docs: consolidate beat-based timing documentation

- Added comprehensive doc/BEAT_TIMING.md user guide
- Updated BEAT_TIMING_SUMMARY.md with verification results
- Updated PROJECT_CONTEXT.md to highlight timing system
- Updated README.md with doc links
- Included architecture diagrams and examples
- Added troubleshooting section

Complete reference for beat-based timeline authoring and shader
animation with musical timing.

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

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+# Beat-Based Timing System
+
+## Overview
+
+The demo uses **beat-based timing** for visual effect sequences, ensuring musical synchronization regardless of BPM changes. All timeline sequences are authored in beats (musical time) and converted to physical seconds at runtime.
+
+**Key Principle:** Variable tempo only affects audio sample triggering. Visual effects run at constant physical time with optional beat-synchronized animation.
+
+---
+
+## Quick Start
+
+### Timeline Authoring
+```seq
+# BPM 120
+SEQUENCE 0 0 "Intro"         # Beat 0 (bar 1)
+  EFFECT + Flash 0 2         # Beats 0-2 (half bar)
+  EFFECT + Fade 4 8          # Beats 4-8 (full bar)
+
+SEQUENCE 16 1 "Drop"         # Beat 16 (bar 5)
+  EFFECT + Heptagon 0 16     # 4 bars
+```
+
+**Conversion:** At 120 BPM, 1 beat = 0.5 seconds, 4 beats = 2 seconds
+
+### Shader Animation
+```wgsl
+@group(0) @binding(2) var<uniform> uniforms: CommonUniforms;
+
+// Use beat_time for musical animation
+let bar_cycle = uniforms.beat_time / 4.0;  // Bars
+let pulse = sin(bar_cycle * TAU);
+
+// Use beat_phase for smooth per-beat effects
+let wave = sin(uniforms.beat_phase * TAU);
+
+// Use time for constant-speed physics
+let rotation = uniforms.time * TAU;
+```
+
+---
+
+## Uniform Structure
+
+All effects receive `CommonPostProcessUniforms` with timing data:
+
+```cpp
+struct CommonPostProcessUniforms {
+  vec2 resolution;        // Screen dimensions (pixels)
+  float aspect_ratio;     // Width/height ratio
+  float time;             // Physical seconds (constant, unaffected by tempo)
+  float beat_time;        // Absolute beats (musical time from audio clock)
+  float beat_phase;       // Fractional beat 0.0-1.0 (smooth oscillation)
+  float audio_intensity;  // Audio peak for beat sync
+  float _pad;            // Alignment padding
+};  // 32 bytes
+```
+
+**Use Cases:**
+- `time`: Physics animation, constant-speed rotation/movement
+- `beat_time`: Bar-based patterns, musical synchronization
+- `beat_phase`: Smooth per-beat pulse/wave effects
+
+---
+
+## Timeline Format
+
+### Time Notation
+
+**Default:** Beats (no suffix)
+```seq
+SEQUENCE 0 0      # Beat 0
+  EFFECT + Flash 0 4    # Beats 0-4
+```
+
+**Explicit Seconds:** Use `s` suffix (rare)
+```seq
+SEQUENCE 2.5s 0   # 2.5 physical seconds
+  EFFECT + Flash 0 4    # Still uses beats for duration
+```
+
+**Explicit Beats:** Use `b` suffix (optional clarity)
+```seq
+SEQUENCE 8b 0     # Same as "8"
+  EFFECT + Flash 0b 4b  # Same as "0 4"
+```
+
+### BPM Declaration
+
+**Required** in all timeline files:
+```seq
+# BPM 120
+```
+
+Specifies beats per minute for runtime conversion to seconds.
+
+---
+
+## Architecture
+
+### Timing Flow
+
+```
+Platform Clock (physical seconds)
+    │
+    ├──► Physical Time ────────┐
+    │    (constant)             │
+    │                           │
+    └──► Audio Time ────┐       │
+         (playback)     │       │
+                        ▼       │
+                 Beat Calculation    │
+                 (BPM * 60)          │
+                        │            │
+                        ▼            ▼
+                   Visual Effects Rendering
+                   (time + beat_time + beat_phase)
+```
+
+### Key Insight
+
