Example Topological Queries: Real-World Use Cases

interface TopologicalQuery {
  // Semantic component (what you're looking for)
  query: string;

  // Topological filters (where in structure)
  coordinates?: {
    x?: number | [number, number] | ((x: number) => boolean);  // Depth
    y?: number | [number, number] | ((y: number) => boolean);  // Alternatives
    z?: number | [number, number] | ((z: number) => boolean);  // Alignment
    t?: number | [number, number] | ((t: number) => boolean);  // Temporal
    n?: number | [number, number] | ((n: number) => boolean);  // Complexity
  };

  // Physics filters (what was happening physically)
  physics?: {
    thrust?: number | ((t: number) => boolean);
    alignment?: number | ((a: number) => boolean);
    gravity?: number | ((g: number) => boolean);
    mass?: number | ((m: number) => boolean);
    escapeIndex?: number | ((e: number) => boolean);
  };

  // Ring filters (recurring patterns)
  ring?: {
    patternType?: string;
    stage?: string;
    cyclePhase?: number;  // 0-1, where in the cycle
  };
}

{
  query: "career change decision new direction",
  coordinates: {
    x: [0, 2],        // High-level decisions, not tactical
    y: (y) => y > 0,  // Explored alternatives
    z: (z) => z < -0.3  // Divergent from current path
  },
  physics: {
    gravity: (g) => g > 0.5  // Under pressure (why pivot)
  }
}

1. "Decided to go freelance instead of seeking employment"
   x=1, y=2, z=-0.6 | gravity=0.7 | 2024-03-15
   → Left stable job path (y=2), divergent direction (z=-0.6)
   → Financial pressure (gravity=0.7)

2. "Exploring creative career vs continuing tech"
   x=0, y=1, z=-0.8 | gravity=0.4 | 2023-09-20
   → Life-level choice (x=0), alternative considered (y=1)
   → Burnout from tech work (gravity from stress)

{
  query: "productive flow deep work completion",
  coordinates: {
    x: [5, 10],      // Deep work, not surface
    n: (n) => n > 4  // Complex, detailed work
  },
  physics: {
    thrust: (t) => t > 6.0,  // High capability
    alignment: (a) => a > 0.7,  // Aligned work
    escapeIndex: (e) => e > 1.0  // Escaping phase
  },
  ring: {
    patternType: "work_cycle",
    stage: "execution"  // In execution phase of work cycle
  }
}

1. "BWB MVP development sprint - completed core features"
   x=8, y=0, z=0.85, n=6 | thrust=6.8, η=1.4 | 2024-11-20
   → Deep focused work (x=8), highly aligned (z=0.85)
   → Peak capability period (thrust=6.8, η=1.4)
   → Execution phase of work cycle

2. "TrajectoryOS Phase 1 implementation marathon"
   x=7, y=0, z=0.78, n=5 | thrust=6.2, η=1.2 | 2024-12-01
   → Sustained deep work, aligned with goals
   → High thrust, escaping phase

Common Pattern:
→ These periods share: x>7, z>0.75, thrust>6, η>1
→ Triggers: Clear goal + minimal constraints + skill match
→ Duration: Average 2 weeks before need for recovery

// Two queries: high belief, low utilization

// Query 1: Find skills with high belief
{
  query: "skills I'm confident in",
  // Returns: skill_beliefs where level > 7
}

// Query 2: Find events using those skills
{
  query: "[skill_name] application practice use",
  coordinates: {
    t: (t) => recent(t, months: 6)  // Last 6 months
  }
}

// Compare counts

Analysis: Underutilized Skills

1. Python (belief: 8.2/10)
   → Only 3 events in last 6 months
   → Last used: 2024-10-15 (2 months ago)
   → Recommendation: Risk of skill decay
   → Suggestion: Build small Python project this month

2. Music Production (belief: 7.5/10)
   → 1 event in last 6 months
   → Currently: All focus on coding
   → Alignment impact: -0.15 (creative outlet missing)
   → Suggestion: Schedule weekly music session

3. SQL (belief: 7.0/10)
   → 8 events, but all shallow (x<3)
   → Opportunity: Deepen SQL knowledge (x→6)
   → Could unlock data-heavy projects

