Cross-Corpus Concordance

Mapping geometor/staudt Across the GEOMETOR Digital Scriptorium & Constructive Canon

This concordance synchronizes the 15 canonical loci of resources/staudt/concordance.json across von Staudt’s Geometrie der Lage (1847), Beiträge zur Geometrie der Lage (1857), and Pasch’s Vorlesungen über neuere Geometrie (1882) with euclid, elements, pappus, hilbert, bertrand-russell, hoenen, altshiller-court, lemoine, divine, and codes.

Master Concordance Table (15 Canonical Loci)

ID	Source Locus	Codex Unit & API	Sister Repositories	Deductive & Algebraic Role
staudt-01	Staudt 1847 Vorwort & § 1 (arts. 1–15)	Codex I Unit 1 · assert_straightedge_only	euclid Book I Post. 1–2; hilbert § 2 Group I; lemoine S = R	Pure incidence foundation; complete exclusion of compass circles and metric ratios.
staudt-02	Staudt 1847 §§ 2–5 (arts. 16–53)	Codex I Unit 1 · construct_parallel_straightedge	euclid I.27–I.31; pappus ideal_elements; hilbert § 4 Group III	Ideal points/lines via parallel sheaves and three-dimensional reciprocity.
staudt-03	Staudt 1847 § 6 (arts. 66–74)	Codex I Unit 2 · construct_harmonic_fourth_straightedge	pappus VII.129–131; altshiller-court Ch. VI; bertrand-russell 1897 § 114	Pure straightedge complete quadrangle definition of $(A, B; C, D) = -1$ and 3D uniqueness proof.
staudt-04	Staudt 1847 §§ 7–8 (arts. 75–98)	Codex I Unit 2 · verify_quadrangle_independence	pappus VII.139; hilbert Kap. V (Desargues); bertrand-russell 1903 Ch. XLV	Harmonic preservation defines projectivity; Fundamental Theorem of Projective Geometry.
staudt-05	Staudt 1847 § 9 (arts. 103–115)	Codex I Unit 3 · pair_separates	pappus involution lemmas; altshiller-court Ch. IX (Involution)	Hyperbolic vs. elliptic involutions; double points as harmonic conjugates of every pair.
staudt-06	Staudt 1847 §§ 18–19 (arts. 235–257)	Codex I Unit 3 · unit3_polar_conic_self_conjugate.svg	pappus Pascal/Brianchon; hilbert Kap. VI; altshiller-court Poles & Polars	Order curve defined as self-conjugate locus $P \in \pi(P)$ of a polar system.
staudt-07	Staudt 1857 Heft 2, § 19 (arts. 256–267)	Codex I Unit 4 · construct_von_staudt_addition	hilbert § 15 segment addition; codes projective arithmetic	Straightedge addition $S = X + Y$ fixing $P_\infty$ via parabolic double perspectivity.
staudt-08	Staudt 1857 Heft 2, § 20 (arts. 268–269)	Codex I Unit 4 · construct_von_staudt_multiplication	pappus VII.139 (commutativity); hilbert §§ 15–16; euclid VI.12	Straightedge multiplication $P = X \cdot Y$ fixing $P_0, P_\infty$; commutative iff Pappus holds.
staudt-09	Staudt 1857 Heft 2, § 29 (arts. 403–404)	Codex I Unit 4 · construct_harmonic_scale, projective_abscissa	bertrand-russell 1897 §§ 118–124; hilbert § 17 coordinates	Harmonic scale (Möbius net) and intrinsic projective abscissae without distance.
staudt-10	Staudt 1857 §§ 19–20 over $\mathbb{Q}(\phi)$	Codex I Unit 4 · verify_golden_throw_identity	divine golden section; euclid II.11 & VI.30; pappus $\mathbb{Q}(\phi)$ ranges	Exact straightedge verification that $P_\phi \cdot P_\phi = P_\phi + P_1$ on any projective carrier.
pasch-01	Pasch 1882 Vorwort, Einleitung, § 1 (pp. 1–17)	Codex II Unit 1 · is_between	hilbert § 3 Axioms II 1–3; bertrand-russell 1903 Ch. XLVI; hoenen Cap. IV	Eight nuclear axioms (Grundsätze I–VIII) of open linear betweenness.
pasch-02	Pasch 1882 § 2 IV. Grundsatz (p. 21) & 10. Lehrsatz (p. 25)	Codex II Unit 2 · demonstrate_pasch_axiom	hilbert § 3 Axiom II 4; hoenen Cap. IV; bertrand-russell 1903 § 378	Pasch's Planar Separation Axiom: triangle entry implies unique opposite-side exit.
pasch-03	Pasch 1882 § 2 applied to Euclid I.16	Codex II Unit 2 · demonstrate_euclid_i16_pasch_gap	euclid Book I Prop. 16; elements G.16; hilbert Theorem 7	Closes Euclid’s exterior-angle crossbar gap where spherical lines fail open betweenness.
pasch-04	Pasch 1882 § 2 applied to Euclid I.21	Codex II Unit 2 · demonstrate_euclid_i21_pasch_gap	euclid Book I Prop. 21; elements G.21; hilbert § 3 Theorem 5	Deductive proof via $\triangle AMC$ that interior ray $BD$ must exit open side $AC$ at $E$.
pasch-05	Pasch 1882 §§ 8–11 & § 12 (pp. 58–100)	Codex II Unit 2 · verify_source_witnesses	hilbert §§ 1, 9–12; hoenen Cap. IV–V; bertrand-russell 1903 Ch. I	Intrinsic sheaf construction of ideal elements and the Hypothetico-Deductive Manifesto (p. 98).