Klein Bottle.

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Buyer translation: this reference page maps the mark to a tool, system, control, deployment, or evidence question. non-orientable · 4D immersion · Klein Bottle is an ambient-mathematics primitive: the space where the spectral measurements live.

register 04 · Geometry spaces· slug klein-bottle· family geometry 🍶 · best-fit emoji
01 ·

Promise. geometry

The contract this mark binds — derived, not asserted.

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

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

02 ·

What this is.

Twelve marks · the ambient mathematics · same construction

Use. non-orientable · 4D immersion.

Source. body + neck + brass self-intersection.

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

03 ·

See it work.

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

Planisphere measures your tool deployment against Klein Bottle 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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04 ·

The board that carries this.

Related marks, and the surface this one funnels to.

Klein Bottle 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
05 ·

Routes here from.

Where this mark is referenced in the Planisphere surface.

Methodology · About

Any internal link in the Planisphere site that names "Klein Bottle" 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
Torus
T² · genus-1 topology
outer + inner ellipse + brass meridian + longitude
Fractal
Sierpinski · self-similarity
recursive triangles + 3 brass voids
Riemann Surface
multivalued · branched sheets
3 stacked sheets + brass branch cut
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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