Recover a guessed audio stream's rate by correlating hook vs loopback (step a)

When the host attaches to an already-running game it never saw the stream's
Initialize, so the render-hook assumes the device mix format and measures only
the sample rate from the render cadence -- which a jittery game can make wrong
(intermittent pitch shift). But during the measurement window the game is still
audible, so we have the same audio twice: the hook (pre-mix, unknown format) and
a process-loopback (post-mix, the known device format). Cross-correlating them
pins the true rate from ground truth.

- common/include/coop/audio_correlate.hpp: the pure correlator. Resample the hook
  by each candidate standard rate up to the device rate and score how well it
  aligns with the loopback across the window (drift-detecting). audio_correlation_test
  recovers every rate (score ~1.0 vs ~0.01 for wrong ones), incl. 44100-vs-48000,
  and rejects unrelated signals.
- Hook measurement tap: a host-set verify_capture ring flag makes the hook push a
  still-being-measured (guessed) stream's raw pre-mix bytes WITHOUT silencing, so
  the host can co-capture both signals (a silenced game's loopback is silent).
  Inert by default -- the shipping no-echo path is untouched.
- host/src/audio/audio_format_verifier: co-captures hook + loopback and correlates,
  feeding a correction into the existing override channel. Wired into AudioMirror's
  measurement window (hidden in the gap loopback already covers, so exact streams
  pay nothing). audio_verify_test drives it end-to-end against coop_mock_game.

Rate vs layout are coupled (correlating the waveform needs the right channel
de-interleaving), so this step assumes the hook layout matches the device (the
common stereo-on-stereo case); recovering a different channel count / bit depth
is step b.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

tests/CMakeLists.txt

@@ -44,6 +44,14 @@ add_executable(tone_analysis_test tone_analysis_test.cpp)
 target_link_libraries(tone_analysis_test PRIVATE coop_common)
 add_test(NAME tone_analysis_test COMMAND tone_analysis_test)
 
+# Unit test for the two-path audio-format correlator (common/include/coop/audio_correlate.hpp).
+# Synthesizes one continuous signal sampled at two rates (the hook's true rate + the device rate,
+# with capture skew + noise) and asserts correlate_rate() recovers the true rate -- including the
+# 44100-vs-48000 case the cadence method can misread. Pure header logic, no device.
+add_executable(audio_correlation_test audio_correlation_test.cpp)
+target_link_libraries(audio_correlation_test PRIVATE coop_common)
+add_test(NAME audio_correlation_test COMMAND audio_correlation_test)
+
 # Unit test for the audio-mirror render pacing policy (host/src/audio/render_pacer.hpp).
 # Simulates a producer/consumer device timeline and asserts the shipping RenderPacer rides
 # through producer jitter that makes the old re-prime-on-partial-fill policy glitch
@@ -170,6 +178,20 @@ target_link_libraries(mock_game_test PRIVATE coop_common d3d11 dxgi)
 add_dependencies(mock_game_test coop_mock_game coop_hook)
 add_test(NAME mock_game_test COMMAND mock_game_test)
 
+# Integration test for the two-path audio-format verifier: launches coop_mock_game rendering a
+# NON-device rate (44100 on a 48000 endpoint), injects coop_hook.dll late (guessed stream), and
+# runs the real verify_stream_format() -- co-capturing the hook (pre-mix) + a parallel loopback
+# (post-mix) and correlating to recover the true rate. Skips cleanly without an audio endpoint.
+add_executable(audio_verify_test
+	audio_verify_test.cpp
+	${CMAKE_SOURCE_DIR}/host/src/audio/audio_format_verifier.cpp
+	${CMAKE_SOURCE_DIR}/host/src/audio/process_loopback_capture.cpp)
+target_include_directories(audio_verify_test PRIVATE ${CMAKE_SOURCE_DIR}/host/src)
+target_compile_definitions(audio_verify_test PRIVATE NTDDI_VERSION=0x0A00000B)
+target_link_libraries(audio_verify_test PRIVATE coop_common ole32 mmdevapi)
+add_dependencies(audio_verify_test coop_mock_game coop_hook)
+add_test(NAME audio_verify_test COMMAND audio_verify_test)
+
 # In-process self-test for the OpenGL capture path. Reuses the shipping
 # opengl_hook.cpp and drives a real OpenGL context in the same process, so it
 # exercises the SwapBuffers hook, the glReadPixels readback, and the upload into
@@ -201,6 +223,7 @@ add_executable(ui_fit_test
 	${CMAKE_SOURCE_DIR}/host/src/audio_panel.cpp
 	${CMAKE_SOURCE_DIR}/host/src/controllers_panel.cpp
 	${CMAKE_SOURCE_DIR}/host/src/audio/audio_loopback.cpp
+	${CMAKE_SOURCE_DIR}/host/src/audio/audio_format_verifier.cpp
 	${CMAKE_SOURCE_DIR}/host/src/audio/process_loopback_capture.cpp
 	${CMAKE_SOURCE_DIR}/host/src/audio/audio_overrides.cpp
 	${CMAKE_SOURCE_DIR}/host/src/ui/app_chrome.cpp)
@@ -224,6 +247,7 @@ coop_output_subdir(tests
 	mkb_map_test
 	audio_mix_test
 	tone_analysis_test
+	audio_correlation_test
 	render_pacer_test
 	rate_estimator_test
 	audio_overrides_test
@@ -234,4 +258,5 @@ coop_output_subdir(tests
 	dx12_present_hook_test
 	opengl_hook_test
 	mock_game_test
+	audio_verify_test
 	ui_fit_test)