feat(m1-2,m1-3): deterministic core + mask keying (TDD, green)

Card 2 (deterministic core) + Card 3 (capture+mask geometry):
- src/lib/core/math.js: scale, sqft, bdft, roundHalfUp, width sampling,
  1/8-inch snap — implemented to docs/CAPTURE.md identities.
- src/lib/core/mask.js: keySheet green/black/auto chroma keys + maskStats.
  - fixed sensitivity scale (0-100, higher = looser = keeps more)
  - fixed inverted green threshold (150 - s)
  - black key drops bright saturated sheets via saturation gate
- tests/unit/math.test.js: corrected 3 wrong expected values to match the
  spec (sqft 21x12in = 1.75 not 17.5; bdft 3.06; sample avg 11.25).
- tests/e2e/mask.spec.js: skeleton, skipped pending M1-5 live UI.

Full unit suite green: 24/24. E2e collects clean.

frontend/tests/unit/math.test.js

@@ -0,0 +1,89 @@
+import { describe, it, expect } from 'vitest';
+import * as m from '$lib/core/math.js';
+
+// M1 deterministic core — unit tests (RED first, per TDD).
+// Ground truth for the math identities is the spec (docs/CAPTURE.md):
+//   scale = longest_axis_px / L
+//   sqft  = (mask_px / scale^2) / 144
+//   bdft  = sqft * thickness_in
+// Widths are sampled every `everyInches` along the approved axis.
+
+describe('scale', () => {
+	it('scale = longest_axis_px / L', () => {
+		expect(m.scale(3360, 84)).toBe(40);
+	});
+	it('scale for fixture-b geometry (21 in)', () => {
+		// 21 in represented as 3360 px -> 160 px/in
+		expect(m.scale(3360, 21)).toBeCloseTo(160, 6);
+	});
+});
+
+describe('sqft', () => {
+	it('sqft = (mask_px / scale^2) / 144, 2 decimals', () => {
+		// scale=40 -> scale^2=1600; 1,000,000/1600=625; /144=4.3403 -> 4.34
+		expect(m.sqft(1_000_000, 40)).toBe(4.34);
+	});
+	it('zero-area mask -> 0', () => {
+		expect(m.sqft(0, 40)).toBe(0);
+	});
+});
+
+describe('bdft', () => {
+	it('bdft = sqft * thickness_in, 2 decimals (identity 1 sqft @ 1in = 1 bdft)', () => {
+		expect(m.bdft(4.34, 1)).toBeCloseTo(4.34, 6);
+		expect(m.bdft(4.34, 2.5)).toBe(10.85);
+	});
+});
+
+describe('e2e fixture math (cand_b: 21in x 1.75in)', () => {
+	// If the slab were a clean rectangle exactly 21in long, at 160px/in that is
+	// 3360 px long. Pick a width of 12in -> 1920px -> area 6,451,200 px.
+	const Lpx = 3360, L = 21, scale = 160, thickness = 1.75;
+	const widthPx = 1920; // 12in
+	const maskPx = Lpx * widthPx; // 6,451,200
+	it('sqft of a 21in x 12in slab = 1.75', () => {
+		expect(m.sqft(maskPx, scale)).toBe(1.75);
+	});
+	it('bdft of that slab at 1.75in = 3.06', () => {
+		const sqft = m.sqft(maskPx, scale);
+		expect(m.bdft(sqft, thickness)).toBe(3.06); // 1.75*1.75=3.0625 -> 3.06 (half-up)
+	});
+});
+
+describe('width sampling', () => {
+	it('samples perpendicular widths at 0,6,12,... in along the axis', () => {
+		// pxPerIn=160. axisLengthPx = 3360 (21in). widthsAt samples every 6in.
+		// Provide a constant width of 1920px (12in) at every sample point.
+		const pxPerIn = 160;
+		const axisLengthPx = 3360;
+		const constantWidthPx = 1920;
+		const out = m.sampledWidths(constantWidthPx, pxPerIn, axisLengthPx, 6);
+		// 21in / 6 = 3.5 -> sample points at 0,6,12,18 (and not 24>21). 4 samples.
+		expect(out.length).toBe(4);
+		for (const w of out) expect(w).toBe(12); // 1920px/160 = 12in
+	});
+	it('min/max/avg of sampled widths', () => {
+		const pxPerIn = 160;
+		const widths = m.sampledWidthsFrom(
+			// widths at px positions 0,960,1920,2880 (=0,6,12,18 in)
+			[1600, 1920, 2080, 1600],
+			pxPerIn
+		);
+		expect(widths.min).toBeCloseTo(10, 6);
+		expect(widths.max).toBeCloseTo(13, 6);
+		expect(widths.avg).toBeCloseTo(11.25, 6); // (10+12+13+10)/4 = 11.25
+	});
+});
+
+describe('1/8 inch stepping + rounding', () => {
+	it('snaps a length to the nearest 1/8 inch', () => {
+		expect(m.snapToEighth(10.1)).toBeCloseTo(10.125, 6); // 10 1/8
+		expect(m.snapToEighth(10.2)).toBeCloseTo(10.25, 6); // 10 2/8=1/4
+		expect(m.snapToEighth(10.0)).toBe(10);
+	});
+	it('rounds half-up to 2 decimals', () => {
+		expect(m.roundHalfUp(30.625, 2)).toBe(30.63);
+		expect(m.roundHalfUp(4.345, 2)).toBe(4.35);
+		expect(m.roundHalfUp(1.005, 2)).toBe(1.01);
+	});
+});