From ef4b7b7386e6bc53e338c8f0d46f66920774b2f8 Mon Sep 17 00:00:00 2001
From: oppiliappan <me@oppi.li>
Date: Thu, 22 Oct 2026 13:28:10 +0100
Subject: [PATCH] web: incorporate new cta flourish

some updates from the design team


Signed-off-by: oppiliappan <me@oppi.li>
---
 .../landing/assets/cta-flourish.svg           |   1 -
 web/src/lib/components/landing/cta/Cta.svelte | 265 ++++++++++--------
 .../lib/components/landing/cta/cta-knot.ts    | 142 +++++++++-
 .../landing/thread/ThreadRail.svelte          |  42 ++-
 .../landing/thread/geometry.test.ts           |  69 ++++-
 .../lib/components/landing/thread/geometry.ts |  32 ++-
 .../landing/thread/thread.svelte.ts           |   3 +
 7 files changed, 412 insertions(+), 142 deletions(-)
 delete mode 100644 web/src/lib/components/landing/assets/cta-flourish.svg

diff --git a/web/src/lib/components/landing/assets/cta-flourish.svg b/web/src/lib/components/landing/assets/cta-flourish.svg
deleted file mode 100644
index 75d65c2a1..000000000
--- a/web/src/lib/components/landing/assets/cta-flourish.svg
+++ /dev/null
@@ -1 +0,0 @@
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\ No newline at end of file
diff --git a/web/src/lib/components/landing/cta/Cta.svelte b/web/src/lib/components/landing/cta/Cta.svelte
index fc4c88b58..be071f2a0 100644
--- a/web/src/lib/components/landing/cta/Cta.svelte
+++ b/web/src/lib/components/landing/cta/Cta.svelte
@@ -1,9 +1,18 @@
 <script lang="ts">
 	import { resolve } from "$app/paths";
 	import { onMount, untrack } from "svelte";
-	import { prefersReducedMotion, Spring } from "svelte/motion";
-	import { LOOSE, PULLED, TIGHT, type CtaState } from "#lib/components/landing/cta/cta-knot.ts";
+	import { cubicInOut } from "svelte/easing";
+	import { prefersReducedMotion, Spring, Tween } from "svelte/motion";
+	import {
+		LOOSE,
+		PULLED,
+		slipknot,
+		TIGHT,
+		type CtaState
+	} from "#lib/components/landing/cta/cta-knot.ts";
 	import { SIGNUP } from "#lib/components/landing/shell/links.ts";
+	import { bezier, straight, trace, type Pt } from "#lib/components/landing/thread/geometry.ts";
+	import Ribbon from "#lib/components/landing/thread/Ribbon.svelte";
 	import { getThread } from "#lib/components/landing/thread/thread.svelte.ts";
 	import EmailForm from "#lib/components/landing/ui/EmailForm.svelte";
 	import Container from "#lib/components/landing/ui/Container.svelte";
@@ -13,9 +22,13 @@
 	 * line runs on into it, bends into "Come" and knots off past "Tangled". Loose, the words
 	 * hang apart and the thread is slack. The words are always there; when the line reaches
 	 * "Come" the thread grows on through them — the hook off "Come", then the link off "get" —
-	 * ties the knot past "Tangled" (the flourish, faded in), and pulling that knot tight pulls
-	 * the words together. Springs, not tweens: each part keeps its momentum through the pull
+	 * runs on out of "Tangled" into a loose slipknot, and yanking that knot tight pulls the
+	 * words together. Springs, not tweens: each part keeps its momentum through the pull
 	 * and the release, so the words slide in and settle with a little give.
+	 *
+	 * Every thread here is the rail's brush (Ribbon): the lead draws on as far as the rail's
+	 * ink runs in; the hook, the link and the knot draw on over tweens, each a share of its
+	 * own length, so the knot stays whole as its springs reshape it.
 	 */
 
 	const thread = getThread();
@@ -32,32 +45,43 @@
 	type Word = "come" | "get" | "tangled";
 	/** In thread order: the pull reaches "Come" first and runs on down the line. */
 	const WORDS: Word[] = ["come", "get", "tangled"];
-	/** A beat after the line reaches "Come" before it pulls (ms). */
-	const DELAY = 150;
 	/** Between one word starting to move and the next (ms). */
-	const STAGGER = 95;
+	const STAGGER = 70;
 	/** How long the hook is held under tension before it's let go (ms). */
-	const HOLD = 500;
+	const HOLD = 360;
+	/** How long the knot is held stretched and turned, from the yank, before it's let go
+	 *  (ms): the tail swings back and settles last, as the words come to rest. */
+	const LET_GO = 420;
 	/**
-	 * Threading it, from the line reaching "Come" (ms): when each thread starts to draw on
-	 * (CSS runs them off `--at`) — the hook off "Come" into "Tangled", then the link off
-	 * "get". The knot is tied as the link lands, and the words pull together as the knot is
-	 * pulled tight.
+	 * Threading it, from the line reaching "Come" (ms): when each thread starts to draw on —
+	 * the hook off "Come" into "Tangled", then the link off "get". As the link lands the line
+	 * runs on out of "Tangled": round the slipknot's loop, then down its bight and back. The
+	 * moment it's tied it's pulled: the knot cinches and the words pull together.
 	 */
-	const AT = { hook: 0, link: 160, knot: 460 };
+	const AT = { hook: 0, link: 120, knot: 270, pull: 580 };
 	/** How long the hook and the link each take to draw on (ms). */
-	const THREADS = 300;
-	/** From the knot showing to it being pulled tight (ms). */
-	const KNOT_PULL = 140;
+	const THREADS = 220;
+	/** Drawing the slipknot (ms): round the loop, down the bight and back. */
+	const KNOT = 310;
+
+	/** How far each thread is drawn on, as a share of its length. */
+	const draw = {
+		hook: new Tween(0, { duration: THREADS, easing: cubicInOut }),
+		link: new Tween(0, { duration: THREADS, easing: cubicInOut }),
+		knot: new Tween(0, { duration: KNOT, easing: cubicInOut })
+	};
 
