back to table · edit · history · where entries came from · files · download
2578 bytes, as of the version from 2026-10-27 18:01 (current). Recorded here, not run.
# Argument selection for T555
The only free parameter is the integer n >= 2, the order of the cyclic
puncture set mu_n = {exp(2*pi*i*j/n): 0 <= j < n}. Its category is
`discrete_index`. The centre is fixed at zero and the punctures lie on the
unit circle, with one at 1. Infinity is an additional puncture on the sphere;
n counts only punctures in the plane. The output is the absolute derivative
at zero of a universal holomorphic covering from the unit disk, taking zero
to zero. It is independent of the rotation used to normalize the source disk.
There is no second quantity, scale parameter, angle grid or free Gamma argument.
The selected extent is every integer 2 <= n <= 30, in increasing order. Each
index specifies a finite cyclic configuration, not a sampled continuous input.
The contiguous range includes the twice-punctured plane, small rotational
symmetries, prime and composite orders, and nonconstructible configurations.
Thirty is a noncanonical editorial cutoff providing coverage beyond the familiar
small cases without concentrating on large orders whose radii approach 1.
Neither individual fame nor a storage target determines admission. The fixed
scale removes redundant dilations. General finite puncture sets would introduce
moduli and constitute a different family, so breadth here means all small cyclic
orders, not adding unrelated shapes or a mesh in those moduli.
Calegari, Dimitrov and Tang, *The Unbounded Denominators Conjecture*, section
5.1, Definition 5.1.1 and Theorem 5.1.4, equation (5.1.5), in the checked
50-page author PDF at https://web.math.princeton.edu/~yunqingt/UDC.pdf,
identifies this uniformization and gives the formula for every integer n >= 2.
The paper uses these coverings in its arithmetic argument. The source establishes
the family, normalization and formula; the finite cutoff is our reference choice.
No exploratory continuous-input group is present, so `reference_sample` and
its `reference_policy` do not apply.
The generator, Programs snippet and completeness note all enumerate 2 through
30. All four rational Gamma arguments are forced by n, and are not independently
selected. The argument-selection review must be performed by the separate critique
actor. This build makes no independent-review attestation.
Policy evidence: ../20261027T175211Z-build-skills/manifest.json in the run archive.
Both archived files, skill-local.md and skill-live.md, have SHA-256
`e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c`.
The attached skill-evidence.json records the manifest path and both digests.