Handbook

MathGenesis visual representations (P0)

MathGenesis stores symbolic math, geometry metadata, and physics models in JSON. Rendering diagrams is a separate concern. This page documents what forge-universe (fu) can draw today, how it differs from kitchensink (ks)…

Updated 2026-07-26

Renderer stack (forge-universe)

All fu renderers consume the same scene JSON (version, camera, nodes[], optional sim). Source of truth: forge-universe/content/docs/renderers.md.

Renderer	Module	Hash	Output	WebGL	Interaction
2D projections	`UniverseProject2D`	`Up2`	SVG ortho + perspective	No	Static
Static gallery	`UniverseStaticCss`	`Us3`	SVG wireframes + CSS cube	No	Click → flyout
Solid flyout	`UniverseSolidFlyout`	`Ufl`	WebGL + XYZ axis panels	Yes	Dronie orbit
Drone flythrough	`UniverseDynamicGl`	`Udr`	WebGL meshes	Yes	Play / pause
Sim bounce	`UniverseSimGl`	`Usb`	WebGL + rigid-body sim	Yes	Play / reset
Construction assets	`asset-renderer.mjs`	`Uca` / `Ucr`	GLB meshes	Yes	Orbit, joints

Mount API (representative):

UniverseProject2D.mount(container, '/assets/scenes/projections-demo.json');
UniverseStaticCss.mount(container, '/assets/scenes/five-solids-static.json');
UniverseSimGl.mount(container, '/assets/scenes/sim-bounce.json');

Live demos (when deployed): 2D projections, Math illustrations P0, static solids, sim bounce.

Node types available today

Implemented in forge-universe/js/universe-world.js:

tetrahedron, hexahedron, octahedron, dodecahedron, icosahedron, sphere
Alias: cube → hexahedron

Not available: arbitrary triangle, segment, line, or labeled coordinate diagrams. There is no automatic MG → scene compiler in P0.

Projection shapes (2D SVG)

projectNodeWireframe returns:

`kind`	Fields	SVG
`wireframe`	`edges`, `points`	`<line>` per edge
`sphereWire`	`polylines`	`<path>` per great-circle ring

Orthographic panels drop one axis; perspective uses scene camera (eye, target, fov).

Example scene: forge-universe/assets/scenes/projections-demo.json — hexahedron + sphere.

MG object → renderer fit (P0)

MG object	MG visual metadata	fu fit today	Notes
Pythagorean (`geometry.euclidean.pythagorean_relation`)	`geometry.representation_mode: synthetic`, `diagram_status: illustrative`	Indirect	`math-illustrations-p0.json` demo at `/demos/math-illustrations-p0.html` — projection literacy, not a 3-4-5 diagram
Projectile drag (migrated — see PhysicsGenesis bridges)	Canonical: `phys.simulation.projectile-quadratic-drag.v1`	Different physics	`UniverseSimGl` integrates rigid-body bounce (`sim-bounce.json`), not quadratic-drag ODEs
GCD / Euclidean algorithm	Discrete / symbolic	None	Handbook text or future SVG; no fu primitive
Platonic geometry context	—	Good	`five-solids-static.json` + `UniverseStaticCss` gallery

kitchensink spatial (not a math engine)

ks provides governed CSS 3D handbook chrome (e.g. math-globe, hash Glb) — ambient spatial decoration, not theorem diagrams or plotters.

Rule of thumb: link MG geometry/physics illustrations to forge-universe scenes; use ks only for handbook layout primitives.

Schema hooks for future visuals

When fu scenes are wired to MG objects, the contract fields live on math-knowledge-object:

Block	Fields	Intent
`geometry`	`primitive_objects`, `relations`, `allowed_constructions`, `construction_steps`	Synthetic geometry diagram spec
`geometry`	`diagram_status`	`illustrative` vs proof-grade diagram
`geometry`	`orientation_convention`, `nondegeneracy_assumptions`	Diagram validity
`physics`	state variables, forces, integrator hints	Simulation scene binding (P1+)

P0 deliverable: documentation and cross-links only. P1 follow-up: fu scene math-illustrations-p0.json after triangle/segment node types or an MG→scene generator exists.

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