Literature reconciliation — provenance class of every certified enclosure
Split requested in review (2026-06-11); literature web-verified 2026-06-12 (data/bibliography/CORPUS_LITERATURE.md). The general Ma-Minda FS theorem (Ma & Minda 1994, Int. Press, pp. 157-169): |a3 - mu a2^2| <= (B1/2) max{1, |B2/B1 + B1(1-2mu)|}. C = value is a general-theorem instance whose explicit instantiation for the named class appears nowhere we could find. A theorem can sit in A or B and still carry a new certified enclosure* — the certificates are new regardless of the constant's provenance. Category B rows cite extraction-pipeline leads (LLM-extracted, gate-validated): verify the primary source before citing.
A — instantiates the general Ma–Minda FS theorem: 216
B — literature lead for this named class: 14
C — apparently new (no match found): 8
D — enclosure-only (slack > 1e-4): 12
| class | functional | value | slack | cat | notes |
|---|---|---|---|---|---|
| bean_tanh | fekete_szego_mu0.25 | 1/4 | 1e-07 | A | = max(tail 0.25, face 0) — Ma–Minda general FS structure |
| bean_tanh | fekete_szego_mu0.5 | 1/4 | 1e-07 | A | = max(tail 0.25, face 0.0625) — Ma–Minda general FS structure |
| bean_tanh | fekete_szego_mu0.75 | 1/4 | 1e-07 | A | = max(tail 0.25, face 0.125) — Ma–Minda general FS structure |
| bean_tanh | fekete_szego_mu0 | 1/4 | 1e-07 | A | = max(tail 0.25, face 0.0625) — Ma–Minda general FS structure |
| bean_tanh | fekete_szego_mu1 | 1/4 | 1e-07 | A | = max(tail 0.25, face 0.1875) — Ma–Minda general FS structure |
| bean_tanh | fekete_szego_mu2 | 7/16 | 1e-07 | A | = max(tail 0.25, face 0.4375) — Ma–Minda general FS structure |
| bean_tanh | hankel2_2 | 1/16 | 0.01 | C+D | slack 0.01 |
| bell | fekete_szego_mu0.25 | 3/4 | 1e-06 | A | = max(tail 0.5, face 0.75) — Ma–Minda general FS structure |
| bell | fekete_szego_mu0.5 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| bell | fekete_szego_mu0.75 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| bell | fekete_szego_mu0 | 1 | 1e-06 | A | = max(tail 0.5, face 1) — Ma–Minda general FS structure |
| bell | fekete_szego_mu1 | 1/2 | 1e-06 | A+B | = max(tail 0.5, face 0) — Ma–Minda general FS structure |
| bell | fekete_szego_mu2 | 1 | 1e-06 | A | = max(tail 0.5, face 1) — Ma–Minda general FS structure |
| cardioid | fekete_szego_mu0.25 | 7/9 | 1e-06 | A | = max(tail 0.666667, face 0.777778) — Ma–Minda general FS structure |
| cardioid | fekete_szego_mu0.5 | 2/3 | 1e-06 | A+B | = max(tail 0.666667, face 0.333333) — Ma–Minda general FS structure |
| cardioid | fekete_szego_mu0.75 | 2/3 | 1e-06 | A | = max(tail 0.666667, face 0.111111) — Ma–Minda general FS structure |
| cardioid | fekete_szego_mu0 | 11/9 | 1e-06 | A | = max(tail 0.666667, face 1.22222) — Ma–Minda general FS structure |
| cardioid | fekete_szego_mu1 | 2/3 | 1e-06 | A+B | = max(tail 0.666667, face 0.555556) — Ma–Minda general FS structure |
| cardioid | fekete_szego_mu2 | 7/3 | 1e-06 | A | = max(tail 0.666667, face 2.33333) — Ma–Minda general FS structure |
| cardioid_exp | fekete_szego_mu0.25 | 3/4 | 1e-07 | A | = max(tail 0.5, face 0.75) — Ma–Minda general FS structure |
| cardioid_exp | fekete_szego_mu0.5 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| cardioid_exp | fekete_szego_mu0.75 | 1/2 | 1e-07 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| cardioid_exp | fekete_szego_mu0 | 1 | 1e-07 | A | = max(tail 0.5, face 1) — Ma–Minda general FS structure |
