The Twelve-Component Computational Apparatus of BSB Cgm 7958 (Hartlieb, Bavaria 1456) as Comparator-Lens for the Voynich Manuscript

We propose Bayerische Staatsbibliothek, München, Cgm 7958, a fifteenth-century Bavarian compilation in the Johannes Hartlieb stylistic tradition, date-locked to 1456 by a four-way computus colophon, as a primary-source-verified comparator-lens for the structural apparatus of Yale, Beinecke MS 408. Twelve apparatus components A–L are catalogued against the BSB digital facsimile, composed of nine folio-pinned components (C, D, E, G, H, I, J, K, L), each anchored to a specific folio surface with verbatim Bavarian Middle High German prose, and three umbrella categories (A, B, F) that name engine-level structures spanning multiple folios: a letter grid (A, umbrella), mod-9 / mod-19 / mod-28 / mod-30 arithmetic (B, umbrella, operations performed on other components), a weekday-value circle (C, fol. 16r), a nine-Capitel sum-lookup pair-result table (D, fols. 16v–18r), a four-quadrant outcome wheel (E, fol. 14r), an Aristoteles–Plato–Halij–Hartlieb on-page authority chain (F, umbrella, anchored at fol. 21v inside the broader Pythagoras–Ptolomeus–Plato–Aristotiles–Halij tradition cross-witnessed at Chart.A.558), a twenty-eight-mansiones-lunae table (G, fol. 2v), a planetary value-plus-colour table (H, fol. 20v), a twenty-five-row multi-exotic-alphabet inventory (I, fols. 22r–23v), a Latin sign-legend (J, fol. 23v), an iconographic legend (K, fol. 24r), and the dated sanctorale-plus-computus colophon (L, fols. 24v–25v). All nine folio-pinned components are verified against primary-source facsimile, with per-component completion gaps (component G 27/28 names, component J 8/10 entries, component K partial transcription) noted in the twelve-components section and listed as substrate-attested next moves in the implications and open frontier section. Five cross-witnesses (Gotha Chart.A.558, Heidelberg Cpg 3, Cpg 5, Cpg 65, Cpg 6) corroborate the apparatus at component level and place the tradition inside the MS 408 carbon-date window 1404–1438. The reading is comparator-lens, not identity claim: the known apparatus is the lens, the open manuscript is the target, and a substrate-anchored differentiator method scores residual asymmetries against shared baseline. The named readings in the falsification matrix fail one or more tests recorded in this paper; this bounded result does not claim exhaustive refutation of every historical proposal. The comparator-lens reading is advanced as the substrate-anchored frame the paper defends. An independent 2026 statistical study by Layfield and Davis finds sequence-sensitive and section-sensitive distributional structure under its LSA design. That text-channel result is adjacent to, not confirmation of, this paper's apparatus-channel reading. The paper situates MS 408 as one branch within the Wittelsbach-Burgundian / Salerno-Frederick II / Padua-Prague / Upper-Rhine corridor, not its centre.