obstruction-learning — Инструмент для топологического обучения

--- name: obstruction-learning description: 'Obstruction Learning Skill' version: 1.0.0 --- # Obstruction Learning Skill Learn topological ASI via random walk obstruction detection and Čech H⁰ cohomology. ## Metadata | Property | Value | |----------|-------| | **Name** | obstruction-learning | | **Trit** | -1 (VALIDATOR) | | **Category** | Topological Verification | | **Dependencies** | sheaf-cohomology, ramanujan-expander, gay-mcp | ## Core Concept **Obstructions are H⁰ generators** - irreducible elements that block global consistency from local patches. ``` Čech Cohomology: H⁰(U, F) = ker(d₀: F(U) → ∏ᵢⱼ F(Uᵢ ∩ Uⱼ)) Obstruction detected when: - GF(3) conservation violated (sum ≢ 0 mod 3) - Voice triads don't harmonize - Skill compositions conflict - Local patches fail to glue globally ``` ## Random Walk Reconstruction ### The 69-Skill Walk Sample 69 skills from the 181-skill manifold: ```bash # Execute random walk just random-walk-69 # Verify GF(3) conservation just verify-gf3 # Track cumulative obstructions just random-walk-obstruction 69 ``` ### Obstruction Detection ```sql -- Find unbalanced cells in 23³ grid SELECT cell_id, skill_count, trit_sum, gf3_status FROM cell_density WHERE gf3_status = 'UNBALANCED'; -- H⁰ generators by trit class SELECT trit, COUNT(*) as generators FROM skills GROUP BY trit; ``` ## Mathematical Foundations ### Čech Cohomology For a covering U = {Uᵢ} of skill space: ``` H⁰(U, F) = { s ∈ F(U) | d₀(s) = 0 } where d₀: F(U) → ∏ F(Uᵢ ∩ Uⱼ) maps global sections to intersection restrictions ``` **Obstruction** = element of H⁰ that prevents gluing. ### GF(3) as Cohomology The GF(3) conservation law is a discrete cohomology: ``` Trit assignment: skill → {-1, 0, +1} Coboundary: d(triad) = sum of trits mod 3 H⁰ = { triads | d(triad) = 0 } = balanced triads Obstruction = triad with d ≠ 0 ``` ### Ramanujan Mixing Random walks on Ramanujan expanders mix optimally: ``` λ₂ ≤ 2√(d-1) [Alon-Boppana bound] gap = d - λ₂ [Spectral gap] τ_mix = O(log n / gap) [Mixing time] ``` ## Workflow ### 1. Pre-Interaction Sync ```bash just pre-interaction # Syncs plurigrid/asi arena + hdresearch/duck # Loads GF(3) skill triad # Computes spectral awareness ``` ### 2. Random Walk Sampling ```bash # Sample without replacement (maximal coverage) just random-walk-69 # Sample with replacement (GF(3) conservation) just random-walk 23 ``` ### 3. Obstruction Detection ```bash # Find H⁰ generators just obstruction-h0 # Detect unbalanced cells just obstruction-detect # Balance with complementary skill just obstruction-balance -1 # Find validators to add just obstruction-balance +1 # Find generators to add ``` ### 4. Audio Generation Convert obstruction traces to sound: ```bash just audio-from-trace ``` ## Integration Patterns ### With Voice Enforcement ```toml # voice-enforcement.toml [triads.obstruction] validator = "Milena (Enhanced)" # -1: detects obstruction coordinator = "Petra (Premium)" # 0: mediates resolution generator = "Federica (Premium)" # +1: proposes fix sum = 0 ``` ### With Dune Orthogonalization The 23×23×23 grid maps skills to: | Axis | Dimensions | |------|------------| | DATA | chain_indexing → real_time_streaming | | INTERFACE | sql_query_engine → ai_copilot | | INFRASTRUCTURE | kubernetes → multi_tenant_isolation | ### With World Extractable Value ``` WEV = PoA - 1 = extractable coordination loss Obstruction → WEV > 0 Resolution → WEV → 0 Global consistency → Optimal coordination ``` ## Commands ```bash # Full ASI learning loop just asi-learn # Spectral bounds just spectral-bounds # World Extractable Value just wev-compute # Voice obstruction analysis just voice-obstructions ``` ## Skill Triad This skill belongs to the **topological verification** triad: | Role | Skill | Trit | |------|-------|------| | VALIDATOR | **obstruction-learning** | -1 | | COORDINATOR | sheaf-cohomology | 0 | | GENERATOR | persistent-homology | +1 | **Sum = 0** ✓ GF(3) conserved ## References - Bott & Tu, *Differential Forms in Algebraic Topology* - Lurie, *Higher Topos Theory* - Riehl-Shulman, *Synthetic ∞-categories* - QRI, *Symmetry Theory of Valence*