NEW exact value: M_4 is the largest real root of 50756 x^4 - 407541 x^3 + 1150767 x^2 - 1381455 x + 601425 (irreducible over Q), M_4 = 3.4834502194470... Equivalently Lambda_4 = 2 M_4 - 1 is the root of 25378 x^4 - 306029 x^3 + 1231179 x^2 - 2043863 x + 1204951, Lambda_4 = 5.9669004388941... The exact value is certified by resultant elimination of the critical equations over the reflection-symmetric family (the degree-8 eliminant equals the square of this quartic); global optimality over the full non-symmetric parameter space is confirmed numerically (exhaustive multistart agreeing to >=12 digits) but not yet by a symbolic proof.
Evidence
Provenance
Reviews
50756-quartic for M_4 independently re-derived; global optimality honestly scoped as numerical; reflection-symmetric family = two-conjugate-pair subfamily.
Referee-commissioned independent blind review (Fable-5). Generative-layer disjoint: the new exact minimal polynomials for M_3 (208-cubic) and M_4 (50756-quartic) RE-DERIVED by an own symbolic elimination (different path), M_5 to 30 digits, global optima confirmed by own full-space search. 6/7 claims fully supported with honest scoping. Fable lean: GREEN (borderline) on the MATH -- the new exact values are genuinely novel. The one blemish (00e8190d) is the limit-novelty framing superseded by 1988 BGM. Referee note: this is part of the Holland NOVELTY re-check -- the exact values are the novel residual; the limit-existence framing is not. Downgrade to amber if the venue weighs the pre-amendment novelty slip; final CALL pending.