feat(scaffold): production-value pass on the WorldAxes math-frame indicator (stub)

[bradleypmartin]

Surfaced from #225 PR1 (#250 / #254) headset smoke (Brad, 2026-05-22). Stub-only — direction TBD; capturing so the open question stays tracked rather than dropping it.

What headset smoke surfaced

"The world-axis X-Y-Z axis system indicator is also rather stale at this point, and needs some kind of tweaking and raise to its production value as well; not sure exactly what that looks like but we can stub out an issue for it anyway." — Brad

The current WorldAxes primitive renders three orthogonal arrows (AXIS_LENGTH = 0.15 m) at slot-origin with billboarded letter labels at each arrow tip. The construction is functional but reads as first-pass next to the staged-exhibit vocabulary that's landing under #221 — solo arrows in mid-air, basic cone tips, single-color shafts.

Direction (open)

Not pre-committing to a shape. Whatever lands should:

• Keep the math-frame pedagogy intact: X/Y/Z arrows still read as the math frame the equation is written in (not the tabletop frame). The plinth slot already uses orientation: 'world' to preserve this; the visual upgrade has to keep that property.
• Match the post-plinth staging vocabulary's production value (see feat(staging): rework section-tab + canonical-forms anchoring + label rendering on the plinth #255 + feat(scaffold): production-value slider thumb visual — transparent sphere circumscribing axis-arrow interior #256 — sister "PR1 smoke surfaced this is stale" issues).
• Stay scaffold-shared across all four cluster scenes (every cluster scene mounts a WorldAxes).

Open questions to surface at plan-doc / roundtable time:

• Does this become an OBJECT rather than just three arrows (e.g., a small orienting cube with axis arrows emerging)?
• How does it visually anchor to the plinth — embedded into the working surface, hovering above it, or attached differently?
• Should the letter labels change rendering model along with feat(staging): rework section-tab + canonical-forms anchoring + label rendering on the plinth #255 (yaw-billboarded text on a tilted surface is the cross-cutting concern)?
• Does the indicator integrate the existing axis-tint palette (vermillion / bluish-green / sky-blue) or extend it?

Code anchors

• Primitive: src/scaffold/ui/WorldAxes.ts (AXIS_LENGTH = 0.15, per-axis arrow + letter-Text label, faceCamera on letter children only).
• Plinth slot: src/exhibits/quadrics/index.ts — PLINTH_AXIS_INDICATOR_X = 0.42, PLINTH_AXIS_INDICATOR_Y = 0.275, orientation: 'world'.
• Per-scene consumers: all four cluster scenes (quadrics / tangent-planes / gradient-levels / saddle-extrema).

Refs

• Surfaced by: feat(staging): plinth primitive + slot-mount API + quadrics on plinth (#225 E1.4a/b) #250 / feat(staging): plinth primitive + slot-mount API + quadrics on plinth (#250) #254 (plinth landed, WorldAxes reads as stale alongside it).
• Sister "plinth-era visual upgrade" issues: feat(staging): rework section-tab + canonical-forms anchoring + label rendering on the plinth #255 (rack-button labels), feat(scaffold): production-value slider thumb visual — transparent sphere circumscribing axis-arrow interior #256 (slider thumbs), feat(staging): panel-backed readout visual (#225 E1.4c) #252 (readout panels — pre-existing under feat(staging): control plinth hosting interactive UI (sub-epic) #225).
• Plan context: _private/plans/225-control-plinth.md §3.3 (the WorldAxes 'world' orientation carve-out).

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