N24 — QNM frequency ratio ιτ⁻¹

N24: Prediction

$T^2$ winding modes give $f_{(0,1)}/f_{(1,0)} = ι_τ⁻¹ ≈ 2.929$ at leading order (V.T168). The Kerr primary ringdown scale remains dependent on remnant mass and spin; this falsification path tests the τ ratio claim, not mass-only ringdown uniqueness. Orthodox Kerr ringdown does not predict this fixed $T^2$ cycle ratio. Experiment: LIGO/Virgo A+, LISA, Einstein Telescope. Timeline: 2029–2035.

Derivation Context

The source derivation uses the $T^2$ horizon fiber with primitive cycles $(1,0)$ and $(0,1)$. If the secondary topology readout is present, the ratio between the inner-cycle and outer-cycle frequencies is fixed by $r/R = ι_τ$. This makes the proposed ratio independent of the common Kerr mass/spin scale at leading order.

Failure would be a robust high-SNR ringdown measurement inconsistent with the $ι_τ⁻¹$ ratio while meeting the analysis requirements for mode identification, start-time stability, and posterior predictive checks. Current public status remains released and consistent, not validated.

Correction record: ERRATUM-005 records the 2026-05-15 correction of mass/spin wording, ratio direction, and generated-page contamination for this test surface.