Pure point Dirichlet spectrum on quasi-conical domains

For every integer dimension at least two, this note constructs some connected open quasi-conical tower whose form-defined Dirichlet Laplacian has a complete orthonormal eigenbasis, spectrum and essential spectrum equal to the nonnegative half-line, dense positive eigenvalues, no zero eigenfunction, and no absolutely or singular continuous spectral subspace. Both expanding cube widths and positive shrinking windows are chosen inductively. The windows are openings in zero-thickness interface screens. No arbitrary preassigned-width, smooth-boundary, Neumann, positive-length passage or effective numerical aperture theorem is asserted. The result answers the precise existential spectral-type question in Krejcirik and Lotoreichik, Bulletin of the London Mathematical Society 56 (2024), Sections 2.2, 3 and 5, and the corresponding Oberwolfach contribution (OWR-14297736-021). Their geometry, freedom of future cube sizes and finite-window convergence are substantive antecedents. Whole spectral families and multiplicity control are credited to Hempel, Seco and Simon (1991), Proposition 1.4, and the warning in KL Remark 3.1. The additional construction exhaustively transports complete finite spectral clusters with summable norm errors. Repeated dense probes prove basis completeness. No new abstract finite-rank diagonalization principle is claimed. Bounded primary-source, author/citation and direct Zenodo searches located no full matching predecessor; historical first priority and current worldwide openness are not certified. Some older full bodies, a restricted finite-dimensional gap-note body, and unindexed or nonpublic work remain outside the comparison. The companion source archive preserves all 39 frozen candidate files, distinct geometric and spectral audits, an explicitly superseding source-reading correction, priority searches and a fresh priority challenge. Offline checks reproduce integrity and finite diagnostics; they do not formally certify the PDE theorem or exhaustive priority. AI tools were used extensively in development, writing, reproduction, verification and adversarial review. This is an unrefereed preprint without external human peer review or proof-assistant certification. The note and authored companion material are CC BY 4.0.