Joined offsets

The actual fixture supplies source points, a metric, relative sides, scale wholes and permitted parameter supports. The driver binds one common calibration into the request and selects the path reader. No output corner is authored here.

gojo 1;

// A selected metric chart; all three source edges use its actual basis.
let $space = carrier();
let $x = carrier();
let $y = carrier(unit_of($x));
let $length = carrier(unit_of($x));
let $squared = carrier(product_units(unit_of($x), unit_of($x)));
let $ux = span($x, 0, 1);
let $uy = span($y, 0, 1);
let $metric = group(group_on($space, $ux, $uy), frame(
    ($ux -> $ux) -> at($squared, 1), ($ux -> $uy) -> at($squared, 0),
    ($uy -> $uy) -> at($squared, 1)));

// Source observations, with actual shared corners B and C.
let $a = group_on($space, at($x, 0), at($y, 0));
let $b = group_on($space, at($x, 8), at($y, 0));
let $c = group_on($space, at($x, 8), at($y, 6));
let $d = group_on($space, at($x, 0), at($y, 6));
let $ab = $a -> $b;
let $bc = $b -> $c;
let $cd = $c -> $d;

// Relative guides select the inward side; screen orientation is a view choice.
let $side_ab = $a -> group_on($space, at($x, 0), at($y, 1));
let $side_bc = $b -> group_on($space, at($x, 7), at($y, 0));
let $side_cd = $c -> group_on($space, at($x, 8), at($y, 5));
let $offset_ab = group($ab, $metric, orthogonal($ab) -> ?calibration, $side_ab);
let $offset_bc = group($bc, $metric, orthogonal($bc) -> ?calibration, $side_bc);
let $offset_cd = group($cd, $metric, orthogonal($cd) -> ?calibration, $side_cd);
let $scale_ab = span(carrier(), 0, 1);
let $scale_bc = span(carrier(), 0, 1);
let $scale_cd = span(carrier(), 0, 1);
let $whole_ab = span(carrier(), 0, 1);
let $whole_bc = span(carrier(), 0, 1);
let $whole_cd = span(carrier(), 0, 1);

// One support per source edge. Both corners consume the same middle support.
// The reader must also check the order between the two middle-edge trims.
root group(
    group(group($offset_ab, $scale_ab), group($offset_bc, $scale_bc),
          group($offset_cd, $scale_cd)),
    group($whole_ab -> $whole_ab, $whole_bc -> $whole_bc,
          $whole_cd -> $whole_cd));

// The driver refines the same request with one actual shared calibration.
// These are three separate reads; they do not overwrite earlier witnesses.
let $reach = span(carrier(), 0, 1);
root bind(?calibration, $reach -> span($length, 0, 2));
root bind(?calibration, $reach -> span($length, 0, 3));
root bind(?calibration, $reach -> span($length, 0, 4));

Every candidate edge is an ordered relation. Its corner is the same site used by the neighbouring candidate edge. If a join is unfinished, both use the same open joint slot. Each edge also has an admission witness: its result is either the accepted edge or an open edge slot, with the candidate and failed traversal retained.

source → offset request → preparation + exact offset read
neighbouring offsets + shared source corner + supports → corner read
candidate span + its source frame + allowed support → admission read

At distance 2: [accepted edge, accepted edge, accepted edge]
At distance 3: [accepted edge, open edge, accepted edge]
At distance 4: [accepted edge, open edge, accepted edge]

An irrational offset keeps its normal, squared-scale equation and endpoint recipes. The path reader does not invent a joint by choosing points from independently drawn endpoint boxes.

The fixture constructs the displayed coordinates and all three admission outcomes. Tests check source contact, actual shared joints, support windows, reversed parameter frames, collapsed or reversed spans, partial irrational geometry, captured history and numeric restoration. This browser presents checked kernel traces; it does not run Gojo.

This is an open path with bounded straight miters. Parallel corners, caps, round joins, curved offsets, closed regions and crossings between non-neighbouring edges need further contracts. Accepted local spans do not establish a valid filled region.