 	const wordSprings = {
-		come: new Spring(LOOSE.come, feel(1000, 0.2)),
-		get: new Spring(LOOSE.get, feel(1000, 0.2)),
-		tangled: new Spring(LOOSE.tangled, feel(1100, 0.22))
+		come: new Spring(LOOSE.come, feel(820, 0.12)),
+		get: new Spring(LOOSE.get, feel(820, 0.12)),
+		tangled: new Spring(LOOSE.tangled, feel(880, 0.14))
 	};
-	const swoopSpring = new Spring(LOOSE.swoop, feel(550, 0.4));
-	/** Bouncier than the words: the flourish is a loose end, so it swings past and back. */
-	const tiltSpring = new Spring(LOOSE.tilt, feel(650, 0.62));
+	const swoopSpring = new Spring(LOOSE.swoop, feel(480, 0.3));
+	/** Bouncier and slower than the words: the knot's tail is a loose end, so it swings past
+	 *  and back, and it's the last thing to come to rest. */
+	const tiltSpring = new Spring(LOOSE.tilt, feel(680, 0.45));
+	/** The yank: quick off the mark into the stretch, then eases back into tight. */
+	const cinchSpring = new Spring(LOOSE.cinch, feel(520, 0.3));
 
 	/** Threading: the threads drawing on, then the knot. */
 	let written = $state(false);
@@ -66,26 +90,30 @@
 	let timers: ReturnType<typeof setTimeout>[] = [];
 	const later = (fn: () => void, ms: number) => timers.push(setTimeout(fn, ms));
 
-	/** Threads the headline, ties the knot, and pulls it all tight as the knot closes. */
+	/** Threads the headline and ties the knot, then pulls it all tight. */
 	function write() {
 		written = true;
-		later(pull, AT.knot + KNOT_PULL - DELAY);
+		later(() => (draw.hook.target = 1), AT.hook);
+		later(() => (draw.link.target = 1), AT.link);
+		later(() => (draw.knot.target = 1), AT.knot);
+		later(pull, AT.pull);
 	}
 
 	function pull() {
-		WORDS.forEach((w, i) =>
-			later(() => (wordSprings[w].target = TIGHT[w]), DELAY + i * STAGGER)
-		);
-		later(() => {
-			swoopSpring.target = PULLED.swoop;
-		}, DELAY);
+		cinchSpring.target = PULLED.cinch;
+		WORDS.forEach((w, i) => later(() => (wordSprings[w].target = TIGHT[w]), i * STAGGER));
+		swoopSpring.target = PULLED.swoop;
 		later(() => {
 			swoopSpring.target = TIGHT.swoop;
-		}, DELAY + HOLD);
-		// The flourish is yanked round as "Tangled" starts in, and let go a beat after the hook.
-		const tug = DELAY + WORDS.indexOf("tangled") * STAGGER;
+		}, HOLD);
+		// The knot's tail is yanked round as "Tangled" starts in, and held — stretched and
+		// turned — until the words are nearly home, then let go to swing back and settle.
+		const tug = WORDS.indexOf("tangled") * STAGGER;
 		later(() => (tiltSpring.target = PULLED.tilt), tug);
-		later(() => (tiltSpring.target = TIGHT.tilt), tug + 320);
+		later(() => {
+			tiltSpring.target = TIGHT.tilt;
+			cinchSpring.target = TIGHT.cinch;
+		}, tug + LET_GO);
 	}
 
 	/** Straight to a state, no motion: tight for reduced motion. */
@@ -96,6 +124,8 @@
 		for (const w of WORDS) wordSprings[w].set(state[w], { instant: true });
 		swoopSpring.set(state.swoop, { instant: true });
 		tiltSpring.set(state.tilt, { instant: true });
+		cinchSpring.set(state.cinch, { instant: true });
+		for (const t of Object.values(draw)) void t.set(state === TIGHT ? 1 : 0, { duration: 0 });
 	}
 