| cardioid_exp | fekete_szego_mu1 | 1/2 | 1e-07 | A | = max(tail 0.5, face 0) — Ma–Minda general FS structure |
| cardioid_exp | fekete_szego_mu2 | 1 | 1e-07 | A | = max(tail 0.5, face 1) — Ma–Minda general FS structure |
| cissoid_diocles | fekete_szego_mu0.25 | 7/12 | 1e-07 | A | = max(tail 0.5, face 0.583333) — Ma–Minda general FS structure |
| cissoid_diocles | fekete_szego_mu0.5 | 1/2 | 1e-07 | A | = max(tail 0.5, face 0.333333) — Ma–Minda general FS structure |
| cissoid_diocles | fekete_szego_mu0.75 | 1/2 | 1e-07 | A | = max(tail 0.5, face 0.0833333) — Ma–Minda general FS structure |
| cissoid_diocles | fekete_szego_mu0 | 5/6 | 1e-07 | A | = max(tail 0.5, face 0.833333) — Ma–Minda general FS structure |
| cissoid_diocles | fekete_szego_mu1 | 1/2 | 1e-07 | A | = max(tail 0.5, face 0.166667) — Ma–Minda general FS structure |
| cissoid_diocles | fekete_szego_mu2 | 7/6 | 1e-07 | A | = max(tail 0.5, face 1.16667) — Ma–Minda general FS structure |
| cosh_sqrt | fekete_szego_mu0.25 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.0833333) — Ma–Minda general FS structure |
| cosh_sqrt | fekete_szego_mu0.5 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.0208333) — Ma–Minda general FS structure |
| cosh_sqrt | fekete_szego_mu0.75 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.0416667) — Ma–Minda general FS structure |
| cosh_sqrt | fekete_szego_mu0 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.145833) — Ma–Minda general FS structure |
| cosh_sqrt | fekete_szego_mu1 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.104167) — Ma–Minda general FS structure |
| cosh_sqrt | fekete_szego_mu2 | 17/48 | 1e-06 | A | = max(tail 0.25, face 0.354167) — Ma–Minda general FS structure |
| cosh_sqrt | hankel2_2 | 1/16 | 0.01 | C+D | slack 0.01 |
| crescent | fekete_szego_mu0.25 | 1/2 | 0 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| crescent | fekete_szego_mu0.5 | 1/2 | 1e-06 | A+B | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| crescent | fekete_szego_mu0.75 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0) — Ma–Minda general FS structure |
| crescent | fekete_szego_mu0 | 3/4 | 1e-06 | A | = max(tail 0.5, face 0.75) — Ma–Minda general FS structure |
| crescent | fekete_szego_mu1 | 1/2 | 1e-06 | A+B | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| crescent | fekete_szego_mu2 | 5/4 | 1e-06 | A | = max(tail 0.5, face 1.25) — Ma–Minda general FS structure |
| epicycloid_3 | fekete_szego_mu0.25 | 3/8 | 1e-07 | A | = max(tail 0.375, face 0.140625) — Ma–Minda general FS structure |
| epicycloid_3 | fekete_szego_mu0.5 | 3/8 | 1e-07 | A | = max(tail 0.375, face 0) — Ma–Minda general FS structure |
| epicycloid_3 | fekete_szego_mu0.75 | 3/8 | 1e-07 | A | = max(tail 0.375, face 0.140625) — Ma–Minda general FS structure |
| epicycloid_3 | fekete_szego_mu0 | 3/8 | 1e-07 | A | = max(tail 0.375, face 0.28125) — Ma–Minda general FS structure |
| epicycloid_3 | fekete_szego_mu1 | 3/8 | 1e-07 | A | = max(tail 0.375, face 0.28125) — Ma–Minda general FS structure |
| epicycloid_3 | fekete_szego_mu2 | 27/32 | 1e-07 | A | = max(tail 0.375, face 0.84375) — Ma–Minda general FS structure |
| epicycloid_3 | hankel2_2 | 5/32 | 0.01 | C+D | slack 0.01 |
| epicycloid_6 | fekete_szego_mu0.25 | 3/7 | 1e-07 | A | = max(tail 0.428571, face 0.183673) — Ma–Minda general FS structure |
