diff --git a/components/graph-canvas.ts b/components/graph-canvas.ts
index d058059..3056716 100644
--- a/components/graph-canvas.ts
+++ b/components/graph-canvas.ts
@@ -623,6 +623,10 @@ export class GraphCanvasRenderer {
 	private builtVersion = -1; // version the cache was built at
 	private nodesPath: Path2D | null = null;
 	private shaftsPath: Path2D = new Path2D();
+	/** Supports shafts draw THINNER (owner, 2026-09-29): their own path +
+	 *  stroke pass at edgeWidth × supportsWidth. Arrowheads share the one
+	 *  heads path at full geometry (owner pick: shaft only). */
+	private supportsShaftsPath: Path2D = new Path2D();
 	private headsPath: Path2D = new Path2D();
 	private regionCanvas: HTMLCanvasElement | null = null;
 	/** World rect the bitmap covers (drawImage target coords). */
@@ -1232,11 +1236,14 @@ export class GraphCanvasRenderer {
 		// Edge shafts + arrowheads: tip lands on the target disc edge. Both
 		// relation types draw the same arrow for now — the double-shaft
 		// glyph was rejected (2026-09-15); differentiation is pending a new
-		// approach. CanvasEdge.type is plumbed for whatever comes next —
-		// except the supports draw toggle (owner, 2026-09-29): off skips
-		// the paths entirely (a draw-only hide; the sim still feels them).
+		// approach. Two owner rulings 2026-09-29: the supports draw toggle
+		// (off skips the paths entirely — a draw-only hide; the sim still
+		// feels them) and the supports SHAFT thickness split (supports get
+		// their own path stroked at edgeWidth × supportsWidth; heads stay
+		// full-geometry in the one shared path).
 		const arrowLen = settings.arrowLength;
 		const shafts = new Path2D();
+		const supportsShafts = new Path2D();
 		const heads = new Path2D();
 		for (const e of data.edges) {
 			if (!settings.showSupports && e.type === "supports") continue;
@@ -1246,14 +1253,16 @@ export class GraphCanvasRenderer {
 			if (!a || !b) continue;
 			const g = arrowGeometry(a, b, nodeR, nodeR, arrowLen);
 			if (!g) continue;
-			shafts.moveTo(g.shaftFrom.x, g.shaftFrom.y);
-			shafts.lineTo(g.shaftTo.x, g.shaftTo.y);
+			const path = e.type === "supports" ? supportsShafts : shafts;
+			path.moveTo(g.shaftFrom.x, g.shaftFrom.y);
+			path.lineTo(g.shaftTo.x, g.shaftTo.y);
 			heads.moveTo(g.tip.x, g.tip.y);
 			heads.lineTo(g.left.x, g.left.y);
 			heads.lineTo(g.right.x, g.right.y);
 			heads.closePath();
 		}
 		this.shaftsPath = shafts;
+		this.supportsShaftsPath = supportsShafts;
 		this.headsPath = heads;
 
 		// Cluster regions are NOT built here: they rasterize into their own
@@ -1620,12 +1629,20 @@ export class GraphCanvasRenderer {
 
 		// 3. Edges: shafts + arrowheads from cached paths; width constant on
 		// screen (÷ k), geometry in world units (scales with the graph).
+		// Supports shafts: a second, thinner stroke (owner, 2026-09-29) —
+		// heads share the one fill at full geometry (shaft-only ruling).
+		// A true 0-width stroke is undefined on canvas: the ratio's 0 end
+		// floors to a hairline (0.5px on screen — hiding is the toggle's).
 		if (settings.edgeWidth > 0) {
 			ctx.strokeStyle = data.colors.edge;
 			ctx.fillStyle = data.colors.edge;
 			ctx.lineWidth = settings.edgeWidth / k;
 			ctx.lineCap = "round";
 			ctx.stroke(this.shaftsPath);
+			if (settings.showSupports) {
+				ctx.lineWidth = Math.max(settings.edgeWidth * settings.supportsWidth, 0.5) / k;
+				ctx.stroke(this.supportsShaftsPath);
+			}
 			ctx.fill(this.headsPath);
 		}
 