 	const knot = $derived({
@@ -112,21 +142,25 @@
 	let come: HTMLElement | undefined = $state();
 	let get: HTMLElement | undefined = $state();
 	let tangled: HTMLElement | undefined = $state();
-	/** The words' laid-out boxes (tight, no offset) relative to the CTA, the em, the T's width
-	 *  and the rail's x in the CTA. */
+	let tie: HTMLElement | undefined = $state();
+	/** The words' laid-out boxes (tight, no offset) relative to the CTA, the em, the T's width,
+	 *  where the knot is tied off "Tangled" (from the word's corner) and the rail's x in the
+	 *  CTA. */
 	let base = $state<{
 		come: Box;
 		get: Box;
 		tangled: Box;
 		em: number;
 		tee: number;
+		tie: readonly [number, number];
 		x0: number;
 	} | null>(null);
 
 	function measure() {
 		// The word's text, inside its embossed span.
 		const tee = tangled?.firstElementChild?.firstChild;
-		if (!cta || !heading || !come || !get || !tangled || !tee || !thread.els.root) return;
+		if (!cta || !heading || !come || !get || !tangled || !tie || !tee || !thread.els.root)
+			return;
 		const cr = cta.getBoundingClientRect();
 		const em = parseFloat(getComputedStyle(heading).fontSize);
 		// Measured mid-animation, so take the offset it's laid out with back out: read off the
@@ -148,13 +182,17 @@
 		t.setStart(tee, 0);
 		t.setEnd(tee, 1);
 		const root = thread.els.root.getBoundingClientRect();
+		// The knot's anchor and the word move together, so their offset holds mid-animation.
+		const tr = tangled.getBoundingClientRect();
+		const kr = tie.getBoundingClientRect();
 		base = {
 			come: box(come),
 			get: box(get),
-			// "Tangled" rides with its flourish, moved by their wrapper.
+			// "Tangled" rides with its knot, moved by their wrapper.
 			tangled: box(tangled, tangled.parentElement ?? tangled),
 			em,
 			tee: t.getBoundingClientRect().width,
+			tie: [kr.left - tr.left, kr.top - tr.top],
 			x0: thread.railX - (cr.left - root.left)
 		};
 	}
@@ -186,15 +224,39 @@
 		const ex = t.l + base.tee * 0.9;
 		const ey = t.t + em * 0.08;
 		const { reach, belly } = knot.swoop;
+		const tied = slipknot(
+			t.l + base.tie[0],
+			t.t + base.tie[1],
+			cinchSpring.current,
+			tiltSpring.current
+		);
+		// Down, round the bend (≈ a quarter circle), along to "Come".
+		const corner: Pt = [x0, cy - bend];
+		const turned: Pt = [x0 + bend, cy];
 		return {
-			// Down, round the bend (≈ a quarter circle), along to "Come".
-			leadLen: cy - bend + bend * 1.55 + (lead - x0 - bend),
-			paths: [
-				`M${x0},0 L${x0},${cy - bend} C${x0},${cy - bend * 0.35} ${x0 + bend * 0.35},${cy} ${x0 + bend},${cy} L${lead},${cy}`,
-				`M${hx},${hy} C${hx + (ex - hx) * reach},${hy + belly * em} ${ex},${hy + (ey - hy) * 0.2} ${ex},${ey}`,
-				// Never backwards, if "Tangled" overshoots in towards "get".
-				`M${g.r + em * 0.11},${gy} L${Math.max(g.r + em * 0.11, t.l - em * 0.11)},${gy}`
-			]
+			lead: trace([
+				[x0, 0],
+				corner,
+				...bezier(
+					[corner, [x0, cy - bend * 0.35], [x0 + bend * 0.35, cy], turned],
+					Math.max(8, Math.ceil(bend))
+				).slice(1),
+				[lead, cy]
+			]),
+			hook: trace(
+				bezier(
+					[
+						[hx, hy],
+						[hx + (ex - hx) * reach, hy + belly * em],
+						[ex, hy + (ey - hy) * 0.2],
+						[ex, ey]
+					],
+					48
+				)
+			),
+			// Never backwards, if "Tangled" overshoots in towards "get".
+			link: straight([g.r + em * 0.11, gy], [Math.max(g.r + em * 0.11, t.l - em * 0.11), gy]),
+			tied
 		};
 	});
 
@@ -203,11 +265,11 @@
 	 * reduced motion the line stands whole, so the lead is all there.
 	 */
 	const spill = $derived(
-		prefersReducedMotion.current && parts ? parts.leadLen + 1 : thread.spill
+		prefersReducedMotion.current && parts ? parts.lead.total + 1 : thread.spill
 	);
-	const arrived = $derived(!!parts && spill >= parts.leadLen - 1);
+	const arrived = $derived(!!parts && spill >= parts.lead.total - 1);
 	$effect(() => {
-		thread.lead = parts?.leadLen ?? 0;
+		thread.lead = parts?.lead.total ?? 0;
 	});
 
