fix(AR-004): the TransNetV2 window stores the model's input, not the frame

The rolling window held frames as decoded — `images_.push_back(f.image)` — and
left the downscale to the backend. TransNetV2's input is 48x27, so the buffer
held roughly 590 MB at 1080p to feed a model that needs about 380 KB. The
config note for `dense_scale` says as much outright: "TransNetV2 downsamples to
48x27 regardless".

This is not a channel capacity, so no amount of tuning channel depths would
ever have found it. It is a `std::deque<cv::Mat>` member, and it is the single
largest allocation in the scene branch.

It is also redundant work. Windows overlap by `kWindow - stride`, so a frame
appears in several of them and was re-downscaled once per window it appeared
in; now it is downscaled once, on arrival.

**The risk here is the invariant, not the memory.** Every model gets the input
it was trained for — a model run off-distribution returns confident, plausible,
wrong output, and for a boundary detector that means fabricated cuts, which are
indistinguishable from real ones in the output. So this reproduces the
backends' preprocessing exactly rather than doing its own: both
ort_backend.cpp and trt_backend.cpp guard mis-sized input with
`convertTo(CV_8UC3)` and then
`cv::resize(..., {kFrameW, kFrameH}, 0, 0, cv::INTER_AREA)`, in that order, and
`to_model_input` performs the same two operations. The backend guard then sees
a correctly-sized frame and does nothing, so the tensor the model receives is
unchanged. The interface has always specified this as the caller's job — "Each
frame must already be kFrameW x kFrameH, BGR, CV_8UC3" — so the node now meets
a contract it was already given.

The tests assert equivalence, not size. They perform the backend's own two
operations independently and compare byte for byte, on a gradient rather than a
flat fill, since INTER_AREA averages and a constant image would compare equal
under almost any resize. Order is pinned too: converting a 4-channel frame
after downscaling averages alpha into the colour channels and gives different
pixels.

Verified in both directions. With INTER_LINEAR substituted for INTER_AREA —
the most plausible way to get this subtly wrong — three assertions fail. With
the backend's own operations, byte-identical at 1920x1080, 640x360 and 720x480.
149/149.

Still unmeasured on real content, as with the previous commit: the equivalence
argument says the model sees the same tensor, but a run comparing scenes.json
before and after on a real clip is what would settle it, and I could not launch
one here.

TRACES: AR-004, AR-010 | SR-002

tests/test_scene_detector_node.cpp

@@ -14,6 +14,9 @@
 
 #include "nodes/scene_detector_node.hpp"
 
