💠 The Jewel — flat to bowl

What this is YOUR SPEC — CAPTURE, not canon GEOMETRY VERIFIED 18/18

You dictated the jewel yesterday: "a gem at the centre that powers it… teardrop… the tiles click in beneath its facets and flap… alter the angle away from horizontal for all of the tiles together and they close into a bowl." Same evening you said the fold math could be done — it has been, on the real tiling engine, and you were right. Kody1 ran every legal vertex figure: a ring carrying exactly half the circle exists, folds to a bowl, and the seam seals edge-to-edge. This page is that object, moving. Where the geometry moved your telling, the page says so out loud — nothing is fudged to look closed.

1 · The jewel at rest

Teardrop-cut, not metal, engraved with a code, seated in a metal frame. The dashed shapes on its facets are the tiles it displays — what could be mounted, not what has been. An empty facet is an honest state.

2 · The fold — drag the slider, spin with a finger

Three tiles carrying five slices of material, five slices open. One thin rhomb at its 36° tip, two thick rhombs at their 72° tips — exactly half of the legal Nook gathering (its other half is its own mirror). Fold them together and the two free edges meet: all rhomb edges are the same length, so the seam seals clean. Socially: 2 stewards + 1 newcomer.

The 60.00° landing is the smooth-material value — engine-verified, 18/18 (fold_vertex_verify.mjs, Kody1). Rigid flat tiles land as a faceted bowl a few degrees shy of it on the edges — and the closed 3-tile bowl is a trihedral corner: it is RIGID, it holds its shape with no flex. That solidity is free; nothing has to be locked. The numbers in the panel are recomputed live by this page, not typed in.

🌞 The companion frame: the five-steward Council sun minus one steward folds to 36.87° — its sine is exactly 0.8, a true 3-4-5 right triangle. Legal, pretty, shallower — shown for contrast, it is not the jewel.

3 · Three settings, one jewel

Your line: "each different role is visualised by a slightly different metallic setting for the gemstone." So standing is read off the metalwork — never off a badge, never off a number. Rank is in the mount; the light is in the stone.

✅ The full six-setting ladder (and its plant telling) is canon — you confirmed it the same evening — and all six settings are now drawn, one per plant stage: 🌱 the ladder.

4 · What the geometry moved — said plainly

Your spec made one checkable claim and I was told to verify before drawing. Verified. Two of the tellings around it turned out to be impossible, and per your own law they are shown as dead, not quietly fixed:

✓ What survives is better than the original: "five" lives on as five slices — five filled wedges of material, five open. Three tiles carry them. The bowl folds to exactly 60° in the material limit, the seam seals because every rhomb edge is equal, and the closed bowl is rigid. And the object is half of a legal gathering whose other half is its own mirror — 2 stewards + 1 newcomer, twice, making a whole.

⚖️ Three taps — the render’s open questions