Cross-Corpus Geometric Concordance

Bidirectional concordance mapping propositions and constructions in Johannes Kepler's Mysterium Cosmographicum (1596/1621), Strena seu de Nive Sexangula (1611), and Harmonices Mundi (1619) to sister repositories across the GEOMETOR canon and exact symbolic verifiers in geometor.kepler.

Kepler Cross-Corpus Concordance

Kepler Locus	Geometric Proposition / Invariant	Sister GEOMETOR Canon	Symbolic Verifier (geometor.kepler)
Mysterium Praefatio (1596, pp. 6–10)	July 19, 1595 Graz Great-Conjunction equilateral triangle ($r_{\text{in}} / R_{\text{out}} = 1/2$, $Q = 1/4$) & square ($Q = 1/2$)	euclid / elements IV.2–5, XIII.12	mysterium_spheres.construct_mysterium_planar_nesting
Mysterium Cap. II & XIV (1596, pp. 22–26, 46–49)	Curved vs. Straight (Cusanus); 5 Platonic solids nested between 6 Copernican orbs (Terra = 1)	euclid / elements XIII.13–18; proclus Prologue	mysterium_spheres.compute_nested_planetary_radii
Mysterium Cap. XII–XIII (1596, pp. 41–45)	Two Great Treasures ([I.47] & [II.11]); polar-duality equality ($Q_{\text{Cube}} = Q_{\text{Oct}} = \frac{1}{3}$, $Q_{\text{Dod}} = Q_{\text{Ico}} = \frac{5+2\sqrt{5}}{15}$)	divine / pacioli / wildberger quadrance	mysterium_spheres.verify_polar_duality_ratios
Epistola ad Mästlinum (Oct 1597; Frisch I, p. 377)	Kepler Right Triangle $(1, \sqrt{\phi}, \phi)$ with $Q_a : Q_b : Q_c = 1 : \phi : \phi^2$ and Mästlin’s $1/\phi \approx 0.6180340$	model get_kepler_field ($\mathbb{Q}(\sqrt{\phi})$); elements II.11, VI.13	harmonices_geometry.construct_kepler_right_triangle
Strena §§1–9 (1611, pp. 3–11)	Sixfold snow crystals, bee honeycomb trihedra, Rhombic Dodecahedron ($\sqrt{2}:1$, $120^\circ$) & Rhombic Triacontahedron ($\phi:1$, $144^\circ$)	pappus Synagoge V.1–3; pacioli rhombic solids	strena_packing.analyze_rhombic_dodecahedron & analyze_rhombic_triacontahedron
Strena §§10–14 (1611, pp. 11–15)	Planar 7-circle rosette (kissing 6) & 3D FCC/HCP Kepler Sphere-Packing Conjecture (kissing 12, $\frac{\pi}{3\sqrt{2}}$)	fundamentals 6-circle rosette; phyllotaxis packing	strena_packing.verify_kepler_sphere_packing & construct_hexagonal_rosette
Strena §§15–19 (1611, pp. 15–19)	Pentamerous blossoms & self-propagating Fibonacci recurrence $1, 1, 2, 3, 5, 8, 13, 21 \to \phi$ (Cassini $(-1)^n$)	phyllotaxis parastichy lattices; divine	strena_packing.compute_fibonacci_phyllotaxis
Harmonices Mundi I, Defs./Props. I–XLIV	Refutation of Ramus on Book X; eight degrees of scibilitas for constructible $n$-gons ($3,4,5,6,8,10,12,15,16$)	euclid IV.10–16, X, XIII.1–11; proclus; hoenen	harmonices_geometry.classify_polygon_scibilitas
Harmonices Mundi I, Props. XLV–L	Inscibilitas of the Regular Heptagon ($x^3 + x^2 - 2x - 1 = 0$) & Bürgi's cossic sextic ($y^6 - 7y^4 + 14y^2 - 7 = 0$)	hilbert quadratic field towers	harmonices_geometry.verify_heptagon_cubic_obstruction
Harmonices Mundi II, Props. I–XXVIII	Complete 11 uniform Archimedean planar tilings, star congruence Figure Aa, 13 Archimedean solids, & stellated dodecahedra	pappus Synagoge V.19; divine star pentagram	harmonices_geometry.enumerate_archimedean_planar_tilings
Harmonices Mundi V, Cap. I, III–IX	Aphelion/perihelion consonances ($4:5, 5:6, 2:3, 15:16, 24:25, 5:12$) & Kepler’s Third Law $(T_1/T_2)^2 = (a_1/a_2)^3$	ptolemy Harmonics; wildberger rational laws	harmonices_geometry.verify_kepler_third_law