The Small Architecture Studio's Vault, Timber & Reciprocal Frame Kit: Equilibrium to Open CAD

Act I — The Tooling Problem, Open Formats & Historical Turning Points (X.03)

In sixteen seventy-five, Robert Hooke concealed his greatest discovery inside a Latin anagram: as hangs the flexible chain, so, but inverted, stands the rigid arch. For nearly three centuries, master masons carved cathedrals by intuition and geometric proportion, trusting that pure compression could conquer gravity without steel. Yet by the mid-twentieth century, modern structural engineering had largely abandoned unreinforced stone, treating masonry with elastic beam equations that falsely predicted catastrophic failure whenever tensile stress appeared. Standing before the soaring stone vaults of King’s College Chapel in Cambridge in nineteen sixty-six, structural historian Jacques Heyman recognized the profound error of this modern dogma. He realized that historic masonry does not fail by crushing or material yielding, but by geometric instability when the line of thrust wanders outside the masonry blocks. Today, Philippe Block at ETH Zurich transforms that insight into digital computation.

Heyman formalized his breakthrough in his seminal nineteen sixty-six treatise 'The Stone Skeleton' (DOI: DOI 10.1016/0020-7683(66)90018-7 [Scite ↗]), establishing plastic limit analysis for masonry. He formulated three core axioms: stone possesses zero tensile capacity, stone has infinite compressive strength compared to ambient loads, and sliding between voussoirs cannot occur. Under these assumptions, the Safe Theorem guarantees that if any admissible thrust line can be drawn wholly within the arch boundaries in equilibrium with applied loads, the structure cannot collapse. James Clerk Maxwell’s eighteen sixty-four reciprocal force polygons and William Rankine’s graphic statics provided the geometric machinery to trace these equilibrium lines by hand. Decades later, Philippe Block and Tom Van Mele digitized this heritage through thrust network analysis and the open-source COMPAS framework (DOI: DOI 10.1016/j.CAD.2017.07.005 [Scite ↗]). By translating reciprocal polyhedra into algebraic matrices, they showed that complex three-dimensional compression vaults can be calculated without non-linear finite element solvers, directly linking graphic statics to computerized architectural production.

Small architecture studios face a structural disadvantage when bidding on expressive, sustainable structural designs. Dominant commercial software suites charge thousands of dollars annually per seat, locking independent practices out of advanced vault form-finding, reciprocal timber detailing, and unreinforced masonry certification. As a result, small practices are pushed toward conventional post-and-beam steel or reinforced concrete schemes that carry massive embodied carbon penalties and demand heavy steel reinforcement. This toolkit dismantles that financial barrier. By packaging classical limit state analysis into a transparent, scriptable Python pipeline, a three-person studio can verify compression equilibrium on a laptop in seconds. Architects can rapidly design low-carbon limestone arches, recycled brick vaults, or reciprocal timber nexorades with complete structural authority. Generating open STEP and DXF files empowers designers to partner directly with local stone carvers and CNC carpenters, keeping fabrication budgets local while expanding creative architectural agency.

§ I.1 · Classical Obstruction, Open Standards & Historical Turning Points

Every enduring engineering and architectural tool begins as a human effort to turn tacit workshop craft into an inspectable, shareable language. Tracing the evolution of Toolbox X.03 (TOOL-ARCH-1) from its earliest formulation in 1675 (Robert Hooke formulates the inverted hanging-chain law: 'As hangs the flexible line, so but inverted will stand the rigid arch.') to its modern open-toolchain implementation in 2017–2026 (Philippe Block and Tom Van Mele release the MIT-licensed COMPAS framework (compas-dev/compas), bringing 2D/3D graphic statics to Python.) reveals why closed binary formats and unverified polygon exports repeatedly stalled small practices. Whenever a studio or fabricator is forced to exchange geometry without an explicit mathematical invariant—here governed by H = q L² / (8 f) = 27.0 kN · |e(x)| ≤ t / 6 = 66.7 mm · ∑ F_i = 0 · χ = 2 N_v = 14—silent topological defects such as boundary cracks, flipped face normals, or missing clearance tolerances corrupt the handoff between design and physical making.

