fix(physics): restore relative slingshot response

A full comparison against the 175-record ledger found stale guessed coordinates
in both relative slingshot chains. Circles 56/58/71/73 and lines 57/59/72/74
were displaced by up to 70 pixels. The corrected record-57 geometry then
exposed a second issue: readable C and Rust had collapsed two independent
binary response projections into one.

Transcribe the accumulated initializer coordinates exactly. Use the
swapped-component projection only to sign the current tangential response
`abs(normal_velocity) * response_tangent`, and use the standard dot product for
`spin_delta * 0.02 * response_tangent`. Correct the readable C evidence and
Rust together, extend live tracing with the six-byte spin field, and seal the
stopped-Wine transition from `(75530,354765)/(3000,15)` to
`(77369,356597)/(1839,1832)` with Real48 spin `-5.28` in both harnesses.

Test Plan:
- stopped Wine 11.15 record-57 injection/trace -- matched position, velocity, and spin
- `cargo test --workspace --all-targets --all-features` -- 123 passed
- `cargo clippy --workspace --all-targets --all-features -- -D warnings` -- passed
- `bash original/tools/test_reconstructed_c.sh` -- passed
- `python3 original/tools/audit_reconstruction.py --require-complete` -- passed with zero incomplete or unclassified units
- `python3 -m py_compile original/tools/trace_original_state.py original/tools/inject_original_state.py` -- passed
- `rumdl check --flavor commonmark RECONSTRUCTION.md CHANGELOG.md` -- passed
- `git diff --cached --check` -- passed

original/reconstructed/tdkpin_physics.c

@@ -191,7 +191,7 @@ static int32_t normal_velocity_checked(
         velocity_x, velocity_y, normal_x, normal_y, normal_length);
 }
 
-static int32_t tangent_velocity_unchecked(
+static int32_t tangent_direction_unchecked(
     int32_t velocity_x,
     int32_t velocity_y,
     BorlandReal48 normal_x,
@@ -207,6 +207,22 @@ static int32_t tangent_velocity_unchecked(
         borland_i32_to_real48(normal_length))));
 }
 
+static int32_t spin_velocity_unchecked(
+    int32_t velocity_x,
+    int32_t velocity_y,
+    BorlandReal48 normal_x,
+    BorlandReal48 normal_y,
+    int32_t normal_length)
+{
+    return borland_real48_round_to_i32(borland_real48_divide(
+        borland_real48_add(
+            borland_real48_multiply(
+                borland_i32_to_real48(velocity_x), normal_x),
+            borland_real48_multiply(
+                borland_i32_to_real48(velocity_y), normal_y)),
+        borland_i32_to_real48(normal_length)));
+}
+
 static int32_t speed_milli(int32_t velocity_x, int32_t velocity_y)
 {
     return distance_milli(velocity_x, velocity_y);
@@ -927,7 +943,16 @@ static void apply_collision_response(
         tdkpin_add_score_from_caller_frame(caller_bp, candidate->score);
     }
     int32_t length = candidate_normal_length(candidate);
-    int32_t projection = tangent_velocity_unchecked(
+    /* Raw 1000:ef19..f16a keeps the contact-direction and spin projections
+     * separate. The swapped-component value selects the sign of the current
+     * tangential response; the standard dot product updates retained spin. */
+    int32_t tangent_direction = tangent_direction_unchecked(
+        motion->velocity_x,
+        motion->velocity_y,
+        candidate->normal_x,
+        candidate->normal_y,
+        length);
+    int32_t spin_projection = spin_velocity_unchecked(
         motion->velocity_x,
         motion->velocity_y,
         candidate->normal_x,
@@ -936,14 +961,9 @@ static void apply_collision_response(
 
     BorlandReal48 spin_delta = borland_real48_multiply(
         borland_real48_multiply(
-            borland_i32_to_real48(projection), g_real48_point_zero_two),
+            borland_i32_to_real48(spin_projection),
+            g_real48_point_zero_two),
         candidate->response_tangent);
-    spin_delta = borland_real48_multiply(
-        borland_i32_to_real48(absolute_wrap(candidate->normal_velocity)),
-        spin_delta);
-    if (projection < 0) {
-        spin_delta = negate_real48(spin_delta);
-    }
     BorlandReal48 discarded = borland_real48_divide(
         borland_real48_sqrt(borland_real48_multiply(
             absolute_real48(spin_delta), g_real48_twenty)),
@@ -951,17 +971,21 @@ static void apply_collision_response(
     (void)discarded;
     discarded = (BorlandReal48){{0,0,0,0,0,0}};
 