+#include <opencv2/imgproc.hpp>
+#include <utility>
+
 #include <vector>
 
 namespace {
@@ -84,3 +87,105 @@ TEST_CASE("too few frames to have a cadence yields an inert window",
 TEST_CASE("a single observed interval is enough", "[scene][AR-011]") {
     CHECK(SceneDetectorFunc::dedup_window_sec({1.0 / 24.0}) == 0.5 / 24.0);
 }
+
+// ── AR-004 — the window stores the model's input, not the decoded frame ───────
+//
+// TRACES: AR-004, AR-010 | SR-002 | UT-003
+//
+// The rolling window held frames as decoded, at full resolution, and left the
+// downscale to the backend — ~590 MB at 1080p to feed a model whose input is
+// 48x27, about 380 KB. Not a channel capacity, so no amount of tuning channel
+// depths would have found it.
+//
+// The risk in fixing it is the project invariant: every model gets the input it
+// was trained for. A model run off-distribution returns confident, plausible,
+// wrong output, and here that means fabricated shot boundaries — which would be
+// indistinguishable from a real cut in the output.
+//
+// So these cases do not check that the frames got smaller. They check that the
+// pixels are *identical* to what the backend would have produced from the full
+// frame, by performing the backend's own two operations independently and
+// comparing byte for byte. Both ort_backend.cpp and trt_backend.cpp guard
+// mis-sized input with convertTo(CV_8UC3) then
+// cv::resize(..., {kFrameW, kFrameH}, 0, 0, cv::INTER_AREA), in that order.
+namespace {
+
+cv::Mat gradient(int w, int h) {
+    // Structured content, not a flat fill: INTER_AREA averages, so a constant
+    // image would compare equal under almost any resize and prove nothing.
+    cv::Mat m(h, w, CV_8UC3);
+    for (int y = 0; y < h; ++y)
+        for (int x = 0; x < w; ++x)
+            m.at<cv::Vec3b>(y, x) = cv::Vec3b(
+                static_cast<uchar>((x * 7 + y * 3) % 256),
+                static_cast<uchar>((x * 13 + y * 5) % 256),
+                static_cast<uchar>((x * 3 + y * 11) % 256));
+    return m;
+}
+
+bool identical(const cv::Mat& a, const cv::Mat& b) {
+    if (a.size() != b.size() || a.type() != b.type()) return false;
+    cv::Mat diff;
+    cv::absdiff(a, b, diff);
+    return cv::countNonZero(diff.reshape(1)) == 0;
+}
+
+}  // namespace
+
+TEST_CASE("the window frame is what the backend would have produced",
+          "[scene][AR-004]") {
+    for (auto [w, h] : {std::pair{1920, 1080}, std::pair{640, 360}, std::pair{720, 480}}) {
+        INFO("source " << w << "x" << h);
+        const cv::Mat full = gradient(w, h);
+
+        // The backend's own guard, performed here independently.
+        cv::Mat expected;
+        cv::resize(full, expected, {ISceneDetector::kFrameW, ISceneDetector::kFrameH},
+                   0, 0, cv::INTER_AREA);
+
+        const cv::Mat got = SceneDetectorFunc::to_model_input(full);
+
+        REQUIRE(got.cols == ISceneDetector::kFrameW);
+        REQUIRE(got.rows == ISceneDetector::kFrameH);
+        REQUIRE(got.type() == CV_8UC3);
+        CHECK(identical(got, expected));
+    }
+}
+
+TEST_CASE("a frame already at model size is passed through untouched",
+          "[scene][AR-004]") {
+    // The backend skips its guard for a correctly-sized frame, so this path must
+    // not resize either — resampling an already-48x27 image would change it.
+    const cv::Mat exact = gradient(ISceneDetector::kFrameW, ISceneDetector::kFrameH);
+    CHECK(identical(SceneDetectorFunc::to_model_input(exact), exact));
+}
+
+TEST_CASE("conversion happens before the resize, as the backend does it",
+          "[scene][AR-004]") {
+    // Order matters: converting a 4-channel frame after downscaling averages
+    // alpha into the colour channels and gives different pixels. The backends
+    // convert first, so this must too.
+    cv::Mat four(360, 640, CV_8UC4, cv::Scalar(10, 20, 30, 255));
+    cv::Mat typed;
+    four.convertTo(typed, CV_8UC3);
+    cv::Mat expected;
+    cv::resize(typed, expected, {ISceneDetector::kFrameW, ISceneDetector::kFrameH},
+               0, 0, cv::INTER_AREA);
+
+    CHECK(identical(SceneDetectorFunc::to_model_input(four), expected));
+}
+
+TEST_CASE("the window's memory is bounded by the model input, not the source",
+          "[scene][AR-004]") {
+    // The point of the change, stated as a number: a full window of 1080p
+    // frames is ~590 MB as decoded and ~380 KB as model input.
+    const cv::Mat full = gradient(1920, 1080);
+    const cv::Mat small = SceneDetectorFunc::to_model_input(full);
+
+    const std::size_t decoded = full.total()  * full.elemSize();
+    const std::size_t stored  = small.total() * small.elemSize();
+
+    INFO("decoded " << decoded << " B, stored " << stored << " B");
+    CHECK(stored * 1000 < decoded);          // three orders of magnitude
+    CHECK(stored == ISceneDetector::kFrameW * ISceneDetector::kFrameH * 3u);
+}