D2 · formal · [A/S/I]

The plane

Two independent coordinates; relations and constraints. D2 is the plane ℝ² ≃ ℂ with two independent real coordinates, for example z = a + ib. Relations and constraints organize configurations within that carrier. Radius and azimuth give two local coordinates on the punctured stereographic chart.

Inherited structure

Function theory, topology, geometry, and coordinate charts are inherited mathematics [A].

Claim boundary

The plane includes its origin. A smooth graph b = f(a) and the reciprocal meridian x, 1/x each have one independent parameter. Their ambient plane has two coordinates. Arbitrary configuration does not establish dimension two; this definition supplies no missing geometric derivation of D3–D5.

D2 · The plane

D2 is the plane ℝ² ≃ ℂ with two independent real coordinates, for example z = a + ib. Relations and constraints organize configurations within that carrier. Radius and azimuth give two local coordinates on the punctured stereographic chart.

This illustration carries no evidence beyond the typed text above.

Semantic owner: 05_COSMOLOGY/03_FORMAL_SYSTEM/43_D2_FUNCTION_ATLAS_AND_CONFIGURATION.md

μ2 · coordinate construction reduced; physical emergence open

Verdict source: 10_EFR_MU_LIMIT_FORMULA.md §2; the pre-recut μ₂ verdict (48: "μ₂ and μ₃ still fail") now belongs to the representational sequence's state lift (KSC-34)

Independent spatial-coordinate opening

Saturation proposal: A plane does not independently vary a third spatial coordinate.
New capability: Local coordinate space (x, y, z) in ℝ³: a third spatial coordinate varies independently of the plane.
Lower-level recovery: Project (x, y, z) to (x, y), or take a declared planar slice, to recover the D2 description.
Evidence: [A/S] Cartesian construction; [I/C] physical emergence reading
Prediction: Three local coordinates remain independent after declared constraints and redundancies.
Alternatives: Native geometry and physics describe three-dimensional space without this emergence ordering.
Kill criterion: A constraint removes the third freedom, or a probability or state label is mistaken for a spatial coordinate.

Source owner: 05_COSMOLOGY/03_FORMAL_SYSTEM/44_D3_QUANTUM_STATE_REGISTER.md

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