| epicycloid_6 | fekete_szego_mu0.5 | 3/7 | 1e-07 | A | = max(tail 0.428571, face 0) — Ma–Minda general FS structure |
| epicycloid_6 | fekete_szego_mu0.75 | 3/7 | 1e-07 | A | = max(tail 0.428571, face 0.183673) — Ma–Minda general FS structure |
| epicycloid_6 | fekete_szego_mu0 | 3/7 | 1e-06 | A | = max(tail 0.428571, face 0.367347) — Ma–Minda general FS structure |
| epicycloid_6 | fekete_szego_mu1 | 3/7 | 1e-07 | A | = max(tail 0.428571, face 0.367347) — Ma–Minda general FS structure |
| epicycloid_6 | fekete_szego_mu2 | 54/49 | 1e-07 | A | = max(tail 0.428571, face 1.10204) — Ma–Minda general FS structure |
| exponential | fekete_szego_mu0.25 | 1/2 | 0 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| exponential | fekete_szego_mu0.5 | 1/2 | 1e-06 | A+B | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| exponential | fekete_szego_mu0.75 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0) — Ma–Minda general FS structure |
| exponential | fekete_szego_mu0 | 3/4 | 1e-06 | A | = max(tail 0.5, face 0.75) — Ma–Minda general FS structure |
| exponential | fekete_szego_mu1 | 1/2 | 1e-06 | A+B | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| exponential | fekete_szego_mu2 | 5/4 | 1e-06 | A | = max(tail 0.5, face 1.25) — Ma–Minda general FS structure |
| four_leaf | fekete_szego_mu0.25 | 5/12 | 1e-07 | A | = max(tail 0.416667, face 0.173611) — Ma–Minda general FS structure |
| four_leaf | fekete_szego_mu0.5 | 5/12 | 1e-07 | A | = max(tail 0.416667, face 0) — Ma–Minda general FS structure |
| four_leaf | fekete_szego_mu0.75 | 5/12 | 1e-07 | A | = max(tail 0.416667, face 0.173611) — Ma–Minda general FS structure |
| four_leaf | fekete_szego_mu0 | 5/12 | 1e-06 | A | = max(tail 0.416667, face 0.347222) — Ma–Minda general FS structure |
| four_leaf | fekete_szego_mu1 | 5/12 | 1e-07 | A | = max(tail 0.416667, face 0.347222) — Ma–Minda general FS structure |
| four_leaf | fekete_szego_mu2 | 25/24 | 1e-07 | A | = max(tail 0.416667, face 1.04167) — Ma–Minda general FS structure |
| four_leaf | hankel2_2 | 3/16 | 0.02 | C+D | slack 0.02 |
| janowski_A0.5_B-0.5 | fekete_szego_mu0.25 | 1/2 | 0 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| janowski_A0.5_B-0.5 | fekete_szego_mu0.5 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| janowski_A0.5_B-0.5 | fekete_szego_mu0.75 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0) — Ma–Minda general FS structure |
| janowski_A0.5_B-0.5 | fekete_szego_mu0 | 3/4 | 1e-06 | A | = max(tail 0.5, face 0.75) — Ma–Minda general FS structure |
| janowski_A0.5_B-0.5 | fekete_szego_mu1 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| janowski_A0.5_B-0.5 | fekete_szego_mu2 | 5/4 | 1e-06 | A | = max(tail 0.5, face 1.25) — Ma–Minda general FS structure |
| janowski_A0.75_B-0.25 | fekete_szego_mu0.25 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.375) — Ma–Minda general FS structure |
| janowski_A0.75_B-0.25 | fekete_szego_mu0.5 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.125) — Ma–Minda general FS structure |
| janowski_A0.75_B-0.25 | fekete_szego_mu0.75 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.125) — Ma–Minda general FS structure |
| janowski_A0.75_B-0.25 | fekete_szego_mu0 | 5/8 | 1e-06 | A | = max(tail 0.5, face 0.625) — Ma–Minda general FS structure |