{
  query: "React learning progress development",
  coordinates: {
    // No x filter - want to see progression from shallow to deep
    z: (z) => z > 0.3  // Exclude random experiments
  },
  // Sort by t (temporal order)
  sortBy: "t"
}

React Learning Trajectory (Jan 2023 → Dec 2024)

Depth (x)
   ↑
10 │                                    ⭐ (future: mastery)
   │                               ⭐
 8 │                          ●
   │                    ●
 6 │              ●
   │         ●
 4 │    ●
   │  ●
 2 │●
   │
 0 └──────────────────────────────────────────→ Time
   Jan'23              Jan'24              Dec'24

Events plotted:
● Jan'23 (x=1): "Started React tutorial"
● Mar'23 (x=2): "First component built"
● May'23 (x=3): "Todo app project"
● Jul'23 (x=5): "Hooks deep dive" ← Inflection point
● Sep'23 (x=5): "Context API mastery"
● Dec'23 (x=6): "Built personal portfolio"
● Mar'24 (x=7): "Started BWB (complex app)"
● Nov'24 (x=8): "BWB MVP complete"
⭐ Projected (x=10): Aug 2025

Learning Pattern Detected:
→ Cycle: Study (2 weeks) → Build (3 weeks) → Reflect (1 week)
→ Depth increases +1.5 per cycle
→ Currently in Build phase, cycle 7/10 to mastery

{
  query: "understood finally clicked breakthrough insight",
  coordinates: {
    x: (x) => x > 4,     // Not trivial learning
    n: (n) => n > 3,     // Detailed notes (captured insight)
    // Look for jumps in y (explored alternative that worked)
    y: [1, 3]
  },
  physics: {
    // Often during aligned, moderate thrust periods
    alignment: (a) => a > 0.6
  }
}

1. "Finally understood React hooks mental model"
   x=5, y=1, z=0.6, n=8 | 2023-07-12
   → Explored hooks (alternative to classes, y=1)
   → Deep understanding (x=5), detailed notes (n=8)
   → Content: "The key is hooks are just closures! Everything clicked..."

2. "Grokked the TrajectoryOS physics equations"
   x=7, y=2, z=0.75, n=6 | 2024-12-10
   → Tried different mental models (y=2)
   → Deep study (x=7), complex derivations (n=6)
   → Content: "It's just F=ma but for life! Thrust = capability × direction..."

Common Pattern:
→ Breakthroughs occur at x∈[5,8] (moderate-deep)
→ Usually involve y>0 (trying alternatives)
→ High n (detailed capture of insight)
→ Often trigger skill level jumps (+2 to +3 points)

// Query 1: Successful project context
{
  query: "BWB project work progress",
  coordinates: {
    t: (t) => withinRange(t, project.startDate, project.endDate)
  }
}

// Query 2: Failed project context
{
  query: "[failed_project] work progress",
  coordinates: {
    t: (t) => withinRange(t, failed.startDate, failed.endDate)
  }
}

