gojo 1;

// Establish a native line from a point, then an ordered segment on that line.
// No page direction, Euclidean metric or world coordinate grid is selected.
let $origin = point(carrier(),0);
let $line = crystal(orthogonal($origin -> $origin));
let $a = point($line,0);
let $b = point($line,6);
let $edge = $a -> $b;
let $origin_attachment = $origin -> $a;

// Choose a line participation through the segment's orthogonal possibility.
// Its opposite is structurally available; neither direction means screen-up.
let $outlet = orthogonal($edge);
let $cross = crystal(orthogonal($a -> $a));
let $cross_start = point($cross,0);
let $d = point($cross,4);
let $cross_span = $cross_start -> $d;
let $selection = $outlet -> $cross_span;
let $common_origin = $a -> $cross_start;

// In a selected affine product read, these are independent coordinate roles.
// The reader checks their attachments and freezes the ordered native spans.
// It does not infer a physical metric or discover independence from measurements.
let $foundation = group($edge, $selection, $common_origin);
root group($origin_attachment, $foundation);
root group($edge, $outlet -> ?cross_span, $common_origin);

// Crystallizing the foundation supplies ?basis. One coordinate tick then
// means one WHOLE selected leg, with the native calibration retained.
// These requests read native participation through that established basis.
root group(?basis, group(at($line,0), at($cross,0)));
root group(?basis, group(at($line,6), at($cross,0)));
root group(?basis, group(at($line,0), at($cross,4)));
root group(?basis, group(at($line,6), at($cross,4)));
root group(?basis, group(at($line,3), at($cross,2)));
root group(?basis, group(at($line,3), ?unobserved_cross));
root group(?basis, ?unobserved_point);

// The opposite ordered cross-span selects another valid coordinate convention.
// Signed locations, reversed frames and an opposed carrier face remain distinct.
let $opposite_cross = $cross_start -> point($cross,-4);
root group($edge, $outlet -> $opposite_cross, $common_origin);

// The original six-edge procedure consumes points in the justified basis.
let $parameter = carrier();
let $domain = span($parameter,0,1000);
let $grade = group(?sample, $domain, $domain, ?basis);
let $ab = ports(?start, ?control_a, $grade) -> ?q0;
let $bc = ports(?control_a, ?control_b, $grade) -> ?q1;
let $cd = ports(?control_b, ?end, $grade) -> ?q2;
let $abc = ports(?q0, ?q1, $grade) -> ?r0;
let $bcd = ports(?q1, ?q2, $grade) -> ?r1;
let $result = ports(?r0, ?r1, $grade) -> ?curve_point;
let $construction = action(
    ports(?start, ?control_a, ?control_b, ?end, $grade),
    frame($ab,$bc,$cd,$abc,$bcd,$result),
    ports(?curve_point), ?interpolation_residue_policy, $domain);
root group($construction, frame(bind(?sample,at($parameter,500))),
    frame(?basis,?start,?control_a,?control_b,?end));