 	// The line reaching "Come" is what writes it out and pulls the knot tight.
@@ -225,7 +287,8 @@
 		const ro = new ResizeObserver(measure);
 		if (cta) ro.observe(cta);
 		const io = new IntersectionObserver(
-			() => {
+			(entries) => {
+				if (entries.some((e) => e.isIntersecting)) thread.reached = true;
 				// Once pulled tight it stays tight: scrolling back up doesn't undo it.
 				if (prefersReducedMotion.current) jump(TIGHT);
 			},
@@ -253,26 +316,24 @@
 >
 	<svg class="cta-thread" aria-hidden="true">
 		{#if parts}
-			{@const [leadD, ...rest] = parts.paths}
-			<path
-				d={leadD}
-				stroke-dasharray="{spill} {parts.leadLen + 1}"
-				visibility={spill > 0.5 ? "visible" : "hidden"}
-			/>
-			{@const [hook, link] = rest}
-			<path
-				class="drawn"
-				d={hook}
-				pathLength="1"
-				style:--at="{AT.hook}ms"
-				style:--for="{THREADS}ms"
+			{@const { lead, hook, link, tied } = parts}
+			<Ribbon line={lead} drawn={spill} seed={7} taper={[0, 0]} />
+			<Ribbon line={hook} drawn={draw.hook.current * hook.total} seed={3} taper={[4, 6]} />
+			<Ribbon
+				line={link}
+				drawn={draw.link.current * link.total}
+				seed={4}
+				width={2}
+				swell={0.3}
+				taper={[16, 16]}
 			/>
-			<path
-				class="drawn"
-				d={link}
-				pathLength="1"
-				style:--at="{AT.link}ms"
-				style:--for="{THREADS}ms"
+			<Ribbon
+				line={tied.line}
+				drawn={draw.knot.current * tied.line.total}
+				seed={6}
+				swell={0.08}
+				taper={[0, 6]}
+				profile={tied.weight}
 			/>
 		{/if}
 	</svg>
@@ -289,12 +350,7 @@
 					><span class="tw" style:translate={shift(knot.tangled)}
 						><span class="w" bind:this={tangled}
 							><span class="solid">Tangled</span></span
-						><span
-							class="flourish"
-							aria-hidden="true"
-							style:--at="{AT.knot}ms"
-							style:rotate="{tiltSpring.current}deg"
-						></span></span
+						><span class="tie" aria-hidden="true" bind:this={tie}></span></span
 					></span
 				>
 			</h2>
@@ -328,56 +384,23 @@
 		pointer-events: none;
 		z-index: 1;
 	}
-	.cta-thread path {
-		fill: none;
-		stroke: var(--thread);
-		stroke-width: 1.8;
-		stroke-linecap: round;
-		stroke-linejoin: round;
-	}
 
-	/* Threading it: each thread draws on in turn from `--at`, through words that are always
-	   there. Only once mounted with motion; reduced motion and no script show it threaded. */
-	/* "Tangled" and its flourish move together on the spring; the flourish sits outside the
-	   word, past its box. The flourish: a fixed
-	   41 × 91 mark 4px past the word, its knot level with the letters — 31px down the line
-	   on desktop, ~10 on the smaller type. It's the exported mark as a mask, filled with the
-	   thread's colour so it follows the theme, and it fades in where the knot is tied. */
+	/* Threading it: each thread draws on in turn, through words that are always there. Only
+	   once mounted with motion; reduced motion and no script show it threaded. */
+	/* "Tangled" and its knot move together on the spring. The knot is drawn with the
+	   section's other threads, from this anchor: 4px past the word, with its knot level with
+	   the letters — 31px down the line on desktop, ~10 on the smaller type — where the mark
+	   it replaced sat (a fixed 41 × 91 box). */
 	.tw {
 		position: relative;
 		display: inline-block;
 	}
-	.flourish {
+	.tie {
 		position: absolute;
 		left: calc(100% + 4px);
 		top: 10px;
-		z-index: 1;
-		width: 41.3px;
-		height: 91.04px;
-		background: var(--thread);
-		mask: url("../assets/cta-flourish.svg") 0 0 / 100% 100% no-repeat;
-		/* Turned about its knot, where it's tied off at the top. */
-		transform-origin: 20% 8%;
-		pointer-events: none;
-	}
-	.armed .flourish {
-		opacity: 0;
-	}
-	.armed.written .flourish {
-		opacity: 1;
-		transition: opacity 0.4s ease var(--at);
-	}
-	.armed .drawn {
-		stroke-dasharray: 1;
-		stroke-dashoffset: 1;
-		visibility: hidden;
-	}
-	.armed.written .drawn {
-		stroke-dashoffset: 0;
-		visibility: visible;
-		transition:
-			stroke-dashoffset var(--for) var(--ease-in-out) var(--at),
-			visibility 0s var(--at);
+		width: 0;
+		height: 0;
 	}
 
 	.heading {
@@ -401,8 +424,8 @@
 		margin-top: -0.055em;
 	}
 	/* Phones: a longer line from "get" — 45px at 375 — so "Tangled"'s
-	   flourish hangs clear of the copy under it. It gives way on narrower screens so the
-	   flourish stays on the page. */
+	   knot hangs clear of the copy under it. It gives way on narrower screens so the
+	   knot stays on the page. */
 	@media (width < 48rem) {
 		/* Pulled up into the section above's padding; the footer's own 40px top padding
 		   adds to the room under the button. */
@@ -418,7 +441,7 @@
 		.l2 {
 			gap: var(--pull-gap);
 		}
-		/* Where the gap gives way, the copy narrows with it, to end short of the flourish:
+		/* Where the gap gives way, the copy narrows with it, to end short of the knot:
 		   "get" (69) + gap + "Tangled" (162) + 4, less 8px of air, at the 48px type. */
 		.cta .copy {
 			max-width: min(300px, var(--pull-gap) + 227px);
@@ -438,7 +461,7 @@
 	}
 