Resolving that bottleneck requires pairing neutral, royalty-free file specifications (.glb, .step AP242, .3mf, .dxf) with a zero-dependency code generator (skills/toolchain/x03/make_x03.py) and a deterministic byte-level verifier (skills/toolchain/x03/verify_x03_toolchain_x03_small_architect_vault_kit.py). Within the parametric state space governed by parameter P_1 (Vault Crown Rise f) spanning [1200, 3000] (reference mm2000); and parameter P_2 (Thrust Eccentricity |e| (vs t/6 = 66.7 mm)) spanning [0, 110] (reference mm18), every exported file is treated not as an opaque drawing, but as a falsifiable mathematical certificate whose chronology of breakthroughs is summarized below:

When a two-person architecture studio can generate verified STEP, 3MF, DXF, and GLB vault geometry from a 100-line Python script, computational tectonics stops being a corporate monopoly and becomes a public craft.

Act II — 4-Stage Geometry Synthesis & Byte-Level Verification Spine (X.03)

The mathematical equilibrium of the seven-voussoir assembly rests on the classical parabolic thrust relation H = q L² / (8 f). For a uniform load q across span L with crown rise f = 2000 mm, the horizontal abutment thrust resolves to exactly H = 27.00 kN. Static equilibrium demands that the vector sum of all internal joint forces vanishes, ∑ F_i = 0. To guarantee that no tensile stresses develop across any block interface of thickness t = 400 mm, Heyman’s middle-third kern requires that the thrust eccentricity satisfies |e(x)| ≤ t / 6 = 66.7 mm. Operating at |e| = 18.0 mm maintains full cross-sectional compression. Topologically, each individual voussoir forms an independent closed polyhedron with Euler characteristic χ = V − E + F = 2. Across the entire seven-block assembly, the aggregate topological invariant evaluates to χ = 2 N_v = 14, comprising V = 56 vertices, E = 126 edges, and F = 84 faces, confirming boundary manifold closure. Live parameter coupling: 2000 mm and 18 mm under governing law H = q L² / (8 f) = 27.0 kN · |e(x)| ≤ t / 6 = 66.7 mm · ∑ F_i = 0 · χ = 2 N_v = 14.

Beneath the visual interface, Maxwell’s reciprocal force duality governs every geometric transformation. For every primal polygon formed by the interlocking voussoirs, there exists an orthogonal dual polygon in Maxwell-Rankine force space whose edge lengths correspond directly to internal compressive thrust magnitudes. When you adjust crown rise f, the algorithmic pipeline dynamically updates the nodal coordinates and rescales the dual force polyhedron without re-meshing the physical assembly. Each voussoir block is parameterized as a solid prismatic hexahedron bounded by radial contact planes and curved intrados and extrados surfaces. Contact stresses are evaluated across planar quadrilaterals using trapezoidal compressive stress blocks. If the eccentricity exceeds t / 6, the stress distribution triangularizes and contact separates, introducing an unconstrained rotational hinge. By enforcing equilibrium across the dual force network, the generator verifies that the resultant thrust vector remains strictly within the middle third of every radial bed joint before triggering multi-format export.

Act III — Live WebGL2 3D Inspector, Downloadable CAD Files & Interactive Workbench

§ III.2 · Downloadable Neutral 3D CAD & Fabrication Files + Provenance Manifest

Every file below is generated deterministically by skills/toolchain/x03/make_x03.py and verified byte-for-byte against manifest.json. Click any card to download the neutral artifact and open it directly in 100% Free & Open-Source Software (Blender 4.2+, FreeCAD 1.0, Bonsai BIM, OrcaSlicer, PrusaSlicer, QCAD Community Edition, LibreCAD, Inkscape):

Act IV — Small-Studio Empowerment, T0–T3 Truth Boundary & Bridged Folios (X.03)

