Sandbox · not part of the app
A separate playground that prototypes the four points the live cosmos leaves out — Steiner’s Cassini derivation and its “out of space” branch, the human-form correspondence, the Moon’s eclipse geometry, and an explicit provenance lens. Reuses the same lemniscate math as the app. Nothing here is linked from the product.
The lemniscate as one frame of the Curve of Cassini. Sweep the focal distance and watch the oval pinch into the lemniscate, then split into two loops — the moment continuity “goes out of space.”
Source Lens · provenance
GA323, L9: “the lemniscate… is a special form of Curve of Cassini” (constant product).
GA323, L10: “I obtain the lemniscate when a=b, and the discontinuous curve when a is greater than b.”
GA323, L9: obliged “to go out of space… to preserve the continuity of the idea.” Rendered here as a projective circle-inversion — a representation, not a literal exit from 3-space.
Grounded in GA323 lectures 8–12 (8–12 January 1921). Curves are teaching-forms, not an ephemeris. To promote anything here into the live app, it would be migrated deliberately with the confidence tags intact.