Torus.

Prepare evidence for Torus review

Buyer translation: this reference page maps the mark to a tool, system, control, deployment, or evidence question. T² · genus-1 topology · Torus is an ambient-mathematics primitive: the space where the spectral measurements live.

register 04 · Geometry spaces· slug torus· family geometry 🍩 · best-fit emoji
01 ·

What this is.

Twelve marks · the ambient mathematics · same construction

Use. T² · genus-1 topology.

Source. outer + inner ellipse + brass meridian + longitude.

Register. 04 · Geometry spaces — one of the ten registers of the PLANiSPHERE corpus library.

02 ·

See it work.

Evidence record you can check — not code you have to trust.

Planisphere measures your tool deployment against Torus and seals the result into a signed, Merkle-rooted evidence record. The grade recomputes on your own hardware; the model state never crosses the boundary.

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03 ·

Promise. geometry

The contract this mark binds — derived, not asserted.

Torus is an ambient-mathematics primitive: the space where the spectral measurements live.

Answers: How does Torus show up in Planisphere's spectral geometry?

04 ·

Adjacent marks, same instrument.

Related marks, and the surface this one funnels to.

Torus is measured into the same evidence record as every other mark in the Geometry spaces register. That measurement becomes compliance-ready buyer evidence at /trust-packet.

Euclidean Plane reg 04 · ℝ² · flat geometry Fractal reg 04 · Sierpinski · self-similarity Hilbert Space reg 04 · ℓ² · infinite-dim inner product Hyperbolic Disk reg 04 · Poincaré model · negative curvature Klein Bottle reg 04 · non-orientable · 4D immersion
05 ·

Routes here from.

Where this mark is referenced in the Planisphere surface.

Methodology · About

Any internal link in the Planisphere site that names "Torus" canonicalises here.

06 ·

Sibling marks. Geometry spaces

Same register · same construction.
Euclidean Plane
ℝ² · flat geometry
grid + axes + brass origin
Hyperbolic Disk
Poincaré model · negative curvature
boundary + 4 geodesic arcs + brass center
Spherical Space
S² · positive curvature
sphere + brass equator + meridians + pole
Manifold
smooth chart · saddle curvature
surface patch + U/V grid + brass curvature lines
Vector Space
ℝⁿ · linear combinations
3 axes + 2 brass basis vectors + origin
Hilbert Space
ℓ² · infinite-dim inner product
nested basis levels + 2 brass orthogonal vectors
Fractal
Sierpinski · self-similarity
recursive triangles + 3 brass voids
Riemann Surface
multivalued · branched sheets
3 stacked sheets + brass branch cut
Klein Bottle
non-orientable · 4D immersion
body + neck + brass self-intersection
Lattice
ℤⁿ · discrete subgroup
point grid + brass unit cell + basis vectors
Tangent Bundle
TM · fibered velocity space
curve + 4 brass tangent vectors at base points

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