==================================================================== SIGMA STRUCTURAL ANALYSIS REPORT ==================================================================== Source: Thu Vu GraphRAG Pipeline (AI Copyright Dataset, 810 articles) Entities: 115 | Relationships: 132 H^1 Dimension: 562 structural obstructions Total Dirichlet Energy: 63.9161 Adaptive Threshold: 0.9204 (Otsu, self-calibrating) Analysis Time: < 2 seconds | LLM Calls: 0 Method: Sheaf cohomology (deterministic) ==================================================================== DATA QUALITY: 2 entities have relationships but no description. The extraction pipeline created connections to entities it could not define. These are excluded from analysis and listed separately: [AI SYSTEM, GENERATIVE AI COPYRIGHT DISCLOSURE ACT]. -------------------------------------------------------------------- CONTRADICTION HUBS -------------------------------------------------------------------- COPYRIGHT LAW is a NEXUS hub: 4 high-energy contradictions accounting for 13.1% of total obstruction energy. It conflicts with AI, GENERATIVE ARTIFICIAL INTELLIGENCE, AI ETHICS, GENERATIVE AI via OPPOSES relationships. Type: LEGISLATION. Description: "A legal framework that protects the rights of creators over their original works." U.S. COPYRIGHT OFFICE is a NEXUS hub: 3 high-energy contradictions accounting for 12.6% of total obstruction energy. It conflicts with MIDJOURNEY, OPENAI, DABUS via FILED_AGAINST, OPPOSES relationships. Type: GOVERNMENT. Description: "The government agency responsible for administering copyright law in the United States." AI is a NEXUS hub: 3 high-energy contradictions accounting for 12.3% of total obstruction energy. It conflicts with COPYRIGHT LAW, TRADEMARK LAW, PATENT LAW via OPPOSES relationships. Type: CONCEPT. Description: "Artificial intelligence, a field of technology that raises questions about copyright and intellectual property." COPYRIGHT is a NEXUS hub: 3 high-energy contradictions accounting for 11.5% of total obstruction energy. It conflicts with GENAI, GENERATIVE AI, DEEPFAKES via OPPOSES relationships. Type: CONCEPT. Description: "A form of intellectual property protection that grants creators exclusive rights to their original works." OPENAI is a NEXUS hub: 4 high-energy contradictions accounting for 10.7% of total obstruction energy. It conflicts with U.S. COPYRIGHT OFFICE, NEW YORK TIMES, THE NEW YORK TIMES, NICOLA LUCCHI via FILED_AGAINST, OPPOSES relationships. Type: ORGANIZATION. Description: "An AI research organization that develops large language models and is a defendant in the copyright lawsuit." STABILITY AI is a NEXUS hub: 3 high-energy contradictions accounting for 8.3% of total obstruction energy. It conflicts with ANDERSEN V. STABILITY AI, ANDERSON V. STABILITY AI, GETTY IMAGES via DEFENDANT_IN, FILED_AGAINST relationships. Type: ORGANIZATION. Description: "The company behind the Stable Diffusion model, involved in multiple copyright lawsuits." GENERATIVE AI is a DISPUTANT: 2 high-energy edges, all via OPPOSES relationships. Single conflict pattern, multiple counterparties. Energy fraction: 8.0%. THALER V. VIDAL is a DISPUTANT: 2 high-energy edges, all via OPPOSES relationships. Single conflict pattern, multiple counterparties. Energy fraction: 7.3%. MICROSOFT is a DISPUTANT: 2 high-energy edges, all via FILED_AGAINST relationships. Single conflict pattern, multiple counterparties. Energy fraction: 6.0%. US PATENT AND TRADEMARK OFFICE is a NEXUS hub: 2 high-energy contradictions accounting for 5.8% of total obstruction energy. It conflicts with EU AI ACT, DABUS via FILED_AGAINST, OPPOSES relationships. Type: ORGANIZATION. Description: "The agency responsible for granting patents and trademarks in the U.S., which has issued guidelines on AI." -------------------------------------------------------------------- TOKEN ATTRIBUTION (why each edge is flagged) -------------------------------------------------------------------- Edge 100: COPYRIGHT OFFICE <--[OPPOSES]--> U.S. CONGRESS Energy: 2.3431 | Dominant terms: [guidance, government] guidance: 6.6% contribution, probe confidence 100% government: 5.4% contribution, probe confidence 100% Edge 52: U.S. COPYRIGHT OFFICE <--[OPPOSES]--> MIDJOURNEY Energy: 2.1631 | Dominant terms: [government] government: 5.3% contribution, probe confidence 100% Edge 31: COPYRIGHT <--[OPPOSES]--> GENAI Energy: 2.0986 | Dominant