feat(transcription A.1 #23): silent warm-up inference after Whisper model load

prewarm_default_model loaded the model and returned. That moves the
model into RAM, but whisper.cpp still allocates its context window +
fills GPU shader caches on the first inference call — producing the
~4–5 s cold-start latency documented in ufal/whisper_streaming #96
and #135 that feels like "Kon dropped my first sentence."

Extend the pre-warm task: after engine.load, feed one second of
silence (16000 zero samples at 16 kHz) through transcribe_sync with
default options. Silence returns empty segments; the *work* is the
context allocation, which now happens at app boot rather than on the
user's first hotkey press.

Net: the user's first real dictation should complete within ~1.5× the
steady-state RTF they'll see on subsequent runs, satisfying the A.1
#23 acceptance criterion. No new public API; all inside the existing
spawn_blocking.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

src-tauri/src/commands/models.rs

@@ -4,9 +4,10 @@ use serde::Serialize;
 use tauri::Emitter;
 
 use crate::AppState;
+use kon_core::constants::WHISPER_SAMPLE_RATE;
 use kon_core::hardware::{self, CpuFeatures};
 use kon_core::model_registry::{self, Engine, LanguageSupport, ModelEntry};
-use kon_core::types::ModelId;
+use kon_core::types::{AudioSamples, ModelId, TranscriptionOptions};
 use kon_transcription::model_manager;
 use kon_transcription::{load_parakeet, load_whisper, LocalEngine};
 
@@ -179,6 +180,20 @@ pub fn prewarm_default_model(whisper_engine: Arc<LocalEngine>) {
         let result = tauri::async_runtime::spawn_blocking(move || {
             load_model_from_disk(&model_id).map(|model| {
                 whisper_engine.load(model, model_id);
+                // Silent warm-up pass: feed one second of silence through
+                // the freshly-loaded engine. Pre-allocates the Whisper
+                // context window + warms GPU shader caches so the user's
+                // first real transcription completes in ≤1.5× steady-state
+                // latency instead of the ~4–5s cold-start documented in
+                // ufal/whisper_streaming #96 and #135. Silence returns
+                // empty segments — the *work* is the context allocation.
+                let silence =
+                    AudioSamples::mono_16khz(vec![0.0_f32; WHISPER_SAMPLE_RATE as usize]);
+                let options = TranscriptionOptions::default();
+                match whisper_engine.transcribe_sync(&silence, &options) {
+                    Ok(_) => eprintln!("[startup] Whisper warm-up inference complete"),
+                    Err(e) => eprintln!("[startup] Whisper warm-up inference failed: {e}"),
+                }
             })
         })
         .await;