// Compare physics and coordinates

┌─────────────────────────────────────────────────────────────┐
│ BWB (Success) vs Previous Startup Attempt (Failed)         │
├─────────────────────────────────────────────────────────────┤
│                                                             │
│ BWB Project (Success):                                      │
│ Duration: 3 months (Sep-Nov 2024)                          │
│                                                             │
│ Coordinates:                                                │
│ • Avg depth: x̄ = 6.8 (deep, focused work)                 │
│ • Primary path: ȳ = 0.3 (stayed course, few pivots)       │
│ • Alignment: z̄ = 0.82 (highly coherent)                   │
│ • Complexity: n̄ = 5.2 (detailed planning)                 │
│                                                             │
│ Physics:                                                    │
│ • Avg thrust: 6.2 → 6.8 (increasing!)                      │
│ • Avg alignment: 0.75 → 0.85 (improving)                   │
│ • Avg gravity: 0.35 (low constraints)                      │
│ • Avg η: 1.15 (escaping throughout)                        │
│                                                             │
│ Ring Pattern:                                               │
│ • Consistent 2-week sprints: Plan → Execute → Demo → Plan │
│ • No broken cycles                                         │
│                                                             │
├─────────────────────────────────────────────────────────────┤
│                                                             │
│ Previous Startup (Failed):                                  │
│ Duration: 6 months (Jan-Jun 2023)                          │
│                                                             │
│ Coordinates:                                                │
│ • Avg depth: x̄ = 3.2 (shallow, scattered)                 │
│ • Pivot chaos: ȳ = 2.1 (too many direction changes)       │
│ • Alignment: z̄ = 0.35 (poor coherence)                    │
│ • Complexity: n̄ = 2.1 (under-planned)                     │
│                                                             │
│ Physics:                                                    │
│ • Avg thrust: 4.2 → 3.1 (declining!)                       │
│ • Avg alignment: 0.45 → 0.25 (degrading)                   │
│ • Avg gravity: 0.75 (high constraints)                     │
│ • Avg η: 0.5 → 0.3 (sinking)                               │
│                                                             │
│ Ring Pattern:                                               │
│ • Started with weekly cycles                               │
│ • Broke down after month 3 (too much pivoting)            │
│ • No consistent pattern in final 2 months                  │
│                                                             │
├─────────────────────────────────────────────────────────────┤
│                                                             │
│ Key Differences:                                            │
│ ✓ Depth: 6.8 vs 3.2 (BWB had focus)                       │
│ ✓ Stability: 0.3 vs 2.1 pivots (BWB stayed course)        │
│ ✓ Alignment: 0.82 vs 0.35 (BWB was coherent)              │
│ ✓ Physics trend: Rising vs falling                         │
│ ✓ Pattern consistency: Maintained vs broke down            │
│                                                             │
│ Root Cause:                                                 │
│ → BWB: Clear vision (high z) + low distractions (low g)   │
│ → Startup: Unclear vision + too many constraints           │
│                                                             │
│ Lesson for Next Project:                                    │
│ → Maintain z > 0.7 (clear direction)                       │
│ → Keep ȳ < 0.5 (limited pivots)                           │
│ → Ensure gravity < 0.5 (minimize constraints)             │
│ → Track η weekly (early warning if drops <1.0)            │
└─────────────────────────────────────────────────────────────┘

{
  query: "exhausted overwhelmed stressed burned out",
  coordinates: {
    // Burnout often occurs during scattered work
    z: (z) => z < 0.3,  // Unaligned, scattered
    n: (n) => n < 2     // Shallow entries (no energy for detail)
  },
  physics: {
    gravity: (g) => g > 0.8,  // High constraints
    mass: (m) => m > 1.2,      // Heavy commitments
    alignment: (a) => a < 0.4  // Low alignment
  }
}

Burnout Instances Found: 4

Instance 1: March 2023
  Trigger: gravity spiked to 0.95 (financial stress + deadline)
  Duration: 3 weeks
  Recovery: Forced 1-week break

Instance 2: August 2023
  Trigger: mass increased to 1.5 (too many projects)
  Duration: 2 weeks
  Recovery: Dropped 2 projects, mass → 0.8

Instance 3: January 2024
  Trigger: alignment dropped to 0.25 (scattered work)
  Duration: 4 weeks
  Recovery: Simplified focus, alignment → 0.6

Instance 4: June 2024
  Trigger: Combination (gravity=0.85, mass=1.3, alignment=0.3)
  Duration: 2 weeks
  Recovery: Complete reset, 2-week vacation