 	@media (width >= 64rem) {
-		.flourish {
+		.tie {
 			top: 31px;
 		}
 		/* The page's rhythm above; the footer sits 96px under the button, which hangs 8px
diff --git a/web/src/lib/components/landing/cta/cta-knot.ts b/web/src/lib/components/landing/cta/cta-knot.ts
index 6b4475787..40545b29a 100644
--- a/web/src/lib/components/landing/cta/cta-knot.ts
+++ b/web/src/lib/components/landing/cta/cta-knot.ts
@@ -2,13 +2,18 @@
  * The knotted CTA: "Come get Tangled" tied together by the rail's thread.
  * Loose, the words hang apart and the thread is slack. When the thread arrives it pulls:
  * the words slide together on springs, "Tangled" in close to "get"; the hook off "Come" is
- * drawn taut and eases back. The flourish off "Tangled" is the exported mark, riding with it:
- * yanked round its knot as it's cinched, then swinging back to hang.
+ * drawn taut and eases back. Off "Tangled" the line ties a slipknot, riding with the word:
+ * drawn on loose — an open loop standing off the word, a short bight hanging under it —
+ * then cinched: the loop collapses to a knot as its slack is pulled down into the bight,
+ * which drops long. Yanked round its knot as it's cinched, it swings back to hang.
  *
  * Word offsets and the hook are in em of the headline, so the pull scales with the type.
+ * The knot is in px, like the rail's: the line's brush is the same at every type size.
  * Tight is the laid-out position (no offset).
  */
 
+import { bezier, trace, type Line, type Pt } from "#lib/components/landing/thread/geometry.ts";
+
 type Offset = readonly [dx: number, dy: number];
 
 /** The hook off "Come" onto the top of the "T": how far along it runs before it turns down
@@ -24,8 +29,10 @@ export interface CtaState {
 	get: Offset;
 	tangled: Offset;
 	swoop: Swoop;
-	/** The flourish off "Tangled", turned about its knot (deg, clockwise). */
+	/** The slipknot off "Tangled", turned about its knot (deg, clockwise). */
 	tilt: number;
+	/** How far the slipknot is pulled: 0 loose, 1 tight (a spring can carry it past). */
+	cinch: number;
 }
 
 export const LOOSE: CtaState = {
@@ -33,14 +40,16 @@ export const LOOSE: CtaState = {
 	get: [-0.42, 0.08],
 	tangled: [1.5, 0.08],
 	swoop: { reach: 0.9, belly: 0.22 },
-	tilt: 8
+	tilt: 8,
+	cinch: 0
 };
 
-/** Under tension, mid-pull: where the hook is drawn, and the flourish yanked round, before
- *  they're let go. */
-export const PULLED: Pick<CtaState, "swoop" | "tilt"> = {
+/** Under tension, mid-pull: where the hook is drawn, and the slipknot yanked — stretched
+ *  past tight and turned round — before they're let go. */
+export const PULLED: Pick<CtaState, "swoop" | "tilt" | "cinch"> = {
 	swoop: { reach: 0.6, belly: -0.06 },
-	tilt: -14
+	tilt: -14,
+	cinch: 1.22
 };
 