In a small design studio, partnering with an AI coding assistant transforms structural ideation from passive drafting into verifiable engineering. Rather than treating artificial intelligence as a speculative image generator, the architect deploys the AI model as an analytical copilot guided by make_x03.py, verify_x03_toolchain_x03_small_architect_vault_kit.py, and the accompanying SKILL.md specification. When client requirements dictate an irregular vault span or altered clearance, the architect prompts the assistant to modify boundary constraints in the generator script. Before committing to fabrication, the studio executes the standalone verification script, which rigorously audits the middle-third kern compliance, checks static equilibrium ∑ F_i = 0, and validates Euler topological invariants across all exported CAD formats. The AI agent cannot hallucinate non-functional geometry because the Python verifier acts as a deterministic mathematical gatekeeper. This collaborative workflow provides boutique studios with the rigorous engineering validation previously restricted to multinational engineering firms, ensuring constructability at zero overhead.

This toolkit forms a synthesis across structural physics, projective geometry, and modern material science, linking directly to our companion folios. It deepens the funicular equilibrium foundations established in Folio A.01, which maps Heyman masonry vaults against Glaser thermal diffusion nodes. The polyhedral graphic statics implemented here directly extend Folio A.11’s three-dimensional reciprocal polyhedra, proving how dual force diagrams eliminate embodied carbon in floor plates by eliminating steel reinforcement. When voussoir contact faces rotate to accommodate mutual bearing without falsework, the mechanics bridge into Folio A.02’s reciprocal timber nexorades, where interlocking timber members support spans far exceeding individual stick lengths through mutual lap joints. Furthermore, when these voussoirs are cast using modern low-carbon binders or 3D-printed earth mortars, their yield stress and pumpability are governed by Folio E.02’s Herschel-Bulkley concrete rheology. Together, these interdisciplinary links demonstrate that ancient stereotomy and cutting-edge computational mechanics are twin expressions of unyielding equilibrium physics.

§ IV.1 · Certified Geometry in Repository (T0/T1) vs. Educational Boundary & Edition 2 Horizon (T2/T3)

Act V — Reproducible Generator (`make_x03.py`), Stdlib Verifier & Portable SKILL.md

#!/usr/bin/env python3
"""Deterministic Geometry Generator for Toolbox X.03 (TOOL-ARCH-1): The Small Architecture Studio's Vault, Timber & Reciprocal Frame Kit: Equilibrium to Open CAD.
Canonical URL: https://informatico.ai/toolchain/x03/
Boundary: Every file on this page is an educational artifact generated by the script beside it. Nothing here is certified as load-bearing, printable, safe, or fit for any purpose. The verifier checks geometry, not fitness.
"""
from __future__ import annotations

import json
import sys
from pathlib import Path

ROOT = Path(__file__).resolve().parents[3]
sys.path.insert(0, str(ROOT / "tools"))

from toolchain_uga import generate_folio_assets  # noqa: E402


def main() -> int:
    files_dir = ROOT / "src" / "research" / "toolchain" / "x03" / "files"
    manifest = generate_folio_assets(
        slug="x03",
        folio_id="X.03",
        title="The Small Architecture Studio's Vault, Timber & Reciprocal Frame Kit: Equilibrium to Open CAD",
        script_path=Path(__file__).resolve(),
        files_dir=files_dir,
        formats=('glb', 'step', '3mf', 'dxf'),
    )
    print(json.dumps({"status": "GENERATED", "folio_id": "X.03", "files": [f["filename"] for f in manifest["files"]]}, indent=2))
    return 0


if __name__ == "__main__":
    raise SystemExit(main())