┌─────────────────────────────────────────────────────────┐
│ Burnout Prediction Model (Ring Pattern)                │
├─────────────────────────────────────────────────────────┤
│                                                         │
│ Warning Stages:                                         │
│ 1. Overcommitment (mass ↑)                             │
│ 2. Alignment drops (z ↓)                               │
│ 3. Gravity increases (g ↑)                             │
│ 4. Burnout (all 3 sustained >2 weeks)                  │
│ 5. Recovery/Reset                                       │
│                                                         │
│ Early Warning Indicators:                               │
│ • mass > 1.1 for 1+ week → Warning                     │
│ • alignment < 0.5 for 2+ weeks → Danger                │
│ • gravity > 0.7 + mass > 1.0 → Critical                │
│                                                         │
│ Current Status (Dec 2024):                              │
│ • mass = 0.9 ✓ (Safe)                                  │
│ • alignment = 0.75 ✓ (Good)                            │
│ • gravity = 0.4 ✓ (Low)                                │
│ • Burnout risk: 12% (Low)                              │
│                                                         │
│ Next predicted burnout: March 2025 (if pattern holds)  │
│ → Historically occurs every 4-5 months                 │
│ → Prevention: Monitor mass and alignment in Feb        │
└─────────────────────────────────────────────────────────┘

{
  query: "creative idea inspiration breakthrough design",
  coordinates: {
    x: [4, 8],  // Moderate to deep creative work
    z: (z) => z < 0.0 || z > 0.8,  // Either experimental or highly aligned
    n: (n) => n > 3  // Captured in detail
  },
  physics: {
    alignment: (a) => a > 0.6,  // Creative but aligned
    gravity: (g) => g < 0.5      // Low pressure (creativity needs space)
  },
  ring: {
    patternType: "creative_cycle",
    stage: "inspiration|creation"  // Not in reflection stage
  }
}

Creative Periods Identified: 8

Top 3:
1. "BWB choreography notation breakthrough" (2024-10-15)
   x=7, y=1, z=-0.4, n=6 | alignment=0.68, g=0.3
   → Deep creative exploration (x=7, y=1)
   → Divergent idea (z=-0.4) that later aligned
   → Low pressure environment (g=0.3)
   → Ring: Inspiration phase, day 2 of 21-day cycle

2. "Music + code fusion idea for Echelon" (2024-09-20)
   x=6, y=2, z=0.85, n=8
   → Explored multiple approaches (y=2)
   → Highly aligned with existing work (z=0.85)
   → Detailed documentation (n=8)
   → Ring: Creation phase, day 12 of cycle

3. "TrajectoryOS escape physics visualization" (2024-12-05)
   x=5, y=0, z=0.72, n=5
   → Pure creation, no exploration needed (y=0)
   → Aligned with physics background (z=0.72)
   → Ring: Inspiration→Creation transition

Creative Cycle Pattern:
┌─────────────────────────────────────────────┐
│        Inspiration (3-5 days)               │
│               ↓                             │
│        Creation (7-10 days)                 │
│               ↓                             │
│        Performance/Share (2-3 days)         │
│               ↓                             │
│        Reflection (3-5 days)                │
│               ↓                             │
│        (Repeat)                             │
│                                             │
│ Total cycle: ~21 days                       │
│ Most creative: Days 2-4, 8-14               │
│ Least creative: Days 16-20 (reflection)     │
└─────────────────────────────────────────────┘

Optimization Insight:
→ Your best creative work happens when:
   • gravity < 0.5 (low pressure)
   • alignment ∈ [0.6, 0.85] (connected but free)
   • In "Inspiration" or early "Creation" phase

→ To maximize creativity:
   • Block days 2-4 and 8-14 of cycle for creative work
   • Keep commitments low (target: gravity < 0.4)
   • Allow some divergence (z as low as -0.5 OK)

{
  query: "collaboration partner working with team",
  coordinates: {
    // Collaborations often create branches (y>0)
    y: (y) => y > 0,
    n: (n) => n > 2  // Documented interactions
  },
  physics: {
    // Compare thrust before, during, after
    // (requires temporal windowing)
  }
}

Collaboration Impact Analysis

Solo Work Baseline:
• Avg thrust: 5.2
• Avg alignment: 0.65
• Avg η: 0.95

During Collaborations:
┌────────────────────────────────────────────────────────┐
│ 1. BWB with dancers (Oct-Nov 2024)                    │
│    Thrust: 6.8 (+30% vs baseline)                     │
│    Alignment: 0.85 (+31%)                              │
│    η: 1.4 (+47%)                                       │
│    → Massive boost! Dancers' feedback accelerated     │
│                                                        │
│ 2. Code review exchange with developer X (Jun 2024)   │
│    Thrust: 5.0 (-4% vs baseline)                      │
│    Alignment: 0.68 (+5%)                               │
│    η: 0.88 (-7%)                                       │
│    → Slight drag, but learned new patterns            │
│                                                        │
│ 3. Music collaboration with friend Y (Mar 2024)       │
│    Thrust: 4.2 (-19%)                                 │
│    Alignment: 0.45 (-31%)                              │
│    η: 0.62 (-35%)                                      │
│    → Negative impact: misaligned goals                │
└────────────────────────────────────────────────────────┘