 export const TIGHT: CtaState = {
@@ -48,5 +57,120 @@ export const TIGHT: CtaState = {
 	get: [0, 0],
 	tangled: [0, 0],
 	swoop: { reach: 0.75, belly: 0 },
-	tilt: 0
+	tilt: 0,
+	cinch: 1
 };
+
+const lerp = (a: number, b: number, t: number) => a + (b - a) * t;
+
+export interface Slipknot {
+	/** One line: out of the word, round the loop, back across itself, down the bight and
+	 *  back up into the knot. */
+	line: Line;
+	/** The brush along it: even round the loop, heavy down the near strand, light back up
+	 *  the far one, as in the mark. */
+	weight: (s: number, total: number) => number;
+	/** The knot's centre: what the tilt turns about. */
+	knot: Pt;
+}
+
+/** Points round a circle, from `from` to `to` (radians, screen angles: y down). */
+function arc(cx: number, cy: number, r: number, from: number, to: number): Pt[] {
+	const n = Math.max(8, Math.ceil((Math.abs(to - from) * r) / 1.5));
+	const out: Pt[] = [];
+	for (let i = 0; i <= n; i++) {
+		const a = from + ((to - from) * i) / n;
+		out.push([cx + r * Math.cos(a), cy + r * Math.sin(a)]);
+	}
+	return out;
+}
+
+/**
+ * The slipknot off "Tangled", as lines for the ribbon: the line comes out of the word,
+ * loops up and round anticlockwise, cuts back down across itself and hangs in a bight —
+ * a teardrop, the near strand dropping nearly straight, the far one running out and back
+ * up into the knot. `ax`/`ay` is the knot's anchor — 4px past the word, level with its
+ * letters — and tight, it sits where the exported mark did (a 41 × 91 box, its knot ~5
+ * in from the corner).
+ *
+ * Cinching takes the slack out of the loop and lets it down into the bight: the loop's
+ * radius falls from 11 to 4 while the bight drops ~30px on each strand. Past 1 the loop
+ * bites smaller still and the bight overshoots, then springs back. The tail — everything
+ * after the loop — is turned by `tilt` about the knot.
+ */
+export function slipknot(ax: number, ay: number, cinch: number, tilt: number): Slipknot {
+	const c = cinch;
+	const r = Math.max(2.6, lerp(11, 4, c));
+	// Where the line leaves the word: the letters' mid-height. The loop stands up off it,
+	// and drifts right as it grows so its near side clears the word.
+	const sy = ay + 9.5;
+	const kx = ax + 5.5 + (r - 4);
+	const ky = sy - r;
+	// The bight: its round bottom drops as it's pulled, and narrows a little.
+	const ru = lerp(13, 10, c);
+	const uy = lerp(ay + 48, ay + 81, c);
+	const lx = ax + 22 - ru;
+	const rx = ax + 22 + ru;
+
+	const a = (tilt * Math.PI) / 180;
+	const cos = Math.cos(a);
+	const sin = Math.sin(a);
+	const turn = ([x, y]: Pt): Pt => {
+		const dx = x - kx;
+		const dy = y - ky;
+		return [kx + dx * cos - dy * sin, ky + dx * sin + dy * cos];
+	};
+
+	// Out of the loop at 135° (its lower left), heading down and right at 45°: straight
+	// across the line it came in on, then on down the near strand.
+	const h = Math.SQRT1_2;
+	const exit: Pt = [kx - h * r, ky + h * r];
+	const across = 0.414 * r + 4;
+	const out: Pt = [exit[0] + h * across, exit[1] + h * across];
+	const reach = 8 + r * 0.6;
+	// Back into the knot at its lower right, heading up and left.
+	const into: Pt = [kx + h * r, ky + h * r];
+	const drop = uy - out[1];
+	const rise = uy - into[1];
+
+	const loop: Pt[] = [
+		[ax - 6, sy],
+		[kx, sy],
+		// Anticlockwise from the bottom (90°) round to 135°: 315° of it.
+		...arc(kx, ky, r, Math.PI / 2, Math.PI / 2 - (Math.PI * 7) / 4).slice(1)
+	];
+	const tail: Pt[] = [
+		exit,
+		out,
+		...bezier(
+			[out, [out[0] + h * reach, out[1] + h * reach], [lx + 2.5, uy - 0.55 * drop], [lx, uy]],
+			32
+		).slice(1),
+		...arc(ax + 22, uy, ru, Math.PI, 0).slice(1),
+		...bezier(
+			[
+				[rx, uy],
+				[rx + 4, uy - 0.45 * rise],
+				[into[0] + 0.3 * (rx - into[0]), into[1] + 0.4 * rise],
+				into
+			],
+			32
+		).slice(1)
+	];
+	// Sampled finer than the rail: the loop is small, and the brush's edge is drawn
+	// sample to sample.
+	const line = trace([...loop, ...tail.slice(1).map(turn)], 1);
+	// Even to the loop's end, then heavy to the bottom of the bight and light back up: by
+	// where along the line the loop ends and the bight bottoms out.
+	const loopEnd = trace(loop, 1).total / line.total;
+	const bottom = loopEnd + ((1 - loopEnd) * (tail.length - 34)) / tail.length;
+	const ease = (t: number) => t * t * (3 - 2 * t);
+	const weight = (s: number, total: number) => {
+		const f = s / total;
+		if (f < loopEnd) return 1;
+		const up = ease(Math.max(0, Math.min(1, (f - loopEnd) / 0.06)));
+		const down = ease(Math.max(0, Math.min(1, (f - (bottom - 0.08)) / 0.16)));
+		return lerp(lerp(1, 1.25, up), 0.72, down);
+	};
+	return { line, weight, knot: [kx, ky] };
+}
diff --git a/web/src/lib/components/landing/thread/ThreadRail.svelte b/web/src/lib/components/landing/thread/ThreadRail.svelte
index a82b64567..fdf47cf34 100644
--- a/web/src/lib/components/landing/thread/ThreadRail.svelte
+++ b/web/src/lib/components/landing/thread/ThreadRail.svelte
@@ -1,6 +1,7 @@
 <script lang="ts">
 	import { onMount, untrack } from "svelte";
-	import { prefersReducedMotion, Spring } from "svelte/motion";
+	import { sineInOut } from "svelte/easing";
+	import { prefersReducedMotion, Spring, Tween } from "svelte/motion";
 	import Container from "#lib/components/landing/ui/Container.svelte";
 	import Knot from "#lib/components/landing/thread/Knot.svelte";
 	import Ribbon from "#lib/components/landing/thread/Ribbon.svelte";
@@ -341,7 +342,9 @@
 		released = true;
 		thread.intro = "done";
 	});
-	const target = $derived(whole && layout ? layout.line.total : released ? scrolled : 0);
+	const target = $derived(
+		(whole || thread.reached) && layout ? layout.line.total : released ? scrolled : 0
+	);
 
