RH Classical via No-Phantom Language (Synthesis)

This is the synthesis paper of Volume VI of the HoTT/Yoneda Riemann hypothesis programme. Volume V proved the conditional theorem $\mathtt{RH\_classical\_of\_no\_phantom\_language\_breakthrough}: \mathtt{NoPhantomLanguageBreakthrough} \to \mathrm{RH}$, reducing classical RH to two named payloads: an off-critical defect kernel (Target 1) and a Yoneda/Blaschke detector calculus (Target 2).

Volume VI's proof sprint produced six papers, each shipping a Lean module, four of which terminate at named obstructions because Vol5 ships an opaque $\mathtt{burnolBlaschkeFactor.modelSpaceCarrier}$ with no introduction rule plus three opaque admissibility atoms $\mathtt{BlaschkeDefectDualizable}$, $\mathtt{BlaschkeDefectPolarized}$, and $\mathtt{BlaschkeDefectRegularized}$.

The synthesis delivers: a wrapper around the Vol5 master theorem ($\mathtt{RH\_classical\_new\_language\_of\_payload}$); a substantive parameterised theorem $\mathtt{RH\_classical\_new\_language\_of\_inputs}$; the single canonical residual obstruction $\mathtt{Vol6FinalObstruction}$ collecting exactly the four named introduction-rule fields from Papers 03–06; and the principal theorem $\mathtt{RH\_classical\_new\_language\_of\_obstruction}$, which derives $\mathrm{RH}$ from any inhabitant of $\mathtt{Vol6FinalObstruction}$ together with an explicit non-opaque detector and $\mathbf{D}_\mathbb{Q}\mathrm{Obj}$ witness. $\texttt{\#print axioms RH\_classical\_new\_language\_of\_obstruction}$ is clean of RH, Nyman density, and Beurling–Nyman.