The 7-Layer GEOMETOR Architecture & 11 Blueprints from codes

How do 33 repositories—ranging from polytonic Greek treatises of Aristotle and Proclus to four-color plates of Oliver Byrne, 53,000 triangle centers of Clark Kimberling, Rational Trigonometry of Norman J. Wildberger, botanical phyllotaxis, and multi-agent program synthesis (seer)—cohere into a single architecture?

Our audit organizes the entire GEOMETOR workspace into seven epistemic and computational layers, placing geometor/codes at Layer 2 as the translational bridge between the primary historical canon (Layers 0–1) and the executable symbolic software stack (Layers 3–6).

( A B ) (Q = 1) ( B A ) (Q = 1) ( A D ) (Q = 4) ( B C ) (Q = 4) [ A B ] [ E F ] / E F / (Q = 3) / F J / (Q = 9/2 - 3*sqrt(5)/2) / I E / (Q = 9/2 - 3*sqrt(5)/2) A = [0, 0] B = [1, 0] C = [-1, 0] D = [2, 0] F = [1/2, sqrt(3)/2] E = [1/2, -sqrt(3)/2] M = [1/2, 0] J = [1/2, sqrt(15)/2] I = [1/2, -sqrt(15)/2] |EF| / |FJ| = phi, Q ratio = phi^2 Golden Chain / I E F J / in 5 steps! AA BB CC DD FF EE MM JJ II + − ⟲ Lbl Gde

Figure 7 — Just-In-Time Emergence of the Golden Chain from the Two-Point Seed (A, B, poles F and E, bisector EF, midpoint M, and golden section points J and I on EF satisfying \(Q(E, J)/Q(E, F) = \phi^2\)). Whereas LeanEuclid, GeoCoq, mathlib4, AlphaGeometry, and Newclid omit the golden ratio altogether, GEOMETOR unfolds exact \(\mathbb{Q}(\phi, \sqrt{3})\) harmonics in five elementary compass steps from (A, B).

The Seven Layers of GEOMETOR (33 Repositories)

Layer 0 — Noetic & Epistemological Grounding (6 Repos)

Establishes what a geometric object is, how universal necessity is intuited in the concrete constructed diagram (abstractio formalis intuitiva), and how axiom groups factor independently:

  • aristotle — Synchronized Bekker Greek and Oxford English Book Codex of Posterior Analytics, Physics, Metaphysics (\(\Theta.9\) diagram actualization), and De Anima.

  • proclus — Multi-track Book Codex and Friedlein concordance of Proclus’s Commentary on Book I, codifying the 6-part proposition anatomy (protasis \(\to\) symperasma) mirrored in LeanEuclid, defs.txt, and @proposition.

  • aquinas — Bilingual Latin/English Book Codex on materia intelligibilis and resolutio ad phantasmata.

  • hoenen — Bilingual Book Codex of De Noetica Geometriae (Hoenen1954), grounding diagrammatic necessity in System E and geometor.model selectors.

  • hilbert — Bilingual German/English Book Codex of Grundlagen der Geometrie (Hilbert1899), linked directly to GeoCoq’s hilbert_axioms.v <-> tarski_axioms.v equivalence proofs.

  • bertrand-russell — Scholarly Book Codex of Foundations of Geometry (1897) and Principles of Mathematics Part VI (1903), connecting relational space to mathlib4 torsors and CindyJS Cayley–Klein polarity.

Layer 1 — Primary Classical & Constructive Scriptorium (8 Repos)

Folio-verified multi-track Book Codices (:layout: book) with calibrated .euclid-graphic SVGs and strict content/code separation (zero embedded Python scripts):

  • euclid — Folio-verified 3-volume Heath Edition of Euclid’s Elements (Books I–XIII, 831 calibrated SVGs).

  • byrne — Visual-symbolic Book Codex of Oliver Byrne’s 1847 Coloured Euclid (Books I–VI), pairing four-color pointer-free glyph pseudocode with interactive SVG illumination.

  • archimedes — Scholarly Book Codex of Heath’s Works of Archimedes (exhaustion, spirals, The Method).

  • apollonius — Scholarly Book Codex of Heath’s Treatise on Conic Sections (symptomata, conjugate diameters, pole–polar).