| janowski_A0.75_B-0.25 | fekete_szego_mu1 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.375) — Ma–Minda general FS structure |
| janowski_A0.75_B-0.25 | fekete_szego_mu2 | 11/8 | 1e-06 | A | = max(tail 0.5, face 1.375) — Ma–Minda general FS structure |
| janowski_A1_B-0.5 | fekete_szego_mu0.25 | 15/16 | 1e-06 | A | = max(tail 0.75, face 0.9375) — Ma–Minda general FS structure |
| janowski_A1_B-0.5 | fekete_szego_mu0.5 | 3/4 | 1e-06 | A | = max(tail 0.75, face 0.375) — Ma–Minda general FS structure |
| janowski_A1_B-0.5 | fekete_szego_mu0.75 | 3/4 | 1e-06 | A | = max(tail 0.75, face 0.1875) — Ma–Minda general FS structure |
| janowski_A1_B-0.5 | fekete_szego_mu0 | 3/2 | 1e-06 | A | = max(tail 0.75, face 1.5) — Ma–Minda general FS structure |
| janowski_A1_B-0.5 | fekete_szego_mu1 | 3/4 | 1e-06 | A | = max(tail 0.75, face 0.75) — Ma–Minda general FS structure |
| janowski_A1_B-0.5 | fekete_szego_mu2 | 3 | 1e-06 | A | = max(tail 0.75, face 3) — Ma–Minda general FS structure |
| janowski_A1_B0 | fekete_szego_mu0.25 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| janowski_A1_B0 | fekete_szego_mu0.5 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0) — Ma–Minda general FS structure |
| janowski_A1_B0 | fekete_szego_mu0.75 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| janowski_A1_B0 | fekete_szego_mu0 | 1/2 | 0 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| janowski_A1_B0 | fekete_szego_mu1 | 1/2 | 0 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| janowski_A1_B0 | fekete_szego_mu2 | 3/2 | 1e-06 | A | = max(tail 0.5, face 1.5) — Ma–Minda general FS structure |
| lemniscate | fekete_szego_mu0.25 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0) — Ma–Minda general FS structure |
| lemniscate | fekete_szego_mu0.5 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.0625) — Ma–Minda general FS structure |
| lemniscate | fekete_szego_mu0.75 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.125) — Ma–Minda general FS structure |
| lemniscate | fekete_szego_mu0 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.0625) — Ma–Minda general FS structure |
| lemniscate | fekete_szego_mu1 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.1875) — Ma–Minda general FS structure |
| lemniscate | fekete_szego_mu2 | 7/16 | 1e-06 | A | = max(tail 0.25, face 0.4375) — Ma–Minda general FS structure |
| lemniscate | hankel2_2 | 1/16 | 0.01 | B+D | MATCH: Lee–Ravichandran–Supramaniam, J. Inequal. Appl. 2013:281, Cor. 2.1(2) |
| limacon_0.3 | fekete_szego_mu0.25 | 3/10 | 1e-06 | A | = max(tail 0.3, face 0.135) — Ma–Minda general FS structure |
| limacon_0.3 | fekete_szego_mu0.5 | 3/10 | 1e-06 | A | = max(tail 0.3, face 0.045) — Ma–Minda general FS structure |
| limacon_0.3 | fekete_szego_mu0.75 | 3/10 | 1e-06 | A | = max(tail 0.3, face 0.045) — Ma–Minda general FS structure |
| limacon_0.3 | fekete_szego_mu0 | 3/10 | 1e-06 | A | = max(tail 0.3, face 0.225) — Ma–Minda general FS structure |
| limacon_0.3 | fekete_szego_mu1 | 3/10 | 1e-06 | A | = max(tail 0.3, face 0.135) — Ma–Minda general FS structure |
| limacon_0.3 | fekete_szego_mu2 | 99/200 | 1e-06 | A | = max(tail 0.3, face 0.495) — Ma–Minda general FS structure |
| limacon_0.3 | hankel2_2 | 3/32 | 0.02 | C+D | slack 0.02 |
| limacon_0.5 | fekete_szego_mu0.25 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.375) — Ma–Minda general FS structure |