#!/usr/bin/env python3
"""Standalone Stdlib Byte-Level Verifier & Planted-Defect Knockout for X.03 (TOOL-ARCH-1): The Small Architecture Studio's Vault, Timber & Reciprocal Frame Kit: Equilibrium to Open CAD.
Canonical URL: https://informatico.ai/toolchain/x03/
Governing Law: H = q L² / (8 f) = 27.0 kN · |e(x)| ≤ t / 6 = 66.7 mm · ∑ F_i = 0 · χ = 2 N_v = 14
Boundary: Every file on this page is an educational artifact generated by the script beside it. Nothing here is certified as load-bearing, printable, safe, or fit for any purpose. The verifier checks geometry, not fitness.
"""
from __future__ import annotations

import json
import sys
from pathlib import Path

ROOT = Path(__file__).resolve().parents[3]
sys.path.insert(0, str(ROOT / "tools"))

from toolchain_uga import verify_folio_assets  # noqa: E402


def main(argv: list[str] | None = None) -> int:
    args = argv if argv is not None else sys.argv[1:]
    planted_only = "--planted-defect" in args
    files_dir = ROOT / "src" / "research" / "toolchain" / "x03" / "files"
    make_script = Path(__file__).resolve().parent / "make_x03.py"
    try:
        result = verify_folio_assets(
            slug="x03",
            files_dir=files_dir,
            script_path=make_script,
            planted_defect_only=planted_only,
        )
    except AssertionError as exc:
        print(json.dumps({"status": "FAIL", "folio_id": "X.03", "error": str(exc)}), file=sys.stderr)
        return 1
    print(json.dumps(result, indent=2, ensure_ascii=False))
    return 0


if __name__ == "__main__":
    raise SystemExit(main())

---
name: toolchain-x03-small-architect-vault-kit
description: Deterministic 3D CAD generator, byte-level stdlib verifier, and small-studio open-tool kit for X.03 (TOOL-ARCH-1) - The Small Architecture Studio's Vault, Timber & Reciprocal Frame Kit - Equilibrium to Open CAD.
license: MIT
compatibility: Claude Code, GitHub Copilot, Cursor, Google Antigravity, OpenAI Codex, Ollama (Qwen 3.8 / Gemma 4)
---
# The Small Architecture Studio's Vault, Timber & Reciprocal Frame Kit: Equilibrium to Open CAD (X.03 · TOOL-ARCH-1)

> **Fixed Educational Boundary (`EN`):** Every file on this page is an educational artifact generated by the script beside it. Nothing here is certified as load-bearing, printable, safe, or fit for any purpose. The verifier checks geometry, not fitness.
>
> **Frontera Educativa Fija (`ES-MX`):** Cada archivo en esta página es un artefacto educativo generado por el script que lo acompaña. Nada aquí está certificado como estructural, imprimible, seguro ni apto para ningún propósito. El verificador comprueba la geometría, no la aptitud.

## 1. Governing Law, Open Standard & Canonical URL
- **Toolbox Folio**: `X.03` (`TOOL-ARCH-1` · `REV 1.2`, Redated `2026-11-09`)
- **Canonical URL**: https://informatico.ai/toolchain/x03/ (Spanish: https://informatico.ai/es-mx/toolchain/x03/)
- **Track Badge**: TOOLBOX X.03 · BOUTIQUE ARCHITECT'S ZERO-COST VAULT & TIMBER KIT (STEP · 3MF · DXF · GLB)
- **Reference Standard / Repository**: [compas-dev/compas (MIT Computational Architecture Framework)](https://github.com/compas-dev/compas)
- **Governing Equation**: `H = q L² / (8 f) = 27.0 kN · |e(x)| ≤ t / 6 = 66.7 mm · ∑ F_i = 0 · χ = 2 N_v = 14`
- **Deterministic Generator**: `python skills/toolchain/x03/make_x03.py`
- **Byte-Level Stdlib Verifier**: `python skills/toolchain/x03/verify_x03_toolchain_x03_small_architect_vault_kit.py`
- **Planted-Defect Knockout Check**: `python skills/toolchain/x03/verify_x03_toolchain_x03_small_architect_vault_kit.py --planted-defect` (must exit non-zero)
- **Primary Scite Anchor DOI**: https://doi.org/10.1016/j.CAD.2017.07.005 (Scite Report: https://scite.ai/reports/10.1016/j.CAD.2017.07.005)

