Divergence With Oscillation, and the Other Powers: The Last Uncomputed Species of the Tolman Ledger, Computed — and the Provenance Prices Stand

Works register item D-202-219-61 (paper #216's Tolman entropy ledger, grade C) at its Wave 20 shape -- a specific, non-generic one-law attractor with provenanced constants AND a provenanced orbit invariant, eta_B named (convertibility factor 7.041), outputting about 11.5 billion units per baryon -- and reports an honest non-closure, narrowed to provenance alone, at INCREMENTAL grade; neither of the crew's two items is closed. No provenanced attractor is exhibited and none is counterfeited: the packet prints why the outside species the predecessors' searches left standing (baryogenesis-style production of eta_B) imports the ledger through the factor 7.041 by construction. What is computed is the residue's two remaining printed-as-uncomputed clauses. (1) Coupling species combining divergence with oscillation at the limit state, G = X^3 (1.5 + sin(1/u))/u and G = X^3 (1.5 + sin(1/u))/sqrt(u): at power 3 both evade under the bisection predecessor solver (unnamed floors 0.976491 and 0.969386, rise-sums 0.023831 and 0.031151), while the fixed-point predecessor solver produces no orbit at all for the /u species (its iterates leave the species' domain) and a different evading floor for the /sqrt(u) species (0.750266, rise-sum 0.290503) -- the implicit step equation is non-monotone in the predecessor variable, so the approached floor is selected jointly by orbit and solver branch, where a branch exists; at power 1 both cross the named floor (steps 32 and 21) with the extra variable already collapsed (X = 0.000138 and 0.001744). The joint price p > gamma - 1 is now invariant across the coupling factor's complete census, in combination as well as singly. (2) Zero-limit branches whose coefficient couples to the entropy with other powers, B = X S^r at beta = 1.4 for r = 1/2 and r = 2 beside the gated r = 1: the self-referential threshold is closed-form, e = 1/(2 (beta - 1 + r)) -- predictions written before the runs (r = 1/2: 0.555556; r = 2: 0.208333; r = 1 recovers 5/14) measured at 0.555 and 0.208, past sums 2884.8962 and 30346.5501, both diverging. After this packet no clause of the item stands printed as uncomputed; its content is provenance, twice over (the attractor's constants; the closure orbit's invariant). No constant was fixed by consulting s/n_B; eta_B named. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.