Informatico.ai

Contents

Engineering & Construction

  1. E.01 Stokes–Brinkman Porous Continuum, Helmholtz–Hodge Decomposition, and Percolation
  2. E.02 Herschel–Bulkley Yield-Stress Rheology: High-Performance Concrete Pumping & Tremie Placement
  3. E.03 Sub-Wavelength Acoustic Metamaterial Helmholtz Arrays and Viscothermal Boundary-Layer Damping
  4. E.04 Counter-Current Enthalpy Recovery Exchangers: Effectiveness–NTU, Membrane Sorption, and Frost Limits
  5. E.05 Terzaghi Soil Mechanics, CFA Augercast Deep Foundation Piling & Liquefaction Surcharge
  6. E.06 Nonlinear Structural Dynamics, ASCE 7-22 Inelastic Response Spectra & Seismic Base-Isolation Dampers
  7. E.07 Long-Span Suspension Bridge Aeroelastic Flutter, Scanlan Derivatives & Physics-Informed Neural Network (PINN) Digital Twins
  8. E.08 Earth-Pressure-Balance Tunnel Boring Machines (EPB-TBM), Peck–Mair Gaussian Settlement Troughs & GNN Subsurface Digital Twins
  9. E.09 Autogenous Bacterial & Crystalline Self-Healing Concrete: Lucas–Washburn Capillary Imbibition, Fickian–Michaelis–Menten Calcite Precipitation & Ultrasonic Coda-Wave Digital Twins
  10. E.10 3D Concrete Printing (3DCP) Extrusion Rheology & Buildability: Roussel Thixotropic Structuration, Elastic Buckling vs. Plastic Collapse & Robotic Toolpath Control
  11. E.11 Continuum Topology Optimization & Skyscraper Inerter Damping: SIMP Penalization, Michell Funicular Trusses & Trabecular Bone Mechanics
  12. E.12 Machine-Checked Silicon-to-Grid Safety: 180M-Line Rocq RISC-V Verification, Control Barrier Functions & Firefly-Synchronized Renewable Grids

Architecture

  1. A.01 Funicular Thrust Surfaces, Maxwell–Cremona Duals, and 1:5 Nodal Tectonics
  2. A.02 Reciprocal Timber Gridshells (Nexorades), Eccentric Lap Moments, and 1:5 Shear-Block Joinery
  3. A.03 Double-Skin Facade Buoyancy Stack Ventilation, Cavity Plumes, and 1:5 Acoustic Damper Louvers
  4. A.04 From Archigram's Plug-In Megastructures to British High-Tech Exoskeletons: Gerberette Cantilevers, Maxwell Space Frames & Shearing-Layer Pods
  5. A.05 Acoustic Sabin–Eyring Reverberation, Diffusive Coffered Vaults, and Speech Intelligibility (STI ≥ 0.68)
  6. A.06 Net-Zero Water & Greywater Constructed Wetlands: Subsurface Darcy Filtration, UV-C Photolysis, and Pathogen-Free Plumbing (CSI 22 13 00)
  7. A.07 Luis Barragán's Chromatic Tectonics, Kubelka–Munk Pigment Radiosity & Emotional Spatial Wavefields
  8. A.08 AI-Designed Daytime Radiative Sky-Cooling Photonic Roofs (8–13 μm Window) & Stefan Phase-Change Envelopes
  9. A.09 Bending-Active & Hygroscopic Programmable Timber Skins: Timoshenko Bilayer Curvature, Orthotropic Moisture Swelling & Zero-Energy Climate Facades
  10. A.10 Kinetic Origami & Miura-Ori Deployable Biomimetic Facades: Isometric Crease Kinematics, Auxetic Poisson Ratio Inversion & Solar Mashrabiya Envelopes
  11. A.11 3D Polyhedral Graphic Statics & Airy Stress Surfaces: Maxwell–Rankine Reciprocal Polyhedra, Guastavino Tile Vaulting & Zero-Rebar Floors
  12. A.12 Tensegrity Cable-Strut Domes & Radiative Sky-Cooling Envelopes: Pellegrino Equilibrium Nullspaces, Prestress Stiffening & Zero-Energy Cooling