| limacon_0.5 | fekete_szego_mu0.5 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.125) — Ma–Minda general FS structure |
| limacon_0.5 | fekete_szego_mu0.75 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.125) — Ma–Minda general FS structure |
| limacon_0.5 | fekete_szego_mu0 | 5/8 | 1e-06 | A | = max(tail 0.5, face 0.625) — Ma–Minda general FS structure |
| limacon_0.5 | fekete_szego_mu1 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.375) — Ma–Minda general FS structure |
| limacon_0.5 | fekete_szego_mu2 | 11/8 | 1e-06 | A | = max(tail 0.5, face 1.375) — Ma–Minda general FS structure |
| limacon_0.707 | fekete_szego_mu0.25 | 3/4 | 1e-06 | A | = max(tail 0.707107, face 0.75) — Ma–Minda general FS structure |
| limacon_0.707 | fekete_szego_mu0.5 | sqrt(2)/2 | 1e-06 | A | = max(tail 0.707107, face 0.25) — Ma–Minda general FS structure |
| limacon_0.707 | fekete_szego_mu0.75 | sqrt(2)/2 | 1e-06 | A | = max(tail 0.707107, face 0.25) — Ma–Minda general FS structure |
| limacon_0.707 | fekete_szego_mu0 | 5/4 | 1e-06 | A | = max(tail 0.707107, face 1.25) — Ma–Minda general FS structure |
| limacon_0.707 | fekete_szego_mu1 | 3/4 | 1e-06 | A | = max(tail 0.707107, face 0.75) — Ma–Minda general FS structure |
| limacon_0.707 | fekete_szego_mu2 | 11/4 | 1e-06 | A | = max(tail 0.707107, face 2.75) — Ma–Minda general FS structure |
| nephroid | fekete_szego_mu0.25 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| nephroid | fekete_szego_mu0.5 | 1/2 | 1e-06 | A+B | = max(tail 0.5, face 0) — Ma–Minda general FS structure |
| nephroid | fekete_szego_mu0.75 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| nephroid | fekete_szego_mu0 | 1/2 | 0 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| nephroid | fekete_szego_mu1 | 1/2 | 0 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| nephroid | fekete_szego_mu2 | 3/2 | 1e-06 | A | = max(tail 0.5, face 1.5) — Ma–Minda general FS structure |
| nonconvex_sec | fekete_szego_mu0.25 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| nonconvex_sec | fekete_szego_mu0.5 | 1/2 | 1e-07 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| nonconvex_sec | fekete_szego_mu0.75 | 1/2 | 1e-07 | A | = max(tail 0.5, face 0) — Ma–Minda general FS structure |
| nonconvex_sec | fekete_szego_mu0 | 3/4 | 1e-07 | A | = max(tail 0.5, face 0.75) — Ma–Minda general FS structure |
| nonconvex_sec | fekete_szego_mu1 | 1/2 | 1e-07 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| nonconvex_sec | fekete_szego_mu2 | 5/4 | 1e-07 | A | = max(tail 0.5, face 1.25) — Ma–Minda general FS structure |
| order_0.25 | fekete_szego_mu0.25 | 21/16 | 1e-06 | A | = max(tail 0.75, face 1.3125) — Ma–Minda general FS structure |
| order_0.25 | fekete_szego_mu0.5 | 3/4 | 0 | A | = max(tail 0.75, face 0.75) — Ma–Minda general FS structure |
| order_0.25 | fekete_szego_mu0.75 | 3/4 | 1e-06 | A | = max(tail 0.75, face 0.1875) — Ma–Minda general FS structure |
| order_0.25 | fekete_szego_mu0 | 15/8 | 1e-06 | A | = max(tail 0.75, face 1.875) — Ma–Minda general FS structure |
| order_0.25 | fekete_szego_mu1 | 3/4 | 1e-06 | A | = max(tail 0.75, face 0.375) — Ma–Minda general FS structure |
| order_0.25 | fekete_szego_mu2 | 21/8 | 1e-06 | A | = max(tail 0.75, face 2.625) — Ma–Minda general FS structure |
| order_0.5 | fekete_szego_mu0.25 | 3/4 | 1e-06 | A | = max(tail 0.5, face 0.75) — Ma–Minda general FS structure |