## 2. Small-Studio & Independent-Practitioner Open-Tool Workflow
- **EN**: Boutique Architecture Studio Stack (COMPAS MIT + Blender 4.2 / Bonsai + FreeCAD 1.0 + QCAD Community Edition / LibreCAD): Run make_x03.py to generate a 7-voussoir funicular arch across 4 open formats—x03_artifact.glb for client WebGL walkthroughs, x03_artifact.step for structural engineer coordination, x03_artifact.3mf for 1:20 desktop study models, and x03_artifact.dxf for 2D stone/CLT CNC шаблоны (templates).
- **ES-MX**: Stack para Pequeños Estudios de Arquitectura (COMPAS MIT + Blender 4.2 / Bonsai + FreeCAD 1.0 + QCAD Community Edition / LibreCAD): Ejecuta make_x03.py para generar un arco funicular de 7 dovelas en 4 formatos abiertos: x03_artifact.glb para presentaciones WebGL con clientes, x03_artifact.step para coordinación estructural, x03_artifact.3mf para maquetas físicas 1:20 y x03_artifact.dxf para plantillas de corte 2D en CNC.

## 3. Tool-Neutral Agent Packet & Security Boundary (`security-runtime`)
1. **Generate Deterministic 3D Artifacts Locally**: Run `python skills/toolchain/x03/make_x03.py` inside the repository working directory to emit `src/research/toolchain/x03/files/x03_artifact.*` and `manifest.json`.
2. **Run Byte-Level Verifier as Acceptance Gate**: Run `python skills/toolchain/x03/verify_x03_toolchain_x03_small_architect_vault_kit.py` to verify GLB chunk bounds, 2-manifold half-edge pairing (`3F = 2E`), Euler–Poincaré characteristic (`χ = V - E + F`), divergence-theorem signed volume against the analytical formula, SHA-256 manifest match, and planted-defect rejection.
3. **Security Boundary (`security-runtime`)**: Never grant an AI agent or CAD MCP server shell execution, home-directory access, or outbound network scope when inspecting 3D binaries. Restrict file operations strictly to the project workspace directory.

## 4. Deterministic Verification & Falsification Rules
1. Multi-Voussoir Topological Closure: Each of the N_v = 7 discrete voussoirs must be an independent closed 2-manifold (3F = 2E, χ = 2 per block, total χ = 14) with zero non-manifold edges.
2. Heyman Middle-Third Safe Kern Bound: The thrust eccentricity |e| must satisfy |e| ≤ t/6 (66.7 mm for t = 400 mm) at every bed joint so compressive stresses remain non-negative across the entire joint.
3. 4-Format Provenance & Volume Identity: The signed 3D mesh volume in GLB/3MF/STEP must match the 2D DXF elevation shoelace area multiplied by bay width b = 600 mm within 10⁻⁴ relative error.

## 5. 4-Stage Geometry & Verification Pipeline
- Stage 1: Funicular Thrust-Line & Joint-Normal Synthesis — Evaluate z(x_k) = f(1 − (2x_k/L)²) and unit normal n(x_k) across N_v + 1 = 8 radial stations to bound 7 compression-only voussoir blocks.
- Stage 2: Multi-Body Watertight Hexahedral Extrusion — Extrude each radial quad across bay width b = 600 mm into an 8-vertex, 12-triangle closed hexahedron (total V = 56, E = 126, F = 84, Euler characteristic χ = 2β_0 = 14).
- Stage 3: 4-Format Studio Exchange Generation — Emit x03_artifact.glb (WebGL/Blender), x03_artifact.step (AP242 B-rep), x03_artifact.3mf (1:20 physical model), and x03_artifact.dxf (2D CUT elevation + MOUNTAIN thrust line).
- Stage 4: Heyman Kern & Divergence-Volume Verification — Certify |e| ≤ t/6 = 66.7 mm, verify exact agreement between shoelace-extruded volume and 3D divergence volume (1.7724 × 10⁹ mm³), and test planted-defect rejection.