diff --git a/components/graph-view.tsx b/components/graph-view.tsx
index 4e55601..c1910a0 100644
--- a/components/graph-view.tsx
+++ b/components/graph-view.tsx
@@ -53,7 +53,8 @@
  * five sliders (node size, edge width, arrowhead length, label size, the
  * zoom threshold), the supports-edges draw toggle (2026-09-29: off hides
  * supports edges from the canvas — draw-only; physics and detail cards
- * still see them), and the cluster-labels checkbox. SERVER-persisted
+ * still see them) with its shaft-thickness slider (0–1 × Edge width,
+ * default 0.5; heads stay full), and the cluster-labels checkbox. SERVER-persisted
  * (data/render-settings.json via /api/graph/render-settings): loaded
  * once after mount, saved debounced on every user change — one source
  * of truth shared by every browser. The label-zoom slider is log-scaled
@@ -532,7 +533,7 @@ function GraphSettingsControl({
 							/>
 							{/* Supports draw toggle (owner, 2026-09-29): hides the single-line
 							    supports edges from the canvas — follows (⟹-meant) stay. Draw-only:
-							    physics + detail cards still see them. Last row of the FIRST
+							    physics + detail cards still see them. Last rows of the FIRST
 							    section; the border-t below starts Regions. */}
 							<label className="flex cursor-pointer items-center justify-between text-[11px] text-muted-foreground">
 								<span>Supports edges</span>
@@ -544,6 +545,21 @@ function GraphSettingsControl({
 									className="accent-primary"
 								/>
 							</label>
+							{/* Supports shaft thickness (owner, 2026-09-29): a LINEAR 0–1
+							    ratio of Edge width (not a ladder — it's a ratio; default 0.5
+							    dead-center anyway, step 0.1 = 11 stops). Grayed out by the
+							    toggle above (the Dilation pattern); 0 floors to a hairline in
+							    the renderer — arrowheads never scale (shaft-only ruling). */}
+							<SettingSlider
+								label="Supports thickness"
+								disabled={!settings.showSupports}
+								min={0}
+								max={1}
+								step={0.1}
+								value={settings.supportsWidth}
+								display={`${Math.round(settings.supportsWidth * 100) / 100}×`}
+								onChange={(v) => changeSettings((cur) => ({ ...cur, supportsWidth: v }))}
+							/>
 						{/* Regions: the blurred cluster tints. Sliders + a fixed-set
 						    dropdown for the bitmap resolution (it's a discrete
 						    choice, not a free number). Server-persisted like the
diff --git a/src/core/render-settings.ts b/src/core/render-settings.ts
index 3fc09a4..600b33b 100644
--- a/src/core/render-settings.ts
+++ b/src/core/render-settings.ts
@@ -59,6 +59,14 @@ export interface GraphRenderSettings {
 	 *  them (settings never shift the graph: camera, one frame), and node
 	 *  detail cards still list them. */
 	showSupports: boolean;
+	/** Relative SHAFT thickness of supports edges (owner, 2026-09-29):
+	 *  a 0–1 multiplier of edgeWidth — default 0.5, the single-line
+	 *  relation reads as the lighter one. SHAFT ONLY: arrowheads keep
+	 *  full Arrowhead-size geometry (owner pick). Linear, not a ladder —
+	 *  it's a ratio; exactly 0 floors to a hairline in the renderer
+	 *  (canvas cannot stroke a true 0-width line; hiding is the toggle's
+	 *  job). */
+	supportsWidth: number;
 	/** Toggle for the cluster region labels (hulls always draw). */
 	clusterLabels: boolean;
 	/** Cluster label font size, px on screen (camera-compensated —
@@ -102,6 +110,12 @@ export function sanitizeRenderSettings(raw: unknown): GraphRenderSettings {
 		labelSize: legacySizes ? DEFAULT_RENDER_SETTINGS.labelSize : ladd(r.labelSize, LABEL_SIZE_LADDER, DEFAULT_RENDER_SETTINGS.labelSize),
 		showSupports:
 			typeof r.showSupports === "boolean" ? r.showSupports : DEFAULT_RENDER_SETTINGS.showSupports,
+		// Linear ratio, not a ladder: real numbers clamp to [0, 1]; anything
+		// else resets to the default.
+		supportsWidth:
+			typeof r.supportsWidth === "number" && Number.isFinite(r.supportsWidth)
+				? clamp(r.supportsWidth, 0, 1)
+				: DEFAULT_RENDER_SETTINGS.supportsWidth,
 		clusterLabels:
 			typeof r.clusterLabels === "boolean" ? r.clusterLabels : DEFAULT_RENDER_SETTINGS.clusterLabels,
 		clusterLabelSize: ladd(
@@ -270,6 +284,7 @@ export const DEFAULT_RENDER_SETTINGS: GraphRenderSettings = {
 	labelZoom: 4,
 	labelSize: 3,
 	showSupports: true,
+	supportsWidth: 0.5,
 	clusterLabels: true,
 	clusterLabelSize: 14,
 	regions: DEFAULT_REGION_TUNING,
diff --git a/tests/render-settings.test.ts b/tests/render-settings.test.ts
index 011ca1a..a01ee74 100644
--- a/tests/render-settings.test.ts
+++ b/tests/render-settings.test.ts
@@ -119,6 +119,7 @@ describe("sanitizeRenderSettings", () => {
 			labelZoom: 2,
 			labelSize: 4,
 			showSupports: false,
+			supportsWidth: 0.3,
 			clusterLabels: false,
 			clusterLabelSize: 20,
 			regions: DEFAULT_REGION_TUNING,
@@ -137,6 +138,19 @@ describe("sanitizeRenderSettings", () => {
 		assert.equal(sanitizeRenderSettings({ showSupports: 0 }).showSupports, true);
 	});
 
+	test("supportsWidth (2026-09-29): linear 0–1 ratio of edgeWidth, default 0.5", () => {
+		// The supports shaft-thickness multiplier: LINEAR (not a ladder —
+		// it's a ratio), real numbers clamp to [0, 1], anything else resets
+		// to the default. The 0 end floors to a hairline in the renderer.
+		assert.equal(sanitizeRenderSettings({}).supportsWidth, 0.5);
+		assert.equal(sanitizeRenderSettings({ supportsWidth: 0 }).supportsWidth, 0);
+		assert.equal(sanitizeRenderSettings({ supportsWidth: 1 }).supportsWidth, 1);
+		assert.equal(sanitizeRenderSettings({ supportsWidth: 0.37 }).supportsWidth, 0.37);
+		assert.equal(sanitizeRenderSettings({ supportsWidth: 1.7 }).supportsWidth, 1);
+		assert.equal(sanitizeRenderSettings({ supportsWidth: -0.3 }).supportsWidth, 0);
+		assert.equal(sanitizeRenderSettings({ supportsWidth: "thick" }).supportsWidth, 0.5);
+	});
+
 	test("the pre-2026-09-13 stored shape (flat, no regions/physics) still loads", () => {
 		// data/render-settings.json on disk predates the nested sections —
 		// those loads must get defaults, not crash, not shift anything.