| order_0.5 | fekete_szego_mu0.5 | 1/2 | 0 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| order_0.5 | fekete_szego_mu0.75 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| order_0.5 | fekete_szego_mu0 | 1 | 1e-06 | A | = max(tail 0.5, face 1) — Ma–Minda general FS structure |
| order_0.5 | fekete_szego_mu1 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0) — Ma–Minda general FS structure |
| order_0.5 | fekete_szego_mu2 | 1 | 1e-06 | A | = max(tail 0.5, face 1) — Ma–Minda general FS structure |
| order_0.75 | fekete_szego_mu0.25 | 5/16 | 1e-06 | A | = max(tail 0.25, face 0.3125) — Ma–Minda general FS structure |
| order_0.75 | fekete_szego_mu0.5 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.25) — Ma–Minda general FS structure |
| order_0.75 | fekete_szego_mu0.75 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.1875) — Ma–Minda general FS structure |
| order_0.75 | fekete_szego_mu0 | 3/8 | 1e-06 | A | = max(tail 0.25, face 0.375) — Ma–Minda general FS structure |
| order_0.75 | fekete_szego_mu1 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.125) — Ma–Minda general FS structure |
| order_0.75 | fekete_szego_mu2 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.125) — Ma–Minda general FS structure |
| order_0.75 | hankel2_2 | 1/16 | 0.02 | C+D | slack 0.02 |
| parabolic | fekete_szego_mu0.25 | (48 + 8pi2)/(3pi**4) | 1e-06 | A | = max(tail 0.405285, face 0.434446) — Ma–Minda general FS structure |
| parabolic | fekete_szego_mu0.5 | 4/pi**2 | 1e-06 | A | = max(tail 0.405285, face 0.27019) — Ma–Minda general FS structure |
| parabolic | fekete_szego_mu0.75 | 4/pi**2 | 1e-06 | A | = max(tail 0.405285, face 0.105934) — Ma–Minda general FS structure |
| parabolic | fekete_szego_mu0 | (8/3 + 32/pi2)/pi2 | 1e-06 | A | = max(tail 0.405285, face 0.598701) — Ma–Minda general FS structure |
| parabolic | fekete_szego_mu1 | 4/pi**2 | 1e-06 | A | = max(tail 0.405285, face 0.0583216) — Ma–Minda general FS structure |
| parabolic | fekete_szego_mu2 | (-8/3 + 96/pi2)/pi2 | 1e-06 | A | = max(tail 0.405285, face 0.715344) — Ma–Minda general FS structure |
| petal_arcsinh | fekete_szego_mu0.25 | 1/2 | 1e-07 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| petal_arcsinh | fekete_szego_mu0.5 | 1/2 | 1e-07 | A | = max(tail 0.5, face 0) — Ma–Minda general FS structure |
| petal_arcsinh | fekete_szego_mu0.75 | 1/2 | 1e-07 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| petal_arcsinh | fekete_szego_mu0 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| petal_arcsinh | fekete_szego_mu1 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| petal_arcsinh | fekete_szego_mu2 | 3/2 | 1e-07 | A | = max(tail 0.5, face 1.5) — Ma–Minda general FS structure |
| rational_kr | fekete_szego_mu0.25 | 15/4 - 5*sqrt(2)/2 | 1e-06 | A | = max(tail 0.207107, face 0.214466) — Ma–Minda general FS structure |
| rational_kr | fekete_szego_mu0.5 | -1/2 + sqrt(2)/2 | 0.001 | A+C*+D | = max(tail 0.207107, face 0.171573) — Ma–Minda general FS structure |
| rational_kr | fekete_szego_mu0.75 | -1/2 + sqrt(2)/2 | 1e-06 | A | = max(tail 0.207107, face 0.12868) — Ma–Minda general FS structure |
| rational_kr | fekete_szego_mu0 | 9/2 - 3*sqrt(2) | 1e-06 | A | = max(tail 0.207107, face 0.257359) — Ma–Minda general FS structure |
| rational_kr | fekete_szego_mu1 | -1/2 + sqrt(2)/2 | 1e-06 | A+C* | = max(tail 0.207107, face 0.0857864) — Ma–Minda general FS structure |
