ENGINEERING COMMISSION — HEMISPHERICAL QUANTUM SELECTOR, HQS 1.0

ROLE AND STANDARD
Act as a mathematical interface engineer, numerical analyst, accessibility specialist and adversarial software tester. Implement Michael Aaron Loftus’s attributed hemispherical-selector concept as the explicitly defined classical model below. Intellectual depth means falsifiable definitions, correct units, reproducible computation and candid limits—not claims of genius, scientific rank, patent novelty or quantum computation. Read the source manuscript and this specification. Keep inventor-provided ideas distinct from the implementation choices. Do not silently substitute an attractive sphere for the required hemisphere.

DELIVERABLE
Build an interactive hemispherical mesh, independent controls, a complete numerical report, an interpretation panel, a reproducible JSON export and runnable source. Deliver the mathematics and code, not merely a rendering. Use ordinary local JavaScript/TypeScript and SVG, Canvas or an existing graphics library. The selector must work without an AI model, paid API, hosted inference, external calculation service or backend vote submission. Pre-generated editorial artwork is optional and must not be represented as evidence of physical hardware.

CANONICAL STATE
Keep exactly five named continuous interaction channels: scale s in [0,2], signed approval angle theta in [-360,360] degrees, X tilt alpha and Z tilt beta each in [-90,90] degrees, and priority gain kappa in [0,1]. Initial state is s=1, theta=alpha=beta=0, kappa=0.5. Separate configuration includes a positive reference radius r0 and weight exponent m in {1,2,3}; default r0=1 and m=3. These configuration values are not additional hidden votes. Reject nonfinite/out-of-range imported inputs. Clamp only documented direct gesture updates. Store degrees in the public JSON and convert once to radians for trigonometry.

SEMANTICS AND SIGN
Positive theta is clockwise when viewed from +localY toward the origin in the untilted X–Z reference frame. Use a right-handed geometric rotation Ry(-theta), NOT Ry(theta). Positive/negative approval endpoints are distinct even though both orientations coincide with the starting orientation. Retain signed unwrapped theta; never reconstruct it solely from atan2, a matrix or a quaternion. Clamp beyond one signed revolution. Approval a=theta/360; illustrative temperature T=100a in index units, not Celsius. Apply the sign only once. Color must never be the only carrier of sign.

WEIGHT AND PRIORITY
Compute r=r0*s; V0=2*pi*r0^3/3; V=V0*s^3; area ratio=s^2; volume ratio=s^3; configured W=s^m. Explain m=1 radius, m=2 area, m=3 volume. Default W=V/V0. Never equate doubled radius with doubled volume. Evaluate priority at zero Y rotation: R0=Rz(beta)Rx(alpha). Set u=(alpha+beta)/180 and P=1+kappa*u. Thus P lies in [0,2] and cannot reverse the sign. Baseline B=W*a; final C=W*a*P. X_vote and Z_vote are explicit aliases of C, not physical x and z. Export all three and keep physical coordinates separate. Increasing priority deepens an opposition score; do not describe it as increasing approval.

GEOMETRY AND ORIENTATION
Use a Y-up local hemispherical shell h=r(sin(phi)cos(psi),cos(phi),sin(phi)sin(psi)), phi in [0,pi/2], psi in [0,2pi). Column-vector rotation order is R=Rz(beta)Rx(alpha)Ry(-theta), rightmost first. Apply R to every mesh point. Do not clip the tilted hemisphere against the global Y=0 plane; clipping would change its volume. R must be orthonormal with determinant +1. Export the 3x3 matrix and scalar-first quaternion qR=qz(beta)*qx(alpha)*qy(-theta). Preserve the original theta because orientation alone loses full-turn sign.

COORDINATE OUTPUT
Export crown normal n=(-sin(beta)cos(alpha),cos(beta)cos(alpha),sin(alpha)), crown position p=r*n, and yaw-sensitive meridian b=R(r,0,0). Normalize v=p/r0, not p/r: the zero-scale case must remain safe. Export the stereographic lift q=(2vx,2vy,2vz,|v|^2-1)/(1+|v|^2). Verify |q|=1 and inverse projection q_xyz/(1-q4)=v. Explain that q is a point on S3, NOT the rotation quaternion and NOT a complete encoding of all five channels. The tip ignores theta and kappa. Five controllable dimensions are not five spacetime dimensions or qubits.

SENSITIVITY REPORT
Return the complete gradient of C with respect to scale, theta-degrees, alpha-degrees, beta-degrees and kappa: (m*s^(m-1)*a*P, W*P/360, W*a*kappa/180, W*a*kappa/180, W*a*u). Confirm these against centered finite differences at interior inputs, using one-sided reasoning at bounds. Show both signs of perturbation for each input. Check mixed partials and analytical coordinate derivatives where claimed. Distinguish derivatives per radian from derivatives per degree. Do not claim infinite precision; state display rounding and floating-point tolerance.

INTERACTION AND ACCESSIBILITY
Offer visibly labeled approval-drag and tilt-drag modes. Two-pointer pinch can control s; anchor distance must be nonzero. At s=0 pinch alone cannot recover a positive scale, so provide a plus button and numeric input. Provide a labeled slider, editable number field and increment/decrement buttons for every channel, plus keyboard-accessible reset and examples. Touch behavior must not block scrolling outside the instrument. No automatic rotation should alter the stored vote. Focus indicators, reduced-motion handling, signed text, readable contrast and narrow-screen layouts are required. A visualization is supplementary: the report must be usable without seeing or dragging it.

RESULT INTERPRETATION
Show radius, actual model volume, all three relative size measures, approval, temperature index, signed priority, multiplier, baseline score, final score, crown and meridian coordinates, orientation matrix, orientation quaternion, S3 lift and five sensitivities. Explain zero approval, zero weight and zero priority as different cases. Use the state/model version/configuration as the source of truth for exported results. Do not send selector inputs to site analytics, query strings, logs, cookies or server endpoints. Plain page analytics, if any, must be disclosed separately.

WORKED FIXTURES
Verify neutral baseline; theta=+360 and -360 with matching visual orientations and opposite score; s=0.5,theta=180,neutral tilt under m=3; s=1,theta=180,alpha=beta=45,kappa=0.5; s=1.5,theta=-120,alpha=-30,beta=0,kappa=0.6; alpha=-beta cancellation; s=0; kappa=1 with both tilts=-90 giving P=0. Calculate expected results from the equations, never invent them. Test exponent alternatives, radius calibration, quaternion/matrix equivalence, deterministic repeatability, finite outputs, geometry norms and invalid input rejection.

AGGREGATION AND ETHICS
If showing a collection, compute S=sum(WPa), D=sum(WP), M=S/D only for D>0; otherwise return no result. Report disagreement as well as mean. Treat dating affinity as separate from mutual consent; refusal and withdrawal override any score. Label pre-legislative examples as nonbinding consultation. Never claim electoral certification, representative sampling, strategy-proofness, fairness, human-level precision or quantum advantage from the formula. Production identity, coercion resistance, audit trails, privacy and budgets are additional systems, not implied features of this demo.

ACCEPTANCE EVIDENCE
Supply executable unit tests; browser evidence that all controls update the report; real JSON export and source download; endpoint sign preservation; narrow-screen layout checks; and explicit statements of what was not tested. Verify that control changes trigger no inference/API requests. Retain the source material and cite external geometry, accessibility and voting-system standards with numbered Chicago notes in first-appearance order plus an alphabetized bibliography. Do not claim tests passed before running them.