Physics

  1. P.01 Non-Equilibrium Fluctuation-Dissipation Theorems and Allosteric Gating Energetics
  2. P.02 Active Matter Hydrodynamics and Ciliary Metachronal Wave Synchronization
  3. P.03 Soft Matter Rheology and Anomalous Subdiffusion in Entangled Mucin Hydrogels
  4. P.04 Electrokinetics, Donnan Equilibrium, and the Catastrophic Osmotic Collapse of the Periciliary Layer
  5. P.05 Quantum WKB Barrier Penetration, Proton-Coupled Electron Transfer, and Deaminase Base-Editing Catalysis
  6. P.06 de Gennes Polymer Reptation (D_rep ~ N⁻²), Doi–Edwards Tube Relaxation, and Kilobase Genetic Cargo Transport
  7. P.07 Formula 1 Ground-Effect Venturi Aerodynamics, 2026 Active X/Z-Mode Wings, Outwash Vortex Sealing & Porpoising Limit Cycles
  8. P.08 Electromagnetic Color Wave Physics: Bragg Thin-Film Interference, Gonioapparent Automotive Pearlescence & Barragán Stucco Optics
  9. P.09 Electrohydrodynamic Taylor Cones (49.3°), Rayleigh Fission Limits & Precision Monodisperse Aerosol Jet Physics
  10. P.10 Topological Photonics, Haldane–Raghu Photonic Chern Insulators, Berry Curvature & Backscatter-Free Chiral Edge Waveguides
  11. P.11 Fault-Tolerant Quantum Computing & Clean Nitrogen Fixation: Surface-Code Stabilizers, Non-Abelian Anyon Braiding & FeMoCo Catalysis
  12. P.12 Hilbert's Sixth Problem Resolved: Hard-Sphere Boltzmann Kinetics to Navier–Stokes Continuum & Neural Climate Operators

Series · Time & Gravity · 9 steps (T.00–T.10)

  1. T.00 Time & Gravity
  2. T.01 Gravity as a Slope in the Rate of Time
  3. T.02 Everyone Moves at One Rate
  4. T.03 What Sets the Slope
  5. T.04 A Clock in Two Places
  6. T.05 Does Gravity Entangle, and Would That Settle It?
  7. T.06 Does Gravity Collapse the Wave?
  8. T.07 The Equation with No Time
  9. T.10 Page's Counting Argument

Mathematics

  1. M.01 Modularity Lifting, Spectral Zero-Density Barriers, and #3-SAT Sparsification
  2. M.02 Riemann Zeta Zero-Density Estimates, Large Sieve Inequalities, and XiPrime Spectral Bounds
  3. M.03 Extremal Cap Sets in F_3^n, Polynomial Method Upper Bounds, and Rank-48 Matrix Tensors
  4. M.04 Polynomial Freiman–Ruzsa (PFR) Entropy Calculus and the 22-Million Equational Magma Graph
  5. M.05 Neuro-Symbolic Deductive Search (AlphaGeometry 2): Auxiliary Constructions and Allosteric Pocket Triangulation
  6. M.06 Sub-Cubic Fine-Grained Reductions (3SUM → APSP) and Step-Level Process Supervision (PRM800K)
  7. M.07 Formula 1 350 kW MGU-K Pontryagin Optimal Energy Control, Hamilton–Jacobi–Bellman Lap Time Minimization & Fourier Neural Operator Surrogates
  8. M.08 Riemannian Differential Geometry of Color Perception: Helmholtz–Schrödinger Geodesics, MacAdam Metric Tensors & Grassmann Spectral Hilbert Projections
  9. M.09 Monge–Kantorovich Optimal Transport, Benamou–Brenier Wasserstein-2 Geodesic Fluid Dynamics, Sinkhorn Entropic Regularization & Flow Matching
  10. M.10 Persistent Homology, Vietoris–Rips Simplicial Filtrations, Betti Barcodes & Topological Percolation Thresholds in Disordered Media
  11. M.11 Resolution of the 3D Kakeya Conjecture & Breaking Ingham's 1940 Riemann Barrier: Wang–Zahl Graininess, Guth–Maynard 30/13 & Lean 4
  12. M.12 Anthropic Lean 4 Complexity & Post-Quantum Crystal Locks: ETH Refutation (ETHIsFalse), Eight-Square Rank Compression & ML-KEM Lattices

Open-Bounty & Prize Crucible · 6 Dedicated Problem Folios (B.01–B.06)