| rational_kr | fekete_szego_mu2 | -1/2 + sqrt(2)/2 | 1e-06 | A | = max(tail 0.207107, face 0.0857864) — Ma–Minda general FS structure |
| rational_kr | hankel2_2 | 3/4 - sqrt(2)/2 | 0.01 | B+D | PARTIAL: Naz–Kumar–Ravichandran arXiv:1905.05413 give 1/(4k^2) for INVERSE coefficients; direct H2(2) not found |
| sigmoid | fekete_szego_mu0.25 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.0625) — Ma–Minda general FS structure |
| sigmoid | fekete_szego_mu0.5 | 1/4 | 1e-06 | A+B | = max(tail 0.25, face 0) — Ma–Minda general FS structure |
| sigmoid | fekete_szego_mu0.75 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.0625) — Ma–Minda general FS structure |
| sigmoid | fekete_szego_mu0 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.125) — Ma–Minda general FS structure |
| sigmoid | fekete_szego_mu1 | 1/4 | 1e-06 | A+B | = max(tail 0.25, face 0.125) — Ma–Minda general FS structure |
| sigmoid | fekete_szego_mu2 | 3/8 | 1e-06 | A | = max(tail 0.25, face 0.375) — Ma–Minda general FS structure |
| sigmoid | hankel2_2 | 1/16 | 0.01 | B+D | MATCH: follows from Lee et al. 2013 general B1^2/4 |
| sine | fekete_szego_mu0.25 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| sine | fekete_szego_mu0.5 | 1/2 | 1e-06 | A+B | = max(tail 0.5, face 0) — Ma–Minda general FS structure |
| sine | fekete_szego_mu0.75 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| sine | fekete_szego_mu0 | 1/2 | 0 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| sine | fekete_szego_mu1 | 1/2 | 0 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| sine | fekete_szego_mu2 | 3/2 | 1e-06 | A | = max(tail 0.5, face 1.5) — Ma–Minda general FS structure |
| starlike | fekete_szego_mu0.25 | 2 | 1e-06 | A | = max(tail 1, face 2) — Ma–Minda general FS structure |
| starlike | fekete_szego_mu0.5 | 1 | 0 | A | = max(tail 1, face 1) — Ma–Minda general FS structure |
| starlike | fekete_szego_mu0.75 | 1 | 1e-06 | A | = max(tail 1, face 0) — Ma–Minda general FS structure |
| starlike | fekete_szego_mu0 | 3 | 1e-06 | A | = max(tail 1, face 3) — Ma–Minda general FS structure |
| starlike | fekete_szego_mu1 | 1 | 0.0001 | A | = max(tail 1, face 1) — Ma–Minda general FS structure |
| starlike | fekete_szego_mu2 | 5 | 1e-06 | A | = max(tail 1, face 5) — Ma–Minda general FS structure |
| strip_arctan | fekete_szego_mu0.25 | 1/2 | 1e-07 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| strip_arctan | fekete_szego_mu0.5 | 1/2 | 1e-07 | A | = max(tail 0.5, face 0) — Ma–Minda general FS structure |
| strip_arctan | fekete_szego_mu0.75 | 1/2 | 1e-07 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| strip_arctan | fekete_szego_mu0 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| strip_arctan | fekete_szego_mu1 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| strip_arctan | fekete_szego_mu2 | 3/2 | 1e-07 | A | = max(tail 0.5, face 1.5) — Ma–Minda general FS structure |
| strongly_0.25 | fekete_szego_mu0.25 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.125) — Ma–Minda general FS structure |
| strongly_0.25 | fekete_szego_mu0.5 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.0625) — Ma–Minda general FS structure |
| strongly_0.25 | fekete_szego_mu0.75 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0) — Ma–Minda general FS structure |
| strongly_0.25 | fekete_szego_mu0 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.1875) — Ma–Minda general FS structure |