 	/*
 	 * The line doesn't jump to the scroll — the ink chases it on a spring, drawing on (or
@@ -362,12 +365,37 @@
 	const overrun = $derived.by(() => {
 		if (!layout || !released) return 0;
 		const past = Math.max(0, penY - layout.end);
-		// At the foot of the page there's no more scroll to draw it on with, so it runs the
-		// rest of the way into the CTA itself — on a tall screen the pen can stop short of it.
-		return atBottom ? Math.max(past, thread.lead + 1) : past;
+		// Once the CTA is in view, or at the foot of the page where there's no more scroll to
+		// draw it on with, it runs the rest of the way into the CTA itself.
+		return atBottom || thread.reached ? Math.max(past, thread.lead + 1) : past;
 	});
+
+	/*
+	 * Once the CTA is in view the line runs the rest of the way into it on its own, however
+	 * far that is: one stroke at a steady pen's pace, easing in and out, rather than the
+	 * spring's catch-up (which snaps to within `INK_LAG` and then whips off).
+	 */
+	const PACE = 1.2;
+	const run = new Tween(0, { easing: sineInOut });
+	let running = $state(false);
+	let runTo = 0;
+	const inked = $derived(running ? run.current : ink.current);
+
 	$effect(() => {
 		const to = target + overrun;
+		if (thread.reached && !prefersReducedMotion.current) {
+			runTo = to;
+			if (untrack(() => running)) {
+				if (untrack(() => run.current === run.target)) void run.set(to, { duration: 0 });
+				return;
+			}
+			const from = untrack(() => ink.current);
+			running = true;
+			void run.set(from, { duration: 0 });
+			const duration = Math.min(1400, Math.max(450, Math.abs(to - from) / PACE));
+			void run.set(to, { duration }).then(() => run.set(runTo, { duration: 0 }));
+			return;
+		}
 		const lag = to - untrack(() => ink.current);
 		const h = untrack(() => vh);
 		if (prefersReducedMotion.current || Math.abs(lag) > 1.5 * h) {
@@ -379,7 +407,7 @@
 		ink.target = to;
 	});
 
-	const drawn = $derived(Math.min(ink.current, layout?.line.total ?? 0));
+	const drawn = $derived(Math.min(inked, layout?.line.total ?? 0));
 
 	/* How far the line has run on into the CTA. */
 	$effect(() => {
@@ -387,7 +415,7 @@
 			thread.spill = 0;
 			return;
 		}
-		const spill = Math.max(0, ink.current - layout.line.total);
+		const spill = Math.max(0, inked - layout.line.total);
 		// Once it's run all the way in, it stays run in.
 		thread.spill = thread.finished
 			? Math.max(
diff --git a/web/src/lib/components/landing/thread/geometry.test.ts b/web/src/lib/components/landing/thread/geometry.test.ts
index c9ce7ee4e..ce1d7078a 100644
--- a/web/src/lib/components/landing/thread/geometry.test.ts
+++ b/web/src/lib/components/landing/thread/geometry.test.ts
@@ -1,11 +1,13 @@
 import { describe, expect, it } from "vitest";
 import {
+	bezier,
 	join,
 	lengthAtY,
 	polyline,
 	ribbon,
 	sample,
-	straight
+	straight,
+	trace
 } from "#lib/components/landing/thread/geometry.ts";
 
 describe("sample", () => {
@@ -32,6 +34,47 @@ describe("sample", () => {
 	});
 });
 
+describe("trace", () => {
+	it("walks a drawn-out curve at an even step", () => {
+		const line = trace(
+			bezier(
+				[
+					[0, 0],
+					[0, 10],
+					[10, 10],
+					[10, 20]
+				],
+				40
+			),
+			2
+		);
+		expect(line.pts[0]).toEqual([0, 0]);
+		expect(line.pts[line.pts.length - 1]).toEqual([10, 20]);
+		for (let i = 1; i < line.len.length - 1; i++)
+			expect(line.len[i] - line.len[i - 1]).toBeCloseTo(2);
+		expect(line.total).toBeGreaterThan(Math.hypot(10, 20));
+	});
+});
+
+describe("bezier", () => {
+	it("runs from the start to the end through the hull", () => {
+		const pts = bezier(
+			[
+				[0, 0],
+				[0, 10],
+				[10, 10],
+				[10, 0]
+			],
+			4
+		);
+		expect(pts).toHaveLength(5);
+		expect(pts[0]).toEqual([0, 0]);
+		expect(pts[4]).toEqual([10, 0]);
+		expect(pts[2][0]).toBeCloseTo(5);
+		expect(pts[2][1]).toBeCloseTo(7.5);
+	});
+});
+
 describe("join", () => {
 	it("runs the lengths on and drops the shared point", () => {
 		const a = straight([0, 0], [0, 4]);
@@ -91,6 +134,30 @@ describe("ribbon", () => {
 		expect(ribbon(line, { seed: 3 })).toBe(ribbon(line, { seed: 3 }));
 		expect(ribbon(line, { seed: 3 })).not.toBe(ribbon(line, { seed: 4 }));
 	});
+
+	it("weighs the brush along the line by its profile", () => {
+		const widths = (d: string) => {
+			const xs = [...d.matchAll(/(-?[\d.]+) (-?[\d.]+)/g)].map((m) => [
+				Number(m[1]),
+				Number(m[2])
+			]);
+			const n = xs.length / 2;
+			// Out along one edge, back along the other: pair each sample with its twin.
+			return xs.slice(0, n).map(([x], i) => Math.abs(x - xs[xs.length - 1 - i][0]));
+		};
+		const plain = widths(ribbon(line, { swell: 0, fray: 0, taper: [0, 0] }));
+		const heavyToLight = widths(
+			ribbon(line, {
+				swell: 0,
+				fray: 0,
+				taper: [0, 0],
+				profile: (s, total) => (s < total / 2 ? 2 : 0.5)
+			})
+		);
+		const n = plain.length;
+		expect(heavyToLight[2]).toBeCloseTo(plain[2] * 2);
+		expect(heavyToLight[n - 3]).toBeCloseTo(plain[n - 3] * 0.5);
+	});
 });
 
