Radius reconciliation
We compute sharp inclusion radii r(φ₁→φ₂) = sup{ r : φ₁(r𝔻) ⊆ φ₂(𝔻) } for the Ma–Minda classes (the discovery machine gft/radius.py), then join every one against the literature so nothing is presented as ours without a real citation. This page is that join. Verdicts are never conflated, and a result is labelled a candidate — never novel — until an external literature check and expert sign-off both clear.
Census
| verdict | count | meaning |
|---|---|---|
| KNOWN | 4 | matches a published value for the same pair (exact agreement) |
| KNOWN_GENERAL | 277 | fixed by a standard inclusion lemma (order-α / Janowski target, or containment) — not a discovery |
| CANDIDATE_IMPROVE | 1 | our exact value sharpens a published non-sharp bound (pending sign-off) |
| CONTRADICTION | 0 | same pair, both claimed sharp, values disagree (audit) |
| UNRESOLVED | 0 | a claim exists but isn't comparable yet (implicit root / flagged) |
| NO_EXTRACTED_CLAIM | 323 | no literature claim extracted so far — not a novelty assertion |
Joined to the literature
| source → target | our radius | verdict | literature |
|---|---|---|---|
| sine → sigmoid | 0.480381 | CANDIDATE_IMPROVE | #176 Theorem 2.9(ii) |
| cardioid → sigmoid | 0.301221 | KNOWN | #176 Theorem 2.7(ii) |
| crescent → sigmoid | 0.389089 | KNOWN | #176 Theorem 2.8(i) |
| exponential → sigmoid | 0.379885 | KNOWN | #176 Theorem 2.6(iii) particular |
| lemniscate → sigmoid | 0.710682 | KNOWN | #176 Theorem 2.6(ii) particular |
The KNOWN rows are exact agreements with published sharp results — an independent check that the engine computes the genuine sigmoid-radius.
- sine → sigmoid (under review — not yet asserted novel): our sharp value
asin((e-1)/(e+1))improves the non-sharp literature bound. Proof →
Generated by scripts/build_reconciliation_radii.py from scripts/reconcile_radii.py output. Re-bake after any new extraction.