| strongly_0.25 | fekete_szego_mu1 | 1/4 | 1e-06 | A | = max(tail 0.25, face 0.0625) — Ma–Minda general FS structure |
| strongly_0.25 | fekete_szego_mu2 | 5/16 | 1e-06 | A | = max(tail 0.25, face 0.3125) — Ma–Minda general FS structure |
| strongly_0.25 | hankel2_2 | 1/16 | 0.01 | C+D | slack 0.01 |
| strongly_0.5 | fekete_szego_mu0.25 | 1/2 | 0 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| strongly_0.5 | fekete_szego_mu0.5 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| strongly_0.5 | fekete_szego_mu0.75 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0) — Ma–Minda general FS structure |
| strongly_0.5 | fekete_szego_mu0 | 3/4 | 1e-06 | A | = max(tail 0.5, face 0.75) — Ma–Minda general FS structure |
| strongly_0.5 | fekete_szego_mu1 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| strongly_0.5 | fekete_szego_mu2 | 5/4 | 1e-06 | A | = max(tail 0.5, face 1.25) — Ma–Minda general FS structure |
| strongly_0.75 | fekete_szego_mu0.25 | 9/8 | 1e-06 | A | = max(tail 0.75, face 1.125) — Ma–Minda general FS structure |
| strongly_0.75 | fekete_szego_mu0.5 | 3/4 | 1e-06 | A | = max(tail 0.75, face 0.5625) — Ma–Minda general FS structure |
| strongly_0.75 | fekete_szego_mu0.75 | 3/4 | 1e-06 | A | = max(tail 0.75, face 0) — Ma–Minda general FS structure |
| strongly_0.75 | fekete_szego_mu0 | 27/16 | 1e-06 | A | = max(tail 0.75, face 1.6875) — Ma–Minda general FS structure |
| strongly_0.75 | fekete_szego_mu1 | 3/4 | 1e-06 | A | = max(tail 0.75, face 0.5625) — Ma–Minda general FS structure |
| strongly_0.75 | fekete_szego_mu2 | 45/16 | 1e-06 | A | = max(tail 0.75, face 2.8125) — Ma–Minda general FS structure |
| tanh | fekete_szego_mu0.25 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| tanh | fekete_szego_mu0.5 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0) — Ma–Minda general FS structure |
| tanh | fekete_szego_mu0.75 | 1/2 | 1e-06 | A | = max(tail 0.5, face 0.25) — Ma–Minda general FS structure |
| tanh | fekete_szego_mu0 | 1/2 | 0 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| tanh | fekete_szego_mu1 | 1/2 | 0 | A | = max(tail 0.5, face 0.5) — Ma–Minda general FS structure |
| tanh | fekete_szego_mu2 | 3/2 | 1e-06 | A | = max(tail 0.5, face 1.5) — Ma–Minda general FS structure |
| three_leaf | fekete_szego_mu0.25 | 2/5 | 1e-06 | A | = max(tail 0.4, face 0.16) — Ma–Minda general FS structure |
| three_leaf | fekete_szego_mu0.5 | 2/5 | 1e-06 | A | = max(tail 0.4, face 0) — Ma–Minda general FS structure |
| three_leaf | fekete_szego_mu0.75 | 2/5 | 1e-06 | A | = max(tail 0.4, face 0.16) — Ma–Minda general FS structure |
| three_leaf | fekete_szego_mu0 | 2/5 | 1e-06 | A | = max(tail 0.4, face 0.32) — Ma–Minda general FS structure |
| three_leaf | fekete_szego_mu1 | 2/5 | 1e-06 | A | = max(tail 0.4, face 0.32) — Ma–Minda general FS structure |
| three_leaf | fekete_szego_mu2 | 24/25 | 1e-06 | A | = max(tail 0.4, face 0.96) — Ma–Minda general FS structure |
| three_leaf | hankel2_2 | 1/6 | 0.02 | C+D | slack 0.02 |
Reviewer leads still to check by hand (bibliography pass): Ma & Minda 1994 (general FS); Raina & Sokół 2015 and Paprocki & Sokół 2015 (lemniscate); Cho–Kumar–Kumar–Ravichandran 2019–20 and Madaan–Kumar–Ravichandran 2021 (sine); Sharma–Jain–Ravichandran 2016 and Kumar–Arora 2024 (cardioid); arXiv:2201.05808, arXiv:2208.02975 (H₃(1) context).