  • pacioli — Multi-track Italian/English/German facsimile codex of De Divina Proportione (1509) with Leonardo’s polyhedral plates.

  • kepler — Scholarly Book Codex of Harmonices Mundi (Books I–II & V) on constructible polygons, star tilings, and \(\mathbb{Q}(\phi)\).

  • lemoine — Bilingual French/English Book Codex of La Géométrographie (Lemoine1902), supplying operational ruler-and-compass complexity (\(R_1, R_2, C_1, C_2, C_3\)).

  • altshiller-court — Two-track Book Codex of College Geometry (1952), anchoring Domain 4 (circle power, coaxial pencils, inversion, poles/polars).

Layer 2 — Comparative Formal Languages & Symbolic Meta-Study (1 Repo)

  • codes (this repository) — Source-level audit of 11 formal, visual, and symbolic geometry architectures, 60-symbol syntax decoder, 69-topic Opus coverage matrix, and 7 Rosetta Stone benchmarks.

Layer 3 — Exact Symbolic Kernel & Visual Workbench (3 Repos)

  • model — Core 100% exact SymPy geometric kernel: Model(..., auto_intersect=False), closed-form radical-axis intersections, ANP algebraic fields, topological selectors, Rational Trigonometry invariants, and @proposition proofs.

  • explorer — Interactive web-based SVG visualization workbench and theme-adaptive .euclid-graphic renderer.

  • trees — Constructive dependency DAG and proof-hypergraph analysis.

Layer 4 — Canonical Constructive & Algebraic Standard Libraries (6 Repos)

  • elements — Executable dependency DAG, .. signature:: / .. step:: pseudocode, and exact constructions evolving into Function-First Principles of Geometry.

  • fundamentals — Elementary compass-and-straightedge unfolding from the two-point seed (A, B).

  • wildberger — Rational Trigonometry (Divine Proportions) formalized via exact polynomial quadrance \(Q\), spread \(s\), and Chromogeometry.

  • etc — Semantic index and symbolic constructor (CenterSymbolicRegistry) for Kimberling’s Encyclopedia of Triangle Centers (X(1)–X(53144)).

  • pappus — Projective geometry library: Pappus Book VII, Desargues, Steiner, harmonic conjugates, cross-ratios, \(\mathbb{Q}(\phi)\) projectivity, and Pascal’s Hexagrammum Mysticum.

  • divine — Automated discovery engine scanning symbolic models for golden sections (\(\phi\)), harmonic ranges, and algebraic proportion chains.

Layer 5 — Natural Morphology, Cosmogony & Machine Reasoning (6 Repos)

  • phyllotaxis — Golden-angle divergence, parastichy lattices, and Fibonacci planar packing.

  • thompson — Scholarly Book Codex of D’Arcy Thompson’s On Growth and Form (1917) on conformal and projective grid transformations.

  • walter-russell — Digital Book Codex of Walter and Lao Russell’s Home Study Course with parametric 2D plates and 3D wave-field models.

  • seer, seer_navigator, seer_sessions — Multi-agent neuro-symbolic Python program-synthesis engine, Textual TUI inspector, and 8,500-trial empirical archive.

Layer 6 — Portal & Platform Infrastructure (3 Repos)

  • geometor.com, .config, .github — Unified cross-corpus portal, canonical engineering standards (STANDARDS.md), agent skills (geometor-construct), and Python 3.13 CI/CD workflows.

Eleven Actionable Engineering Blueprints Flowing from codes

Every external system audited in codes contributes a specific, high-leverage upgrade to GEOMETOR:

  1. Constructive BFMSS Root-Separation Bounds in ``geometor.model.algebra.zero_test`` (Priority 1 — inspired by GeoCoq, Mathlib4, CindyJS): Currently, algebra.zero_test (lines 247-251) falls back to abs(expr.evalf(80)) < 1e-65 when count_ops(expr) > 25 to avoid exponential primitive_element blowup. Replacing that heuristic threshold with constructive Burnikel–Fleischer–Mehlhorn–Schirra (BFMSS) algebraic degree/mahler-measure separation bounds turns evalf(N) into a 100% mathematically sound zero certificate at arbitrary DAG depth.

