Trace-Level Support Reduction under the Bost–Connes Quotient

Research Note 48 in the "Geometry of the Critical Line" programme. This note lifts the algebraic quotient picture of RN43 to the trace level. One support filter is proved: fractional-winding orbits are annihilated by the quotient (Proposition 2.1), because any operator reaching a fractional-winding state factors through the obstruction ideal. A second filter — vanishing of composite non-prime-power orbits — is isolated as a trace-level hypothesis (Hypothesis 2.2), supported by the orthogonality of p-adic components in the GNS representation of the KMS state at β = 1/2 but not reproved as a standalone theorem here. Assuming this hypothesis, the quotient trace support is confined to the identity orbit and the prime-power translation orbits — exactly the index set of the Weil explicit formula.