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.
Pavel Kramarenko-Byrd (Wed,) studied this question.