-    projection = borland_real48_round_to_i32(borland_real48_add(
+    BorlandReal48 tangent_response = borland_real48_multiply(
+        borland_i32_to_real48(absolute_wrap(candidate->normal_velocity)),
+        candidate->response_tangent);
+    if (tangent_direction < 0) {
+        tangent_response = negate_real48(tangent_response);
+    }
+    int32_t projection = borland_real48_round_to_i32(borland_real48_add(
         borland_real48_subtract(
             borland_real48_multiply(motion->spin, g_real48_point_four),
             borland_real48_divide(
                 borland_real48_multiply(
-                    borland_i32_to_real48(absolute_wrap(projection)),
+                    borland_i32_to_real48(absolute_wrap(tangent_direction)),
                     discarded),
                 borland_i32_to_real48(motion->speed))),
-        borland_real48_multiply(
-            borland_i32_to_real48(projection),
-            candidate->response_tangent)));
+        tangent_response));
     motion->spin = borland_real48_add(
         borland_real48_multiply(motion->spin, g_real48_point_six),
         spin_delta);

original/reconstructed/tests/test_physics.c

@@ -473,6 +473,51 @@ static void test_out_of_bounds_and_zero_substeps_multiball(void)
     assert(g_render_calls == 2 && g_update_calls == 0);
 }
 
+static void test_live_relative_record_57_transition(void)
+{
+    prepare_fixture();
+    set_ball(72530, 354750, 3000, 0);
+    win16_write_u32(g_window, 0x5a, 15);
+    win16_write_u32(g_window, 0x56, 3800);
+    TdkpinCollisionRecord segment = base_record(2);
+    segment.bounds_min_x_milli = 45000;
+    segment.bounds_min_y_milli = 335000;
+    segment.bounds_max_x_milli = 102000;
+    segment.bounds_max_y_milli = 371000;
+    segment.point1_x_milli = 97000;
+    segment.point1_y_milli = 366000;
+    segment.point2_x_milli = 50000;
+    segment.point2_y_milli = 340000;
+    segment.response_normal =
+        (BorlandReal48){{0x80,0x00,0x00,0x00,0x00,0x00}};
+    segment.response_tangent =
+        (BorlandReal48){{0x7d,0xcd,0xcc,0xcc,0xcc,0x4c}};
+    segment.layer_mask = 2;
+    write_record(57, &segment);
+
+    tdkpin_simulate_ball_and_dispatch_collision(0x0300);
+    assert((int32_t)win16_read_u32(
+               win16_dgroup_pointer(0x07d3)) == 75530);
+    assert((int32_t)win16_read_u32(
+               win16_dgroup_pointer(0x07d7)) == 354765);
+    tdkpin_simulate_ball_and_dispatch_collision(0x0300);
+    assert((int32_t)win16_read_u32(
+               win16_dgroup_pointer(0x07d3)) == 77369);
+    assert((int32_t)win16_read_u32(
+               win16_dgroup_pointer(0x07d7)) == 356597);
+    assert((int32_t)win16_read_u32(
+               win16_far_add_offset(g_window, 0x0baa)) == 1839);
+    assert((int32_t)win16_read_u32(
+               win16_far_add_offset(g_window, 0x0bae)) == 1832);
+    static const uint8_t expected_spin[6] = {
+        0x83, 0x5d, 0x8f, 0xc2, 0xf5, 0xa8};
+    for (uint16_t index = 0; index < 6; index++) {
+        assert(win16_read_u8(win16_far_add_offset(
+                   g_window, (uint16_t)(0x0bce + index))) ==
+               expected_spin[index]);
+    }
+}
+
 int main(void)
 {
     test_free_integration_and_speed_clamp();
@@ -480,5 +525,6 @@ int main(void)
     test_capture_and_trigger_records();
     test_capture_boundary_and_claw();
     test_out_of_bounds_and_zero_substeps_multiball();
+    test_live_relative_record_57_transition();
     return 0;
 }