Pattern:
✓ Collaborations boost trajectory when:
   • Aligned goals (z > 0.7)
   • Complementary skills (not overlapping)
   • Clear roles (low conflict)

✗ Collaborations drag trajectory when:
   • Misaligned goals (z < 0.4)
   • Communication overhead > value
   • Unclear ownership

Recommendation:
→ Prioritize collaborations like BWB (aligned, clear)
→ Avoid collaborations like Music (misaligned)
→ Code reviews: Neutral, good for learning but not thrust

// Query the query logs themselves
{
  // Analyze past queries
  analyzeQueryHistory: {
    timeRange: "last 3 months",
    clusterBy: "semantic_theme"
  }
}

Your Search Patterns (Last 3 Months)

Query Themes:
1. Career/Skills (42% of queries)
   → "React progress", "skill gaps", "learning path"
   → Interpretation: Growth-focused, career building

2. Projects (28% of queries)
   → "BWB status", "TrajectoryOS next steps"
   → Interpretation: Active builder, execution mode

3. Patterns/Meta (18% of queries)
   → "burnout pattern", "creative cycles", "why procrastinate"
   → Interpretation: Self-aware, seeking optimization

4. Past Success (12% of queries)
   → "productive periods", "breakthrough moments"
   → Interpretation: Learning from success

Most Common Filters:
• t: recent (67% of queries)  → Future-focused
• z: >0.5 (54% of queries)    → Seeking alignment
• x: [5,10] (48% of queries)  → Valuing depth

Insight:
→ You're in a "build and optimize" phase
→ High focus on recent, aligned, deep work
→ Pattern-seeking behavior suggests metacognition
→ Little attention to past failures (only 3% of queries)
   → Possible blind spot: May repeat old mistakes

Recommendation:
→ Query past failures explicitly to extract lessons
→ Your meta-awareness is a strength - continue pattern analysis
→ Balance future focus with historical learning

{
  // Find ring patterns
  detectPattern: {
    patternType: "work_focus",
    lookback: "6 months"
  },
  // Project current position forward
  predictNext: {
    horizon: "1 month"
  }
}

┌─────────────────────────────────────────────────────────┐
│ Work Focus Prediction (Jan 2025)                       │
├─────────────────────────────────────────────────────────┤
│                                                         │
│ Detected Pattern: 3-Phase Cycle (8 weeks)              │
│                                                         │
│ Phase 1: Build (3 weeks)                               │
│ Phase 2: Test/Refine (2 weeks)                         │
│ Phase 3: Plan/Learn (3 weeks)                          │
│                                                         │
│ Current Position (Dec 15, 2024):                       │
│ → End of Phase 2 (BWB testing complete)               │
│ → About to enter Phase 3                               │
│                                                         │
│ Prediction for Jan 2025:                                │
│                                                         │
│ Jan 1-21: Phase 3 (Plan/Learn)                         │
│ • Focus: Planning next iteration                       │
│ • Likely activities:                                   │
│   → Research new techniques (x∈[6,8])                  │
│   → Design system architecture                         │
│   → Learning new skills (70% probability: Python ML)   │
│ • Expected physics:                                     │
│   → Thrust: 4.5-5.2 (moderate)                         │
│   → Alignment: 0.6-0.7 (planning phase)                │
│                                                         │
│ Jan 22-31: Transition to Phase 1                       │
│ • Start new build cycle                                │
│ • Likely project: TrajectoryOS Phase 3                 │
│   (based on stated roadmap + current momentum)         │
│                                                         │
│ Confidence: 73%                                         │
│ (Based on 5 past cycles with 80% pattern adherence)    │
│                                                         │
│ Risk Factors:                                           │
│ • External disruption (15% probability)                │
│ • Burnout if overcommit (8% probability)               │
│                                                         │
│ Suggestion:                                             │
│ → Use Jan planning phase to solidify Phase 3 goals    │
│ → Keep gravity < 0.5 to enable smooth transition       │
└─────────────────────────────────────────────────────────┘

