--- name: obstruction-learning-1d29204e654f 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* ## Scientific Skill Interleaving This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem: ### Graph Theory - **networkx** [○] via bicomodule - Universal graph hub ### Bibliography References - `general`: 734 citations in bib.duckdb ## Cat# Integration This skill maps to **Cat# = Comod(P)** as a bicomodule in the equipment structure: ``` Trit: 0 (ERGODIC) Home: Prof Poly Op: ⊗ Kan Role: Adj Color: #26D826 ``` ### GF(3) Naturality The skill participates in triads satisfying: ``` (-1) + (0) + (+1) ≡ 0 (mod 3) ``` This ensures compositional coherence in the Cat# equipment structure. --- Source attribution: plurigrid Original project: https://github.com/plurigrid/asi/blob/293ce9f76e3abcd5ba18db284688bc0d9ac6691d/plugins/asi/skills/obstruction-learning/SKILL.md License: MIT License information: https://opensource.org/license/mit Original upstream instructions; downloaded from Mega AI Hub. ## Upstream license notice MIT License Copyright (c) 2025 SkillCreator.ai Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. 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IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. # Mega AI Hub resource metadata Creator / publisher: plurigrid Original project: https://github.com/plurigrid/asi/blob/293ce9f76e3abcd5ba18db284688bc0d9ac6691d/plugins/asi/skills/obstruction-learning/SKILL.md Attribution basis: Source repository record Fields of work: Data & Analytics, Development & Engineering, Education & Research Roles: Data Scientist, ML / AI Engineer, Researcher Specialties: API, Testing Tools: Just Country applicability: Country not specified Classification basis: Source catalog labels Instruction SHA-256: 8118014824ccbafd387b99cd47b0edbe63ad04553b0921e5d3ecc16e7b4e0c7c