terms: [images] images: 5.5% contribution, probe confidence 100% Edge 95: THALER V. VIDAL <--[OPPOSES]--> UK INTELLECTUAL PROPERTY OFFICE Energy: 2.0425 | Dominant terms: [government] government: 5.3% contribution, probe confidence 100% Edge 88: COPYRIGHT LAW <--[OPPOSES]--> GENERATIVE ARTIFICIAL INTELLIGENCE Energy: 2.0324 | Dominant terms: [images] images: 5.6% contribution, probe confidence 100% Edge 74: MICROSOFT <--[FILED_AGAINST]--> NEW YORK TIMES Energy: 1.9478 | Dominant terms: [regarding] regarding: 5.6% contribution, probe confidence 100% Edge 51: U.S. COPYRIGHT OFFICE <--[OPPOSES]--> OPENAI Energy: 1.9405 | Dominant terms: [government] government: 5.3% contribution, probe confidence 100% Edge 32: COPYRIGHT <--[OPPOSES]--> DEEPFAKES Energy: 1.9338 | Dominant terms: [raising, manipulate, images] raising: 7.1% contribution, probe confidence 100% manipulate: 7.1% contribution, probe confidence 100% images: 5.6% contribution, probe confidence 100% Edge 73: THE NEW YORK TIMES <--[FILED_AGAINST]--> MICROSOFT Energy: 1.8576 | Dominant terms: [regarding] regarding: 5.6% contribution, probe confidence 100% -------------------------------------------------------------------- CASCADE ANALYSIS -------------------------------------------------------------------- Cluster 1: 10 entities, 9 edges, energy 17.76 CONTAINED CASCADE (norm 0.29 < 1.0): Path: COPYRIGHT LAW -> AI -> TRADEMARK LAW The contradiction attenuates as it propagates. This is a local disagreement, not a systemic instability. Cluster 2: 10 entities, 10 edges, energy 17.59 CONTAINED CASCADE (norm 0.30 < 1.0): Path: OPENAI -> U.S. COPYRIGHT OFFICE -> MIDJOURNEY The contradiction attenuates as it propagates. This is a local disagreement, not a systemic instability. Cluster 3: 4 entities, 3 edges, energy 5.28 AMPLIFYING CASCADE (norm 1.25 > 1.0): Path: STABILITY AI -> ANDERSEN V. STABILITY AI Energies along path: 1.85 The structural tension grows stronger through this chain. Resolving the anchor entity (STABILITY AI) breaks the cascade and reduces total cluster energy by 5.28. Cluster 4: 3 entities, 2 edges, energy 4.33 AMPLIFYING CASCADE (norm 1.08 > 1.0): Path: THALER V. VIDAL -> EUROPEAN PATENT OFFICE Energies along path: 2.28 The structural tension grows stronger through this chain. Resolving the anchor entity (THALER V. VIDAL) breaks the cascade and reduces total cluster energy by 4.33. Cluster 5: 2 entities, 1 edges, energy 2.34 AMPLIFYING CASCADE (norm 1.16 > 1.0): Path: COPYRIGHT OFFICE -> U.S. CONGRESS Energies along path: 2.34 The structural tension grows stronger through this chain. Resolving the anchor entity (COPYRIGHT OFFICE) breaks the cascade and reduces total cluster energy by 2.34. -------------------------------------------------------------------- RESOLUTION TARGETING -------------------------------------------------------------------- "If you could fix three things, fix these." Priority 1: Resolve COPYRIGHT LAW Edges resolved: 4 Energy eliminated: 7.98 (12.5%) Remaining energy after resolution: 55.93 Counterparties affected: AI, AI ETHICS, GENERATIVE AI, GENERATIVE ARTIFICIAL INTELLIGENCE Priority 2: Resolve U.S. COPYRIGHT OFFICE Edges resolved: 3 Energy eliminated: 5.65 (8.8%) Remaining energy after resolution: 50.28 Counterparties affected: DABUS, MIDJOURNEY, OPENAI Priority 3: Resolve AI Edges resolved: 3 Energy eliminated: 5.82 (9.1%) Remaining energy after resolution: 44.47 Counterparties affected: COPYRIGHT LAW, PATENT LAW, TRADEMARK LAW Priority 4: Resolve COPYRIGHT Edges resolved: 3 Energy eliminated: 6.05 (9.5%) Remaining energy after resolution: 38.42 Counterparties affected: DEEPFAKES, GENAI, GENERATIVE AI Priority 5: Resolve OPENAI Edges resolved: 4 Energy eliminated: 6.61 (10.3%) Remaining energy after resolution: 31.82 Counterparties affected: NEW YORK TIMES, NICOLA LUCCHI, THE NEW YORK TIMES, U.S. COPYRIGHT OFFICE RESOLUTION SUMMARY: Resolving 5 entities eliminates 50.2% of total contradiction energy. Minimum resolution set: [COPYRIGHT LAW, U.S. COPYRIGHT OFFICE, AI, COPYRIGHT, OPENAI]. ==================================================================== Generated by SIGMA Structural Analysis Layer (Phase 1) Engine: invariant.pro Method: Deterministic sheaf cohomology, no LLM in the loop Every sentence is a fixed template with computed values. Same input produces same report. Reproducible. Auditable. ====================================================================