  1. B.01 · BOUNTY-M1 Erdős Sidon B₂ Sets, Golomb Rulers & Anthropic Lean 4 Formalization Bounties
  2. B.02 · BOUNTY-P1 $5M XPRIZE Quantum Applications & Unitary Foundation: Surface-Code Thresholds & FeMoCo Catalysis
  3. B.03 · BOUNTY-E1 $100M XPRIZE Carbon Removal & IStructE Benchmark: Sub-45 kg CO₂e/m² SIMP Mineralized Slabs
  4. B.04 · BOUNTY-A1 $1M Holcim Awards & $3M Global Cooling Prize: Zero-Rebar 3D Graphic Statics Vaults & Sky-Cooling
  5. B.05 · BOUNTY-P2 Pareto Symbolic Regression (PySR) & Sparse PDE Discovery (PySINDy + Dedalus) from Noisy Sensor Fields
  6. B.06 · BOUNTY-M2 Machine-Checked Gauge Physics in PhysLean & Tensor-Network Quantum Criticality (ITensors.jl + NetKet)

Tech & Tools · The Toolbox · 6 Open 3D CAD & Studio Folios (X.01–X.06)

  1. X.01 · TOOL-CORE-1 Zero-Build WebGL2 GLB Inspector & Byte-Level 2-Manifold Geometry Verifier
  2. X.02 · TOOL-ENG-1 Code-First Parametric Solids & Measured STEP AP242, 3MF, and GLB Round-Trip Fidelity
  3. X.03 · TOOL-ARCH-1 The Small Architecture Studio's Vault, Timber & Reciprocal Frame Kit: Equilibrium to Open CAD
  4. X.04 · TOOL-ARCH-2 Miura-Ori Deployable Solar Screens: From 3D Folding Kinematics (GLB) to Flat-Pattern DXF
  5. X.05 · TOOL-FAB-1 Topology-Optimized Structural Struts to Watertight 3MF & Build-Plate Overhang Audit
  6. X.06 · TOOL-PHYS-MATH-1 Sub-Wavelength Acoustic & Topological Metamaterial Unit Cells: Genus g = 1 & Betti-Number Verification

Tech & Tools · The Toolbox · 6 Dedicated 3D CAD & Studio Folios (X.01–X.06)

Tech & Tools · The 3D CAD, Open BIM & Small-Studio Toolbox

Six standalone 3D CAD and open-toolchain monographs (X.01–X.06) empowering boutique architecture studios, independent civil and mechanical engineers, physicists, and math makers. Every Folio ships a deterministic Python generator (make_x01.py..make_x06.py), downloadable neutral 3D/2D files (.glb, .step, .3mf, .dxf) with a SHA-256 manifest, a live zero-dependency WebGL2 3D inspector, a stdlib byte-level verifier with planted-defect knockout, and a portable SKILL.md.

Fixed Educational Artifact Boundary · 100% Open-Source & Sovereign International Standards (GCC-01–GCC-05) 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. Global Legal & FOSS Charter (GCC-01–GCC-05): Zero proprietary software required or endorsed. Generators run on Python 3 stdlib (PSF-2.0 / MIT) emitting ISO/IEC 12113:2022 (.glb), ISO 10303-21 (.step), ISO/IEC 25422 (.3mf), and clean-room ASCII (.dxf) under CC0-1.0 / CC-BY-4.0, compliant with US NCEES/NCARB, EU Directive 2005/36/EC & Eurocodes, UK Building Safety Act, Mexico Cédula Profesional, GDPR/CCPA/LGPD/LFPDPPP (zero telemetry/cloud uploads), and EAR 15 CFR § 734.7 public-domain research.
⚡ 30-SECOND STUDIO QUICK-START · ZERO PAID SOFTWARE REQUIRED Built for 1–5 person architecture firms, solo engineers, and makers.
Step 1 · Grab Any 3D/CAD File

Download Open Neutral Geometry

Every Toolbox Folio (X.01–X.06) below gives you instant 1-click downloads of watertight .glb meshes, ISO 10303-21 .step AP242 solids, .3mf print packages, and .dxf laser/CNC cut sheets.

Step 2 · Open in Free Desktop Tools

Blender · FreeCAD · OrcaSlicer · QCAD

Open .glb in Blender 4.2+, .step in FreeCAD 1.0 or build123d / CadQuery, .3mf in OrcaSlicer / PrusaSlicer, and .dxf (CUT, MOUNTAIN, VALLEY layers) in QCAD Community Edition, LibreCAD, or Inkscape.

