Paper IIINamed Obstructionmath.NT

Off-Critical Zero Defect Kernel (Target 1)

Abstract

We discharge Target 1 of the Vol V conditional theorem RH_classical_of_no_phantom_language_breakthrough\texttt{RH\_classical\_of\_no\_phantom\_language\_breakthrough}: every off-critical zero of the Riemann zeta function produces a nonzero vector in the canonical Burnol/Blaschke defect model space KB=H2/BBurnolH2K_B = H^2 / B_{\mathrm{Burnol}} H^2. The construction lifts the finite-packet kernel-vector theorem of Vol VI Paper 01 to the canonical Burnol/Blaschke factor along a Möbius transport sα(s)=(s1)/(s+1)s \mapsto \alpha(s) = (s-1)/(s+1) and a singleton Blaschke packet Ps={α(s)}P_s = \{\alpha(s)\}.

The transport step does not close. The upstream surface declares the carrier burnolBlaschkeFactor.modelSpaceCarrier\texttt{burnolBlaschkeFactor.modelSpaceCarrier} via an opaque axiom and gives no introduction rule, no injection, and no identification. The paper therefore (i) closes every step of the pipeline that does not depend on the transport; (ii) states the precise typed proposition OffCriticalDefectKernelBridge\texttt{OffCriticalDefectKernelBridge} that upgrades the conditional principal theorem off_critical_zero_defect_kernel_of_bridge\texttt{off\_critical\_zero\_defect\_kernel\_of\_bridge} to an unconditional one; and (iii) ships Vol6.Obstruction.OffCriticalDefectKernelObstruction\texttt{Vol6.Obstruction.OffCriticalDefectKernelObstruction}, a Lean module recording the exact content of the missing bridge. The Haskell artifact exhibits the singleton kernel-vector construction numerically at the test point s=0.6+14is = 0.6 + 14i.

Artifacts

Lean 4 Module
Vol6.OffCriticalDefectKernel
View on GitHub →
Haskell Numeric Artifact
haskell/paper-03-off-critical-defect-kernel/Main.hs
View on GitHub →
Obstruction Module
Vol6.Obstruction.OffCriticalDefectKernelObstruction
View on GitHub →

Status & Obstructions

Named Obstruction Present
Named obstruction: OffCriticalDefectKernelBridge (Vol5 opaque)

The principal theorem is conditional on inhabiting the named obstruction type. The obstruction module precisely characterizes the missing Vol5 introduction rule. No new sorry, admit, axiom, or opaque is introduced in Vol6.