+**Variable tempo changes `music_time`** (used for audio event triggering), but **visual effects receive `time` (physical)** and **`beat_time` (from audio playback clock)**, not from tempo-scaled music time.
+
+This separation ensures:
+- ✅ Visual effects run at constant frame rate
+- ✅ Beat-synced animations track actual audio playback
+- ✅ Tempo changes don't cause visual stuttering
+
+---
+
+## Implementation
+
+### Beat Calculation (Runtime)
+
+```cpp
+// main.cc - Calculate from audio playback time
+const float absolute_beat_time = current_audio_time * g_tracker_score.bpm / 60.0f;
+const float beat_phase = fmodf(absolute_beat_time, 1.0f);
+
+// Pass to GPU rendering
+gpu_draw(visual_peak, aspect_ratio, physical_time, absolute_beat_time, beat_phase);
+```
+
+### Timeline Compilation
+
+```cpp
+// seq_compiler.cc - Convert beats to seconds at compile time
+std::string convert_to_time(const std::string& value, float bpm) {
+  if (value.back() == 's') return explicit_seconds;  // Pass through
+
+  // Default: treat as beats
+  float beat = std::stof(value);
+  float time = beat * 60.0f / bpm;
+  return time;
+}
+```
+
+**Result:** Generated `timeline.cc` contains physical seconds for effect activation.
+
+---
+
+## Migration
+
+### Existing Timelines
+
+Already migrated with explicit `s` suffix to preserve timing:
+```seq
+SEQUENCE 2.50s 0          # Physical seconds preserved
+  EFFECT + Flash 0.00s 1.00s
+```
+
+### New Content
+
+Use beat notation (recommended):
+```seq
+# BPM 140
+SEQUENCE 0 0 "Intro"
+  EFFECT + Flash 0 4      # 4 beats = 1.71s @ 140 BPM
+  EFFECT + Fade 4 8       # 4 beats = 1.71s
+```
+
+**Benefits:**
+- Natural musical alignment (bars/beats)
+- BPM changes don't break timing
+- Easier to author to music
+
+---
+
+## Examples
+
+### Four-Bar Pattern
+```seq
+# BPM 120
+SEQUENCE 0 0 "Verse 1"
+  EFFECT - Background 0 16    # 4 bars background
+  EFFECT + Flash 0 1          # First beat flash
+  EFFECT + Pulse 4 5          # Second bar pulse
+  EFFECT + Fade 15 16         # Final beat fade
+```
+
+### Multi-Bar Sequence
+```seq
+SEQUENCE 16 0 "Chorus"        # Bar 5
+  EFFECT + Heptagon 0 32      # 8 bars (full chorus)
+  EFFECT + Particles 8 24     # Bars 7-11 (middle)
+```
+
+### Beat-Synced Shader
+```wgsl
+fn fragment_main(@location(0) uv: vec2<f32>) -> @location(0) vec4<f32> {
+  // Pulse every bar (4 beats)
+  let bar_phase = fract(uniforms.beat_time / 4.0);
+  let bar_pulse = smoothstep(0.0, 0.1, bar_phase) *
+                  (1.0 - smoothstep(0.9, 1.0, bar_phase));
+
+  // Smooth per-beat wave
+  let beat_wave = sin(uniforms.beat_phase * TAU);
+
+  // Combine
+  let intensity = bar_pulse * 0.5 + beat_wave * 0.3;
+  return vec4<f32>(color * intensity, 1.0);
+}
+```
+
+---
+
+## Troubleshooting
+
+### Shader Compilation Error: "invalid accessor 'beat'"
+
+**Cause:** Old shader using `uniforms.beat` (deprecated field)
+
+**Fix:** Use `uniforms.beat_phase` or `uniforms.beat_time`
+
+```wgsl
+// OLD (error):
+let x = uniforms.beat;
+
+// NEW:
+let x = uniforms.beat_phase;  // For 0-1 fractional
+let y = uniforms.beat_time;   // For absolute beats
+```
+
+### Timeline Parse Error
+
+**Cause:** Missing BPM declaration
+
+**Fix:** Add BPM at top of file
+```seq
+# BPM 120    ← Required
+SEQUENCE 0 0
+```
+
+### Effects Start at Wrong Time
+
+**Cause:** Mixing beats and seconds without explicit suffixes
+
+**Fix:** Be explicit
+```seq
+SEQUENCE 8 0      # 8 beats (not 8 seconds)
+SEQUENCE 8s 0     # 8 seconds (explicit)
+SEQUENCE 8b 0     # 8 beats (explicit, same as first)
+```
+
+---
+
+## See Also
+
+- **Format Reference:** `doc/SEQUENCE.md` - Complete .seq syntax
+- **Implementation:** `BEAT_TIMING_SUMMARY.md` - Technical details
+- **Effect Creation:** `doc/EFFECT_WORKFLOW.md` - Adding new effects
+- **Timeline Editor:** `tools/timeline_editor/README.md` - Visual editing