 describe("polyline", () => {
diff --git a/web/src/lib/components/landing/thread/geometry.ts b/web/src/lib/components/landing/thread/geometry.ts
index 29a4779bf..2de5bec1c 100644
--- a/web/src/lib/components/landing/thread/geometry.ts
+++ b/web/src/lib/components/landing/thread/geometry.ts
@@ -11,7 +11,7 @@
 
 export type Pt = readonly [x: number, y: number];
 
-type Cubic = readonly [Pt, Pt, Pt, Pt];
+export type Cubic = readonly [Pt, Pt, Pt, Pt];
 
 /**
  * Cubic segments through the points. Each handle runs along its point's tangent for a
@@ -57,6 +57,13 @@ function at([p0, p1, p2, p3]: Cubic, t: number): Pt {
 	];
 }
 
+/** `n` points along a cubic, from its start to its end. */
+export function bezier(c: Cubic, n: number): Pt[] {
+	const out: Pt[] = [];
+	for (let i = 0; i <= n; i++) out.push(at(c, i / n));
+	return out;
+}
+
 /** A line sampled every `step` px along its length, with the running length at each sample. */
 export interface Line {
 	pts: Pt[];
@@ -79,6 +86,13 @@ export function sample(
 		const n = Math.max(4, Math.ceil(chord / 1.5));
 		for (let i = 1; i <= n; i++) dense.push(at(c, i / n));
 	}
+	return trace(dense, step);
+}
+
+/** Walks a dense polyline at an even `step` of arc length: a line as `sample` gives, for a
+ *  curve already drawn out point by point (an arc, a cubic). */
+export function trace(dense: readonly Pt[], step = 2): Line {
+	if (dense.length < 2) return { pts: [...dense], len: dense.map(() => 0), total: 0 };
 	const out: Pt[] = [dense[0]];
 	const len = [0];
 	let walked = 0;
@@ -216,6 +230,9 @@ export interface RibbonOptions {
 	seed?: number;
 	/** Taper over this many px at the start / end. */
 	taper?: readonly [start: number, end: number];
+	/** The brush's weight along the line, as a factor of its width at `s` px of `total`:
+	 *  a stroke that runs thick into thin. */
+	profile?: (s: number, total: number) => number;
 }
 
 /**
@@ -224,7 +241,14 @@ export interface RibbonOptions {
  */
 export function ribbon(
 	{ pts, len, total }: Line,
-	{ width = 1.8, swell = 0.16, fray = 0.16, seed = 1, taper = [3, 3] }: RibbonOptions = {}
+	{
+		width = 1.8,
+		swell = 0.16,
+		fray = 0.16,
+		seed = 1,
+		taper = [3, 3],
+		profile
+	}: RibbonOptions = {}
 ): string {
 	if (pts.length < 2) return "";
 	const slow = noise(seed);
@@ -245,7 +269,9 @@ export function ribbon(
 			taper[0] ? Math.min(1, s / taper[0]) : 1,
 			taper[1] ? Math.min(1, (total - s) / taper[1]) : 1
 		);
-		const half = (width / 2) * (1 + swell * (slow(s / 46) * 2 - 1)) * (0.35 + 0.65 * ends);
+		const weight = profile ? profile(s, total) : 1;
+		const half =
+			(width / 2) * weight * (1 + swell * (slow(s / 46) * 2 - 1)) * (0.35 + 0.65 * ends);
 		const l = half + fray * (quickL(s / 2.2) - 0.5);
 		const r = half + fray * (quickR(s / 2.6) - 0.5);
 		const [x, y] = pts[i];
diff --git a/web/src/lib/components/landing/thread/thread.svelte.ts b/web/src/lib/components/landing/thread/thread.svelte.ts
index cc8d98503..bae91d721 100644
--- a/web/src/lib/components/landing/thread/thread.svelte.ts
+++ b/web/src/lib/components/landing/thread/thread.svelte.ts
@@ -52,6 +52,9 @@ export class Thread {
 	/** The CTA's lead: how far the line runs into it, from the rail to "Come" (px). The CTA
 	 *  sets it, so the rail can run the line all the way in at the foot of the page. */
 	lead = $state(0);
+	/** The CTA has come into view (the CTA sets it): the line runs the rest of the way into it
+	 *  then and there, whatever the scroll. */
+	reached = $state(false);
 	/** The rail's x on the page, where the CTA picks the thread up. */
 	railX = $state(0);
 	/**
-- 
2.54.0