  2. Persist Selector ASTs on ``Step`` & Emit ``LeanEuclid`` System E Proofs (Priority 2 — inspired by LeanEuclid): Because geometor.model.intersect’s five selectors (side_of, between, beyond, on_ray, other_than) map 1-to-1 onto LeanEuclid/SystemE/Theory/Constructions/Intersections.lean, storing the structured selector tuple on Step.primitive enables a direct to_leaneuclid(model) transpiler.

  3. Lemoine Géométrographie Complexity Telemetry (:math:`R_1, R_2, C_1, C_2, C_3`) (Priority 3 — inspired by Lemoine & AlphaGeometry): Zero surveyed external systems track Émile Lemoine’s operational ruler-and-compass cost. Instrumenting Model.construct_line (\(2 R_1 + R_2\)) and Model.construct_circle (\(C_1 + C_2 + C_3\) or \(2 C_1 + C_3\)) computes Simplicity \(S\) and Exactitude \(E\) automatically on every Model.

  4. First-Class Circle Power, Radical Axis, Inversion & Pole–Polar Module (Priority 4 — inspired by Mathlib4, 2D CGA, CindyJS, JGEX): Fills sympy.geometry’s and GeoCoq’s largest classical gap via geometor.model.inversion: exact polynomial circle_power, radical_axis (working seamlessly on disjoint circles!), invert_point, invert_line_or_circle, and polar_line.

  5. Exact :math:`3 times 3` Symmetric Conic Matrices & Plücker 5-Point Pencils in ``geometor.pappus`` (Priority 5 — inspired by CindyJS & Apollonius): Shatters sympy.geometry’s axis-aligned Ellipse limitation (and missing Hyperbola) by representing general conics over SymPy rings as \(3 \times 3\) symmetric matrices \(C\) with division-free adjugate duals \(C^\Delta = \operatorname{adj}(C)\), polar \(\ell = C p\), pole \(p = C^\Delta \ell\), and ConicBy5 Plücker pencils.

  6. Complete Coordinate-Free Area-Method Eliminator in ``geometor.wildberger`` (Priority 6 — inspired by JGEX): Finishes what JGEX left disabled in Area.java (PanelProve.java:112-116): backward point elimination over signed_area2 (\(S_{ABC}\)) and pythagoras_diff (\(P_{ABC}\)) producing short, human-readable algebraic proofs with automatic non-degeneracy conditions (NDGs).

  7. Function-First *Principles of Geometry* (`elements` 2.0) & Cross-System Concordance (Priority 7 — inspired by Mathlib4 & AlphaGeometry): Retires opaque G.1–G.601 serial numbers in favor of snake_case construction functions (equidistant_poles, perpendicular_bisector, parallel_line), mathlib4-style conclusion_of_hypothesis theorem names, @earns tags, defs.txt 68-clause completeness, and concordance={...} links.

  8. 100% Exact Symbolic ``DD + Quadrance/Spread AR`` Closure Engine for ``seer`` (Priority 8 — inspired by AlphaGeometry & Newclid): Replaces AlphaGeometry’s buggy rconst log-table and float64 guards with an exact symbolic Horn-clause + sparse rational Gaussian AR engine over geometor.model quadrances, spreads, and signed areas.

  9. Arbitrary-Precision ``mpmath.pslq`` Minimal-Polynomial Conjecture Scout in ``divine`` (Priority 9 — inspired by CindyJS `PSLQ.js`): Extends CindyJS’s quadratic (n=3) float guess(x) to arbitrary algebraic degree \(d\) using 100-digit mpmath.pslq, immediately certifying candidate golden/cyclotomic relations in QQ.algebraic_field.

  10. Upstream ``sympy.geometry`` Bug-Fix Pull Requests (Priority 10 — audited in `sympy 1.14.0`): Fixes the live missing-parentheses + wrong-vertex bug in Triangle.excenters (polygon.py:2714-2726) and the 2-digit float collinearity bug in Point.affine_rank (point.py:331-335).

  11. Dual Symbolic-Chromatic ``:g:`` Micro-Glyph Mode in ``photon-platform/publish`` (Priority 11 — inspired by Byrne 1847 & Rougeux 2018): Optionally renders inline 14px SVG stroke/wedge/polygon badges beside :g: tokens, uniting classical symbolic identifier precision with Oliver Byrne’s zero-dereference visual pseudocode.