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Burrisphere atlas

Live geometric instrument · [A] chart · [I] overlay

One sphere.
Two shadows.

One point on S² is read from both poles at once. The lower ν chart and upper φ chart are reciprocal views of the same point—not two realities and not two spheres.

φ1.000
ν1.000
φν1.000
B1.000
θ90.0°
ψ90.0°
θ∈(0,π) φ=cot(θ/2) · ν=tan(θ/2) φν=1 · B=sin θ≤1
90.0°
•south · 0° ○north · 180°
90.0°
↺−90° ↻270°
Move the shared point from the selected south boundary through the balance equator to the north boundary. Theta changes phi, nu, and B but leaves axial bearing unchanged. Rotate the shared point around the vertical axis. Psi changes bearing and the selected interpretive M4 reading but leaves theta, phi, nu, and B unchanged. Free coordinate inspection.
What is mathematics—and what is interpretation?

[A] Inherited mathematics. Dual stereographic projection on S². Polar angle θ sets φ=cot(θ/2), ν=tan(θ/2), φν=1 on the open chart, and B=1 on the equator. Axial bearing ψ is the independent coordinate omitted by the one-meridian formula; changing it rotates the point without changing those radial magnitudes. Projection rays stay collinear from pole through point to plane.

[I] Emergentist projection. Four sectors stay on the bottom action plane; they are not sphere territories. Their current highlight follows bearing ψ through a declared reading map, not a mathematical entailment. The Titan axis is separate: • Śiva; ⊙ Viṣṇu; ○ Brahmā. The violet south-to-north sphere path carries no transfer; it is one selected 360° itinerary. This is not a physical trajectory, temporal law, moral ascent, recurrence, or derivation of seven.

[C] Open wager. Mapping real strategies, agents, or lives onto this visual requires separate operational definitions and tests. The figure cannot supply those by resemblance.