Register 04 · Geometry spaces

Riemann Surface.

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

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register 04 · Geometry spaces· reference mark
01 ·

What this is.

Twelve marks · the ambient mathematics · same construction

Use. multivalued · branched sheets.

Source. 3 stacked sheets + brass branch cut.

Register. 04 · Geometry spaces — one of the 17 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 Riemann Surface 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.

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

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

04 ·

Adjacent marks, same instrument.

Related marks, and the surface this one funnels to.

Riemann Surface is a reference mark in the Geometry spaces register. Read the related buyer-facing product context at /evidence.

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 "Riemann Surface" 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
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

See the record Riemann Surface asks for.

The console shows the evidence; the docs show the endpoints; the briefing shows what the product does and does not claim.

Open the Console Read the Docs Read the capability briefing
API ·

When a regulator asks for proof, hand over records — not assurances.

record the duty · seal the receipt · verify offline

Planisphere records each duty event — an output marked, a disclosure shown, a review made — and seals it into a receipt that verifies offline against our published keys. You send hashes, never content. A record is evidence a third party can check; it is not a certification and not a legal determination.

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See how a record is checked