{
  // Find ALL high-escape-index periods
  query: "productive fulfilled energized thriving",
  coordinates: {
    x: [4, 10],  // Substantive work
    z: (z) => z > 0.6,  // Aligned
    n: (n) => n > 2  // Well-documented
  },
  physics: {
    escapeIndex: (e) => e > 1.2,  // Strongly escaping
    thrust: (t) => t > 5.5,
    alignment: (a) => a > 0.7
  },
  // Cluster and analyze
  analyze: {
    extractCommonalities: true,
    buildThriveProfile: true
  }
}

┌──────────────────────────────────────────────────────────────┐
│ Your Optimal Conditions for Thriving                        │
├──────────────────────────────────────────────────────────────┤
│                                                              │
│ Physical Coordinates:                                        │
│ • Depth: x ∈ [6, 9]                                         │
│   → Not too shallow (boring), not too deep (overwhelming)   │
│ • Alignment: z ∈ [0.7, 0.9]                                 │
│   → Clear direction, but room for creativity               │
│ • Alternatives: y ∈ [0, 1]                                  │
│   → Primary path with occasional exploration               │
│                                                              │
│ Life Physics:                                                │
│ • Thrust: >6.0                                              │
│ • Alignment: >0.75                                          │
│ • Gravity: <0.5                                             │
│ • Mass: <1.0                                                │
│ • Escape Index: >1.2                                        │
│                                                              │
│ Ring Patterns:                                               │
│ • Build cycles: 2-3 weeks optimal                           │
│ • Creative cycles: Active, not in reflection               │
│ • Learning cycles: Mid-cycle (applying knowledge)           │
│                                                              │
│ Environmental Factors:                                       │
│ • Solo work with occasional collaboration                   │
│ • Clear deadlines but not crushing                          │
│ • 1-2 major projects (not 3+)                               │
│ • Learning new things while building                        │
│                                                              │
│ Activity Mix:                                                │
│ • 60% building/coding                                       │
│ • 20% learning/research                                     │
│ • 15% planning/design                                       │
│ • 5% reflection/meta                                        │
│                                                              │
│ Anti-Patterns (Avoid):                                       │
│ • Scattered work (z < 0.4) → Leads to low η               │
│ • Too many projects (mass > 1.2) → Leads to burnout        │
│ • Pure learning (no building) → Feels unproductive         │
│ • Pure building (no learning) → Gets stale                 │
│                                                              │
│ Actionable Recommendations:                                  │
│ 1. Maintain 1-2 primary projects maximum                    │
│ 2. Ensure each project has z > 0.7                          │
│ 3. Block 2-week sprints for deep work (x ∈ [6,9])          │
│ 4. Keep constraint load low (gravity target: 0.3-0.4)      │
│ 5. Mix building (60%) with learning (20%)                   │
│ 6. Review monthly: Is η > 1.0? If not, adjust.             │
│                                                              │
│ Current Status vs Optimal:                                   │
│ ✓ Depth: 7.2 (optimal)                                      │
│ ✓ Alignment: 0.78 (optimal)                                 │
│ ✓ Thrust: 6.5 (optimal)                                     │
│ ✓ Gravity: 0.4 (optimal)                                    │
│ ✓ η: 1.25 (optimal)                                         │
│                                                              │
│ → You are currently in OPTIMAL CONDITIONS! Maintain this.   │
└──────────────────────────────────────────────────────────────┘

Semantic Layer:     What was said
   +
Topological Layer:  Where in life structure
   +
Physics Layer:      What was happening dynamically
   +
Temporal Layer:     When and in what order
   +
Pattern Layer:      What cycles exist
   =
Complete Life Understanding