Lommel · parametric, arity 1
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 | {"mu":1} | ✗ | -628.0119 | unscreened | - |
| K | membership | {"mu":2} | ✗ | -335.1167 | unscreened | - |
| K | membership | {"mu":3} | ✗ | -76.8767 | unscreened | - |
| r* | radius | {"mu":1} | - | r ≤ 0.960 | 🔬 screened | numerical_strong |
| r* | radius | {"mu":2} | - | r ≤ 0.960 | 🔬 screened | numerical_strong |
| r* | radius | {"mu":3} | - | r ≤ 0.960 | 🔬 screened | numerical_strong |
| S* | membership | {"mu":10} | - | - | retracted | - |
| S* | membership | {"mu":9} | - | - | retracted | - |
| S* | membership | {"mu":7.5} | - | - | retracted | - |
| S* | membership | {"mu":6.5} | - | - | retracted | - |
| S* | membership | {"mu":5.5} | - | - | retracted | - |
| S* | membership | {"mu":4.5} | - | - | retracted | - |
| S* | membership | {"mu":8} | - | - | retracted | - |
| S* | membership | {"mu":7} | - | - | retracted | - |
| S* | membership | {"mu":6} | - | - | retracted | - |
| S* | membership | {"mu":5} | - | - | retracted | - |
| S* | membership | {"mu":4} | - | - | retracted | - |
| S* | membership | {"mu":1} | - | -189.0256 | retracted | - |
| S* | membership | {"mu":2} | - | -275.0654 | retracted | - |
| S* | membership | {"mu":3} | - | -67.8883 | retracted | - |
| S | membership | {"mu":1} | ✗ | - | unscreened | - |
| S | membership | {"mu":2} | ✗ | - | unscreened | - |
| S | membership | {"mu":3} | ✗ | - | unscreened | - |
| Verifier | Property | Direction | Outcome | Domain r | Witness | Engine |
|---|---|---|---|---|---|---|
| boundary_scan_centered_v31 | starlike | disproves | pass | - | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | - | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | - | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | - | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | - | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | - | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | - | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | - | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | - | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | - | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | - | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | - | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | - | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | - | - | boundary_v3.1 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.311 | [-0.20788032367299988, 0.230874489057977] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.279 | [0.2508315149377759, 0.12233870407449797] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.247 | [0.22243264423118037, 0.10848764935242292] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.224 | [0.20113349120123372, 0.09809935831086664] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.208 | [-0.07791187552137667, 0.19283865882796628] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.484 | [0.2274372739042572, 0.42774730023795904] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.398 | [-0.3915231495378786, 0.06903609483548294] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.350 | [-0.344848227462342, -0.06080604675110077] | gft-0.1.0-reaudit-20260610 |
| boundary_scan_polynomial | starlike | proves | pass | - | - | boundary_v3.0 |
| boundary_scan_polynomial | starlike | proves | pass | - | - | boundary_v3.0 |
| boundary_scan_polynomial | starlike | proves | pass | - | - | boundary_v3.0 |
| boundary_scan_polynomial | starlike | proves | pass | - | - | boundary_v3.0 |
| boundary_scan_polynomial | starlike | proves | pass | - | - | boundary_v3.0 |
| boundary_scan_polynomial | starlike | proves | pass | - | - | boundary_v3.0 |
| boundary_scan_polynomial | starlike | proves | pass | - | - | boundary_v3.0 |
| boundary_scan_polynomial | starlike | proves | pass | - | - | boundary_v3.0 |
| boundary_scan_polynomial | starlike | proves | pass | - | - | boundary_v3.0 |
| boundary_scan_polynomial | starlike | proves | pass | - | - | boundary_v3.0 |
| boundary_scan_polynomial | starlike | disproves | pass | 0.300 | 0.3*exp(i*2.304614) | boundary_v3.0 |
| boundary_scan_polynomial | starlike | proves | pass | 0.999 | - | boundary_v3.0 |
| boundary_scan_polynomial | starlike | proves | pass | 0.999 | - | boundary_v3.0 |
| boundary_scan_polynomial | starlike | proves | pass | 0.999 | - | boundary_v3.0 |
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