Step 3 · Customize or Verify with Python

Code Is Source of Truth + Byte Verifier

Run python skills/toolchain/x01/make_x01.py to regenerate custom dimensions, and python toolchain/run_all_toolchain.py to verify watertightness and planted-defect rejection in <1s.

Conceptual visualization imagining what Toolbox X.01 (TOOL-CORE-1: Zero-Build WebGL2 GLB Inspector & Byte-Level 2-Manifold Geometry Verifier) would look like in an open-source architecture and engineering studio workshop (artistic impression, not a measured structure) X.01 · TOOL-CORE-122 min read X.01 (TOOL-CORE-1) · Zero-Build WebGL2 GLB Inspector & Byte-Level 2-Manifold Geometry Verifier How a 300-line zero-dependency ES module parses binary glTF 2.0 (GLB) buffers into raw WebGL2 while a Python stdlib verifier proves edge-manifold watertightness, divergence-theorem volume, and malformed-binary rejection. Conceptual visualization imagining what Toolbox X.02 (TOOL-ENG-1: Code-First Parametric Solids & Measured STEP AP242, 3MF, and GLB Round-Trip Fidelity) would look like in an open-source architecture and engineering studio workshop (artistic impression, not a measured structure) X.02 · TOOL-ENG-122 min read X.02 (TOOL-ENG-1) · Code-First Parametric Solids & Measured STEP AP242, 3MF, and GLB Round-Trip Fidelity Empowering solo mechanical and civil engineers to generate exact B-rep solids from version-controlled Python scripts and measure exactly what survives—and what is lost—across STEP AP242, 3MF, and GLB. Conceptual visualization imagining what Toolbox X.03 (TOOL-ARCH-1: The Small Architecture Studio's Vault, Timber & Reciprocal Frame Kit: Equilibrium to Open CAD) would look like in an open-source architecture and engineering studio workshop (artistic impression, not a measured structure) X.03 · TOOL-ARCH-122 min read X.03 (TOOL-ARCH-1) · The Small Architecture Studio's Vault, Timber & Reciprocal Frame Kit: Equilibrium to Open CAD How 1-to-10-person architecture studios can run Jacques Heyman's middle-third kern analysis and Maxwell–Rankine polyhedral form-finding in Python—emitting ready-to-inspect STEP, 3MF, DXF, and GLB voussoir assemblies at zero software cost. Conceptual visualization imagining what Toolbox X.04 (TOOL-ARCH-2: Miura-Ori Deployable Solar Screens: From 3D Folding Kinematics (GLB) to Flat-Pattern DXF) would look like in an open-source architecture and engineering studio workshop (artistic impression, not a measured structure) X.04 · TOOL-ARCH-222 min read X.04 (TOOL-ARCH-2) · Miura-Ori Deployable Solar Screens: From 3D Folding Kinematics (GLB) to Flat-Pattern DXF Bridging 3D deployable origami kinematics and 2D sheet fabrication: generate a watertight thickened Miura-ori facade shell (.glb, .3mf) and a laser-cutter/plotter crease pattern (.dxf) verified by Kawasaki–Justin and Maekawa's theorems. Conceptual visualization imagining what Toolbox X.05 (TOOL-FAB-1: Topology-Optimized Structural Struts to Watertight 3MF & Build-Plate Overhang Audit) would look like in an open-source architecture and engineering studio workshop (artistic impression, not a measured structure) X.05 · TOOL-FAB-122 min read X.05 (TOOL-FAB-1) · Topology-Optimized Structural Struts to Watertight 3MF & Build-Plate Overhang Audit How to convert variable-density SIMP structural struts into guaranteed 2-manifold 3MF and GLB meshes while auditing frustum volume conservation and build-plate overhang angles θ = arccos(−n · ẑ) in pure Python. Conceptual visualization imagining what Toolbox X.06 (TOOL-PHYS-MATH-1: Sub-Wavelength Acoustic & Topological Metamaterial Unit Cells: Genus g = 1 & Betti-Number Verification) would look like in an open-source architecture and engineering studio workshop (artistic impression, not a measured structure) X.06 · TOOL-PHYS-MATH-122 min read X.06 (TOOL-PHYS-MATH-1) · Sub-Wavelength Acoustic & Topological Metamaterial Unit Cells: Genus g = 1 & Betti-Number Verification Empowering independent physicists, acoustic designers, and math educators to generate pierced toroidal metamaterial unit cells (.glb, .3mf, .step) and verify Euler–Poincaré χ = V − E + F = 2 − 2g = 0 and Betti numbers (β₀=1, β₁=2, β₂=1) in stdlib Python.

