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

tdkpin-rs/CHANGELOG.md

@@ -10,10 +10,11 @@ and this project adheres to
 
 ### Fixed
 
-- Correct the common Real48 tangent projection to the binary's
-  `spin*0.4 - ((vx*ny + vy*nx)/length)*response_tangent`; live probes now
-  match horizontal drain `(-302,-1809)`, ordinary circle `(94,564)`, and
-  bumper `(197,3096)` transitions instead of rounding a bare coefficient away.
+- Separate the common response's two binary projections: the swapped-component
+  value supplies the sign of `abs(normal_velocity)*response_tangent`, while
+  `(vx*nx+vy*ny)/length * 0.02 * response_tangent` updates spin. Live probes now
+  match horizontal drain `(-302,-1809)`, ordinary circle `(94,564)`, bumper
+  `(197,3096)`, and relative record 57 `(1839,1832)` with spin exactly `-5.28`.
 - Gate dynamic record 174/175 impulse transfer on the other slot's capture age:
   a held ball remains velocity-stationary and the moving response retains its
   full normal velocity instead of always subtracting 1,000.
@@ -67,6 +68,13 @@ and this project adheres to
 - Apply the collision table's predicted-position broadphase bounds before
   type-1/type-2 detection, including the registered five-pixel ball margin,
   and retain unresolved candidates until the selected response phase.
+- Correct the two relative slingshot initializer chains after records 55 and
+  70: circles 56/58/71/73 and lines 57/59/72/74 now accumulate from each
+  preceding path endpoint exactly as the 175-record ledger specifies. The
+  flagless TDK companion lines also retain their zero contact/link field rather
+  than carrying unused synthetic head IDs. Record 57 additionally matches the
+  live original's `(75530,354765)/(3000,15)` to
+  `(77369,356597)/(1839,1832)` transition.
 - Match rectangular type-4 magnetic gates to raw `1000:9b69`: enter only when
   the previous position is inside, then deactivate when the newly predicted
   position exits any edge, replacing a swept-intersection approximation.