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# Argument selection
Selected quantity: squared distance of the constant sequence 1 from the span
of g_k(m)={m/k} in the real Hilbert space with weights 1/[m(m+1)]. The natural
family has N >= 2 and support in {all, squarefree}, in that parameter order.
Complex coefficients have the same minimum: imaginary parts add a nonnegative
squared norm. There is no continuous coupling, alternate weight, branch, sign
selector, or change of quantity between supports.
- **support — arithmetic_structure.** `all` includes every integer denominator
2..N, Bagchi's D(N) (p. 146). `squarefree` includes exactly k with mu(k)^2=1,
explicitly supported by Bagchi's Remarks 4 and 8 (pp. 142, 145). This also
describes the available denominators of the fixed-anchor Vasyunin sum.
Both are actual approximation spaces, not sparsifications chosen by the digits.
- **N — discrete_index.** Every integer 2..30 for each support. N is the largest
allowed denominator, not the number of basis vectors. The full prefix retains
every enlargement and all squarefree plateaus. The cutoff 30 is practical and
noncanonical: at most 29-dimensional certified systems, inspectable optimizer
vectors, and matched endpoints with T641, T707 and T708. Breadth includes both
sourced arithmetic supports before extending only one further. No index is
selected for fame or decimal appearance.
Enumeration is support-major (`all`, then `squarefree`), N increasing, for 58
entries. The squarefree denominators through 30 are 2,3,5,6,7,10,11,13,14,15,17,
19,21,22,23,26,29,30. Nonsquarefree endpoint entries are retained even when equal.
The empty-span control D(1)^2=1 belongs in Comments, not as two generic entries.
The table is `complete: no`. Default generator enumeration, Programs and
complete-note describe these same two prefixes; the program permits extensions.
There are no exploratory reference_sample groups and no excluded quantile data.
Checked primary sources: Bagchi, arXiv:math/0607733v1, p.137 (weight and basis),
p.142 (Remark 4), p.145 (Remark 8 and unitary correspondence), p.146 (D(L));
Báez-Duarte, arXiv:math/0011254v1, equations (1.14), (1.17). The proposal's
reference to Remark 3 for squarefree sequence support is corrected to Remark 8.
See sources.json for exact PDF hashes. Related website metadata was refreshed
before claiming. A sibling's values are not evidence for this selection or digits.
Instruction archive: ../20261111T001542Z-build-skills/manifest.json, SHA-256
c5ee30e128246f511fb7c0e8e37f8b7d2419d5fad25227688a6111fdf9686049;
matching local/live bundle d6661c2f21613524889fa3a57d3c95f8330344ca62e5a856211c08a282b7dbab.
The same manifest is attached as skill-manifest.json. This is the builder's
justification, not an independent argument-selection verdict.