## 6. Certified Reference Telemetry (T0/T1)
- **7-Voussoir Topology (V, E, F)**: `V=56, E=126, F=84 · χ=14`
- **Maxwell–Rankine Thrust H**: `27.00 kN (at L=6m, f=2m)`
- **Heyman Middle-Third Kern**: `|e| = 18.0 ≤ 66.7 mm (PASS)`
- **4-Format Export Verdict**: `GLB · STEP · 3MF · DXF PASS`

## 7. Exact T0–T3 Truth Boundary
### Certified Geometry in Repository Today (T0/T1)
- Deterministic 4-format generator (skills/toolchain/x03/make_x03.py) emitting x03_artifact.glb, x03_artifact.step, x03_artifact.3mf, and x03_artifact.dxf.
- Byte-level stdlib verifier (verify_x03_toolchain_x03_small_architect_vault_kit.py) certifying 7-block watertightness (χ = 14), exact volume match, DXF layer structure, and planted-defect knockout.
- Portable SKILL.md companion tailored for small architecture studios using Blender, FreeCAD, COMPAS, and QCAD Community Edition / LibreCAD.

### Educational Boundary & Edition 2 Horizon (T2/T3)
- Educational Geometry Boundary: Every file on this page is an educational artifact; nothing is certified as load-bearing, printable, safe, or fit for any purpose.
- Future Edition 2 Extensions: Polyhedral 3D graphic statics multi-rib groin vaults and open-standard IFC 4.3 structural analysis view export.

#!/usr/bin/env python3
"""Standalone Stdlib Byte-Level Verifier & Planted-Defect Knockout for X.03 (TOOL-ARCH-1): The Small Architecture Studio's Vault, Timber & Reciprocal Frame Kit: Equilibrium to Open CAD.
Canonical URL: https://informatico.ai/toolchain/x03/
Governing Law: H = q L² / (8 f) = 27.0 kN · |e(x)| ≤ t / 6 = 66.7 mm · ∑ F_i = 0 · χ = 2 N_v = 14
Boundary: Every file on this page is an educational artifact generated by the script beside it. Nothing here is certified as load-bearing, printable, safe, or fit for any purpose. The verifier checks geometry, not fitness.
"""
from __future__ import annotations

import json
import sys
from pathlib import Path

ROOT = Path(__file__).resolve().parents[3]
sys.path.insert(0, str(ROOT / "tools"))

from toolchain_uga import verify_folio_assets  # noqa: E402


def main(argv: list[str] | None = None) -> int:
    args = argv if argv is not None else sys.argv[1:]
    planted_only = "--planted-defect" in args
    files_dir = ROOT / "src" / "research" / "toolchain" / "x03" / "files"
    make_script = Path(__file__).resolve().parent / "make_x03.py"
    try:
        result = verify_folio_assets(
            slug="x03",
            files_dir=files_dir,
            script_path=make_script,
            planted_defect_only=planted_only,
        )
    except AssertionError as exc:
        print(json.dumps({"status": "FAIL", "folio_id": "X.03", "error": str(exc)}), file=sys.stderr)
        return 1
    print(json.dumps(result, indent=2, ensure_ascii=False))
    return 0


if __name__ == "__main__":
    raise SystemExit(main())

§ V.2 · Primary Peer-Reviewed Sources & Open Specification Anchors

1. Heyman, J. (1966). The stone skeleton. International Journal of Solids and Structures, 2(2), 249–279. DOI DOI 10.1016/0020-7683(66)90018-7 [Scite ↗]
2. Block, P., & Ochsendorf, J. (2007). Thrust network analysis: A new methodology for three-dimensional equilibrium. Journal of the International Association for Shell and Spatial Structures, 48(3), 167–173.
3. Van Mele, T., et al. (2017–2026). COMPAS: A framework for computational research in architecture and structures (MIT License). github.com/compas-dev/compas
4. Rippmann, M., & Block, P. (2013). Funicular shell design exploration. ACADIA 2013 Adaptive Architecture, 337–346.