Ma-Minda
The image of the unit disk under \(f\): concentric circles \(|z|=r\) and radial spokes mapped through \(f(z)=z+a_2z^2+\dots\); the bold curve is the boundary \(f(e^{i\theta})\). Rendered in your browser from the certified Taylor coefficients - nothing is computed server-side.
| Property | Kind | Params | Holds | Value / r | Status | Confidence |
|---|---|---|---|---|---|---|
| K | membership | {} | ✓ | 0.0312 | 🔬 screened | numerical_strong |
| r* | radius | {} | - | r ≤ 0.700 | 🔬 screened | numerical_strong |
| S* | membership | {} | ✓ | r ≤ 0.999 | ✓ proven | rigorous_verified |
| S | membership | {} | ✓ | - | 🔬 screened | numerical_strong |
Because starlikeness is proven, these properties follow by classical implications (unconditional edges in the lattice):
| Verifier | Property | Direction | Outcome | Domain r | Witness | Engine |
|---|---|---|---|---|---|---|
| boundary_scan_centered_v31 | starlike | proves | pass | 0.999 | - | boundary_v3.1 |
| boundary_scan_polynomial | starlike | proves | pass | 0.999 | - | boundary_v3.0 |
Papers that explicitly study S*(φ) for this φ - conservatively tagged from the corpus (explicit φ formula, class symbol, or unambiguous name). Quote = the supporting passage.