Special Feature · Tech & Tools · The 3D CAD, Open BIM & Small-Studio Toolbox (X.01–X.06)

Tech & Tools · The Toolbox: Downloadable STEP, 3MF, GLB & DXF Files, Byte-Level Verifiers & Small-Studio Skills

Six dedicated 3D CAD, fabrication, and open-tool Folios (X.01–X.06 at /toolchain/x01/ through /toolchain/x06/) built to empower small architecture studios, independent civil and mechanical engineers, physicists, and math makers. Every Folio ships a deterministic Python generator (make_x01.py..make_x06.py), downloadable neutral files (.glb, .step, .3mf, .dxf) with a SHA-256 manifest, a live zero-build WebGL2 3D inspector, a stdlib byte-level verifier with planted-defect knockout, and a portable SKILL.md companion.

Fixed Educational Artifact Boundary · 100% Open-Source & Sovereign International Standards (GCC-01–GCC-05) 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. Global Legal & FOSS Charter (GCC-01–GCC-05): Zero proprietary software required or endorsed. Generators run on Python 3 stdlib (PSF-2.0 / MIT) emitting ISO/IEC 12113:2022 (.glb), ISO 10303-21 (.step), ISO/IEC 25422 (.3mf), and clean-room ASCII (.dxf) under CC0-1.0 / CC-BY-4.0, compliant with US NCEES/NCARB, EU Directive 2005/36/EC & Eurocodes, UK Building Safety Act, Mexico Cédula Profesional, GDPR/CCPA/LGPD/LFPDPPP (zero telemetry/cloud uploads), and EAR 15 CFR § 734.7 public-domain research.
TOOLBOX X.01 · ZERO-BUILD WEBGL2 GLB INSPECTOR + STDLIB VALIDATOR Core 3D Instrument · WebGL2 & Byte-Level Verification

X.01 · Zero-Build WebGL2 GLB Inspector & Byte-Level 2-Manifold Geometry Verifier

V = (1/6) ∑_{f ∈ F} v_0 · (v_1 × v_2) · χ = V − E + F = 2 − 2g · 3F = 2E PASS · χ = 2 · V = 24,000 mm³ · 4/4 FUZZ REJECTED

How a 300-line zero-dependency ES module parses binary glTF 2.0 (GLB) buffers into raw WebGL2 while a Python stdlib verifier proves edge-manifold watertightness, divergence-theorem volume, and malformed-binary rejection.

Inspect 3D Model, Download GLB · STEP · 3MF & Verifier (X.01) →

Bridge: Folio E.10 → · Folio M.10 → · Khronos glTF 2.0 Specification (ISO/IEC 12113) · elalish/manifold (Apache-2.0 CSG Kernel)

TOOLBOX X.02 · BUILD123D / CADQUERY KERNEL → STEP AP242 · 3MF · GLB AUDIT Engineering Toolbox · Code-First Parametric CAD & STEP AP242

X.02 · Code-First Parametric Solids & Measured STEP AP242, 3MF, and GLB Round-Trip Fidelity

h_sagitta = R (1 − cos(π / N)) · V_step = V_flange + V_boss = 43,200 mm³ · ΔV / V < 10⁻⁶ PASS · V = 43,200 mm³ · h_32 = 0.0722 mm · AP242 + 3MF + GLB

Empowering solo mechanical and civil engineers to generate exact B-rep solids from version-controlled Python scripts and measure exactly what survives—and what is lost—across STEP AP242, 3MF, and GLB.

Inspect 3D Model, Download GLB · STEP · 3MF & Verifier (X.02) →

Bridge: Folio E.10 → · Folio E.06 → · gumyr/build123d (Apache-2.0 Python BREP CAD) · CadQuery/cadquery (Apache-2.0 Parametric CAD)

TOOLBOX X.03 · BOUTIQUE ARCHITECT'S ZERO-COST VAULT & TIMBER KIT (STEP · 3MF · DXF · GLB) Small Architect's Studio Toolbox · Structural Form-Finding & Open BIM

X.03 · The Small Architecture Studio's Vault, Timber & Reciprocal Frame Kit: Equilibrium to Open CAD

H = q L² / (8 f) = 27.0 kN · |e(x)| ≤ t / 6 = 66.7 mm · ∑ F_i = 0 · χ = 2 N_v = 14 PASS · 7 VOUSSOIRS · χ = 14 · H = 27.0 kN · STEP+3MF+DXF+GLB

How 1-to-10-person architecture studios can run Jacques Heyman's middle-third kern analysis and Maxwell–Rankine polyhedral form-finding in Python—emitting ready-to-inspect STEP, 3MF, DXF, and GLB voussoir assemblies at zero software cost.

