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3664 bytes, as of the version from 2026-10-28 05:42 (current). Recorded here, not run.
# Argument selection for T572
The table holds one named quantity: the intrinsic Riemannian volume of the
rank-exactly-r stratum in the Bures metric. Field, matrix size, and actual rank
specify the space whose volume is measured. They do not select different
quantities. The variation of the support subspace is included.
The instructions used are archived in
`agents/runs/20261028T051113Z-build-skills/manifest.json`; the attached
`skill-manifest.json` is an unchanged copy. Both the local and live skill have
SHA-256 `e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c`.
This build justification is not the independent critique's acceptance.
## Every free parameter
| Parameter | Role | Selection and reason |
| --- | --- | --- |
| `field` | Intrinsic distinction between two sourced geometries | Both `real` and `complex`, meaning beta=1 and beta=2. Real symmetric and complex Hermitian density matrices are the two cases proved in Sommers–Życzkowski v3, section V and (5.15). We do not extend the formal beta expression to unsupported fields. |
| `N` | Discrete index | Every integer matrix size from 2 through 16. Matrix size is the dimension of the state Hilbert space. This finite initial segment covers small and moderate spaces, including rebit/qubit, qutrit and composite-system sizes, without claiming a distinct application for each size. The cutoff 16 is a noncanonical practical choice independent of numeral notation. The trivial one-dimensional state space is outside the declared domain N>=2. |
| `rank` | Discrete geometric index | Every actual rank 1 through N at each selected N. This gives pure states, all intermediate boundary strata and the interior, rather than only one boundary depth at increasingly large N. Rank is not a sampled eigenvalue or a continuous parameter relabelled as an integer. |
The selection has 135 spaces per field and 270 entries in total. It is a
triangular portion of a discrete matrix family, not a Cartesian mesh of
continuous arguments. There are no exploratory continuous inputs. Including
both fields and all admissible ranks gives breadth before further depth in N.
The rows are ordered by field (`real`, then `complex`), increasing N, and
increasing actual rank. No quaternionic continuation, metric rescaling, or
statistical quantile is included.
Sommers–Życzkowski, *Bures volume of the set of mixed quantum states*, corrected
17 February 2005 version, https://arxiv.org/abs/quant-ph/0304041v3, defines the
metric in (3.5), gives the general rank volume in (5.15), and gives the
projective-space specialisation in (5.16). The complex expression (4.19) is
explicitly corrected by note [54]. The retrieved PDF uses these equation
numbers, rather than the sequential numbers in the queue proposal.
The bound was retained after measurement: the longest serialized 100-digit
value is 107 characters; the actual flat entry block, with parameter fields and
four geometric comments, remains well below the 160 KB working target. The
smallest volume is about 2.48e-227, which is represented with relative accuracy;
small magnitude causes no loss of the requested significant digits. Extending
N further is cheap but would add only higher-dimensional cases, not another
kind of geometric space. The finite extent is a reference choice, not a
claim that all sizes beyond 16 lack interest.
The parameter declarations state the domains `field` in {real, complex},
N>=2, and 1<=r<=N. The completeness note, default generator enumeration, and
checks all describe the finite selection above. A separate critique must
assess these justifications and fingerprint the current draft and generator.