.1, including its derivation from the Laplacian spectrum;
Love §225(c). No second geometric parameter is independently sampled.
4. **Elliptical reference sample:** `ellipse-3-2`, `ellipse-2-1`,
`ellipse-3-1`, `ellipse-4-1`.
Purpose: reference values for smooth sections from near-round to
elongated, in contrast to rectangles with corners.
Bounds: semiaxes (r,1) for r=3/2,2,3,4. Coverage: a short distinct slice;
the disk supplies r=1. The elementary formula does not justify repeating
the denser rectangle selection. These ratios are noncanonical reference
choices, independent of decimal notation, without a claim of documented
use of every ratio. Source checked: Love §225(b), equation (16), plus
direct quadratic Poisson solutions in checks.py.
The 19-domain selection covers smooth, polygonal, mixed and slit boundaries
before extending either aspect-ratio family deeply. A large numerical PDE
mesh for arbitrary polygons would cost much more for substantially weaker
precision guarantees; it is outside this initial reference. No probability,
quantile, percentile, median, quartile or critical-value inputs are used.
The free ratios inside symbolic identifiers are explicitly assessed here;
calling them symbolic does not remove their reference status.
## Normalization: intrinsic
`unit-length` and `unit-area` exhaust the two chosen invertible conventions
for the same domain. The reference area A gives T_unit-area=T_unit-length/A^2
and its exact inverse. Both have every domain, the same precision and cheap
conversion. There is no quantity selector. The square's two identities remain
present even though A=1. Source checked: van den Berg–Buttazzo–Pratelli (1.5).
Reference dimensions: the disk and half-disk have radius one; the equilateral
triangle has side one; the right triangle has both perpendicular legs one;
the slit disk has radius one with 0<theta<2*pi, no identification across the
slit. Rectangles have sides (p/q,1); ellipses have semiaxes (p/q,1).
Enumeration is disk, equilateral triangle, right isosceles triangle, half-disk,
slit disk, the ten rectangles in increasing ratio, and the four ellipses in
increasing ratio. Each lists `unit-length` then `unit-area`. The parameters
define the domain of the object; the finite selection belongs in completeness.
## Sources actually inspected
- https://arxiv.org/pdf/1910.14593, equations (1.1), (1.4), (1.5).
- https://arxiv.org/pdf/2105.07477, Proposition 2.1, PDF page 5. The triangle
projection coefficients on that page contain a discrepancy documented in
derivations.md; they are not used for the triangle's production values.
- A. E. H. Love, *A Treatise on the Mathematical Theory of Elasticity*,
second edition, §224 and §225, printed pp. 310–311 (PDF pp. 328–329),
https://brittlebooks.library.illinois.edu/brittlebooks_open/Books2011-02/loveau0001tremat/loveau0001tremat.pdf.
- https://oeis.org/A180310, https://oeis.org/A180311,
https://oeis.org/A180314, definitions, formulas and archived b-files.
The separate critic should assess these four domain groups and the full
normalization parameter, using a reference_policy for each reference group.
Fingerprint generate.py and every source controlling the final selection;
argument-selection.md and checks.py should also be included for review
freshness. No acceptance sidecar is produced by this build.