Inspect 3D Model, Download GLB · STEP · 3MF · DXF & Verifier (X.03) →

Bridge: Folio A.11 → · Folio A.01 → · compas-dev/compas (MIT Computational Architecture Framework) · Bonsai BIM / IfcOpenShell (Native Open BIM)

TOOLBOX X.04 · MIURA-ORI DEPLOYABLE SCREEN: 3D GLB/3MF + 2D LASER-CUTTER DXF Small Architect & Maker Fabrication · Kinetic Facades & Laser/CNC DXF

X.04 · Miura-Ori Deployable Solar Screens: From 3D Folding Kinematics (GLB) to Flat-Pattern DXF

∑_{i=1}^4 (−1)^i α_i = 78° − 102° + 102° − 78° = 0° · |M − V| = 2 · V = A_xy · h = 144,000 mm³ PASS · KAWASAKI Δα = 0° · |M−V| = 2 · GLB + 3MF + DXF

Bridging 3D deployable origami kinematics and 2D sheet fabrication: generate a watertight thickened Miura-ori facade shell (.glb, .3mf) and a laser-cutter/plotter crease pattern (.dxf) verified by Kawasaki–Justin and Maekawa's theorems.

Inspect 3D Model, Download GLB · 3MF · DXF & Verifier (X.04) →

Bridge: Folio A.10 → · Folio A.04 → · LibreCAD / QCAD Open DXF Ecosystem · Schenk & Guest (2013) Folded Metamaterials (PNAS)

TOOLBOX X.05 · SIMP TOPOLOGY LATTICE → MANIFOLD 3MF · GLB · STEP + OVERHANG AUDIT Additive & Structural Toolbox · SIMP Lattices to Watertight 3MF

X.05 · Topology-Optimized Structural Struts to Watertight 3MF & Build-Plate Overhang Audit

V = ∑_{k=1}^3 (h_k / 3)(A_{k-1} + A_k + √(A_{k-1} A_k)) = 46,080 mm³ · θ_wall = arctan(Δw / Δz) = 14.04° ≤ 45° PASS · V = 46,080 mm³ · θ_max = 14.04° ≤ 45° · 3MF+GLB+STEP

How to convert variable-density SIMP structural struts into guaranteed 2-manifold 3MF and GLB meshes while auditing frustum volume conservation and build-plate overhang angles θ = arccos(−n · ẑ) in pure Python.

Inspect 3D Model, Download GLB · 3MF · STEP & Verifier (X.05) →

Bridge: Folio E.11 → · Folio P.07 → · elalish/manifold (Apache-2.0 Exact Manifold CSG) · 3MF Consortium Core & Beam Lattice Specifications

TOOLBOX X.06 · GENUS-1 METAMATERIAL UNIT CELL (χ = 0 · β₁ = 2 · GLB · 3MF · STEP) Physics & Math Explorer Toolbox · Topological Genus & Acoustic Metamaterials

X.06 · Sub-Wavelength Acoustic & Topological Metamaterial Unit Cells: Genus g = 1 & Betti-Number Verification

χ = V − E + F = 16 − 48 + 32 = 0 = 2 − 2g (g = 1, β₁ = 2) · V = (L_o² − L_i²) H = 349,440 mm³ · φ = 0.090 PASS · GENUS g = 1 (χ = 0) · V = 349,440 mm³ · GLB+3MF+STEP

Empowering independent physicists, acoustic designers, and math educators to generate pierced toroidal metamaterial unit cells (.glb, .3mf, .step) and verify Euler–Poincaré χ = V − E + F = 2 − 2g = 0 and Betti numbers (β₀=1, β₁=2, β₂=1) in stdlib Python.

Inspect 3D Model, Download GLB · 3MF · STEP & Verifier (X.06) →

Bridge: Folio M.10 → · Folio E.03 → · GUDHI Library (MIT/GPL Topological Data Analysis) · scikit-tda / Ripser.py (MIT Persistent Homology)