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4211 bytes, as of the version from 2026-10-30 06:50 (current). Recorded here, not run.
# Argument selection for T616
This assessment uses the matching canonical skills archived in
`agents/runs/20261030T025528Z-build-skills/manifest.json`. Both copies have
SHA-256 `28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199`.
It is the builder's justification, not the independent critique acceptance.
The table has one quantity, the axial moment of inertia divided by total mass
and squared surface radius, and one parameter, the exact rational polytropic
index n. Its mathematical domain is 0 <= n < 5. Physical scale, central density,
angular momentum, tidal order and radial coordinate are not free parameters.
A nonrotating spherical density profile determines a moment about any diameter;
no rotation perturbation or relativistic compactness is assumed.
The enumeration is exactly 0, 1/2, 1, 3/2, 2, 5/2, 3, 7/2, 4, 9/2, in that
order. The following disjoint groups exhaust it.
* **Intrinsic: 0 and 1.** The incompressible and linear Lane–Emden equations
have exact profiles, yielding I/(MR^2)=2/5 and 2/3-4/pi^2. These are structural
anchors, independent of any reference sampling. Yip, Chan and Leung (2017),
section 2, and Princeton's *Polytropes*, equations (poly.9), establish the
profiles. At zero, constant interior density has a surface jump.
* **Documented application: 3/2 and 3.** These idealized stellar indices describe
nonrelativistic/convective and ultrarelativistic/radiative models. Princeton's
*Polytropes*, page 3, and Wenbin Lu's *Polytropic Star*, pages 1–2 and its
radiative-envelope section, supply the applications. They are not asserted
to describe particular observed stars accurately.
* **Exploratory reference sample: 1/2, 2, 5/2, 7/2, 4, 9/2.** These are simple
nonlinear algebraic density–enthalpy laws rho/rho_c=theta^n. The purpose is
recognition of their dimensionless axial inertia constants. No documented
application is asserted for each exponent. The underlying equations and
inertia convention are checked in Lu, equations (1)–(10), and Yip and Leung
(2017), sections 3, 9.1 and Appendix C.4.
The reference policy is:
```json
{
"purpose": "Exploratory identification of axial inertia constants of simple algebraic Lane-Emden density-enthalpy laws outside the intrinsic and stellar application cases.",
"bounds": "Only 1/2, 2, 5/2, 7/2, 4 and 9/2; these are the remaining integer or half-integer exponents in 0 <= n <= 9/2 after assigning 0, 1, 3/2 and 3 to the other groups.",
"coverage_rationale": "Cover integral and square-root algebraic laws from stiff through centrally concentrated finite models before adding higher denominators or approaching the noncompact endpoint n=5 more closely. The same background selection allows comparison with radius, mass and density concentration without adding a new physical parameter.",
"noncanonical_acknowledged": true,
"notation_independent": true,
"sources_checked": true
}
```
The denominator-two criterion means that the density becomes an integer
monomial after theta=t^2. This is algebraic simplicity, not an intrinsic
selection theorem. Both that denominator bound and the cutoff 9/2 are
noncanonical reference choices. Higher denominators, asymptotic sequences near
five and a sampled radial profile are deferred. The existing selection covers
both analytic limits and distinct stellar applications before extending into
softer mathematical models. There is no assertion of radial dynamical stability
for n>3. At n=5, the radius is infinite and the axial inertia integral diverges;
no artificial zero or infinity is stored for the finite-radius normalization.
This is the same background family as live T613, T614 and T615, read from the
website in this run. The inertia is a different named observable, with an extra
radial factor in its density integral, not a transcription of those tables.
The finite extent gives ten compact entries; a longer list is not a target.
All digits are accompanied by agreement checks and an independent radial
formulation. Supporting sources establish the model and conventions, not a
publication using every exploratory exponent. Source URLs, exact downloaded
hashes and locators are in source-manifest.json.