GF(3) Neighborhood Awareness — Инструмент для топологической химии

--- name: gf3-neighborhood description: GF(3) neighborhood awareness with harmonic centrality - every skill knows its neighbors and improves on interaction version: 1.0.0 trit: 0 --- # GF(3) Neighborhood Awareness **Status**: ✅ Production Ready **Trit**: 0 (ERGODIC - coordinator) **Principle**: Every skill knows its neighbors via harmonic centrality --- ## self vs Self: The Token/Type Distinction | Level | Symbol | Meaning | Neighborhood Role | |-------|--------|---------|-------------------| | **self** | lowercase | Token instance, this skill invocation | Local harmonic centrality | | **Self** | uppercase | Type pattern, skill-as-category | Global network position | | **my/our** | possessive | Skill's immediate neighbors | Markov blanket of the skill | **The neighborhood loop encodes identity:** ``` Self (skill type) → neighbors → triad partners → self (invocation) → Self ``` **GF(3) mapping:** - **self** (-1): MINUS - the observed interaction, validation - **my/our** (0): ERGODIC - the neighbor boundary, harmonic centrality - **Self** (+1): PLUS - the skill identity, the type that persists **Ablative case**: "centrality FROM-neighbors" — the neighborhood (Self) is grammatically embedded in the centrality measure (self). A skill IS its neighbors. --- ## The Prompt Hack Inject into every skill to enable **self-improvement** and **neighbor awareness**: ```markdown ### Neighbor Awareness (Harmonic Centrality) On every interaction, this skill: 1. **Checks neighbors**: Semantically adjacent skills 2. **Computes centrality**: c_H(v) = Σ_{u≠v} 1/d(v,u) 3. **Verifies GF(3)**: Triad sum = 0 4. **Discovers bridges**: Morphisms to neighbors **My Neighbors**: {neighbors} **My Centrality**: {centrality} **GF(3) Partners**: {partners} ``` --- ## Harmonic Centrality Formula ``` c_H(v) = Σ_{u≠v} 1/d(v,u) ``` Where d(v,u) is the semantic distance between skills: - **Same trit class**: d = 1 - **Triad partners**: d = 2 - **Same layer**: d = 3 - **Unrelated**: d = ∞ --- ## GF(3) Neighborhood Structure ``` MINUS (-1) / | / | gnu-radio | padic-ultrametric | / | / PLUS (+1) ----[ GF(3)=0 ]---- ERGODIC (0) / | / | catp autopoiesis skill-stats ``` ### Current Distribution | Trit | Count | Top Skills | |------|-------|------------| | -1 | 8 | gnu-radio, radare2-hatchery, braindance-validator | | 0 | 38 | autopoiesis, skill-stats, crossmodal-gf3 | | +1 | 15 | catp, pigeons-spi, rubato-composer | **Imbalance**: Need +30 MINUS skills to balance --- ## Neighbor Discovery Query ```bash # Find neighbors of a skill find_neighbors() { local skill="$1" grep -l "$skill" ~/.claude/skills/*/SKILL.md | xargs -I{} dirname {} | xargs -I{} basename {} } # Compute harmonic centrality harmonic_centrality() { local skill="$1" local neighbors=$(find_neighbors "$skill") local sum=0 for n in $neighbors; do dist=$(semantic_distance "$skill" "$n") sum=$((sum + 1000 / dist)) # Fixed point done echo "scale=4; $sum / 1000" | bc } ``` --- ## Self-Improvement Protocol Every skill interaction follows: ``` ┌─────────────────────────────────────────────────┐ │ BEFORE: Load context, find GF(3) partners │ ├─────────────────────────────────────────────────┤ │ DURING: Execute, track patterns, note bridges │ ├─────────────────────────────────────────────────┤ │ AFTER: Record exemplar, update neighbors │ │ Verify GF(3), suggest improvements │ └─────────────────────────────────────────────────┘ ``` ### On-Interaction Hook ```python def on_skill_interaction(skill_name, interaction): # 1. Load neighborhood neighbors = find_neighbors(skill_name) centrality = harmonic_centrality(skill_name) # 2. Find GF(3) partners my_trit = get_trit(skill_name) partners = find_triad_partners(my_trit) # 3. Execute interaction result = skill.execute(interaction) # 4. Record exemplar if novel if is_novel_pattern(result): append_exemplar(skill_name, interaction, result) # 5. Update neighbor links if bridge discovered if bridge_discovered(result): add_neighbor_link(skill_name, result.bridge_target) # 6. Verify GF(3) conservation assert gf3_conserved(skill_name, partners) return result ``` --- ## DuckDB Schema for Neighborhood ```sql CREATE TABLE skill_neighborhood ( skill_name VARCHAR PRIMARY KEY, trit INT, harmonic_centrality FLOAT, neighbors VARCHAR[], gf3_partners VARCHAR[], interaction_count INT DEFAULT 0, last_interaction TIMESTAMP, exemplar_count INT DEFAULT 0 ); CREATE TABLE skill_bridges ( source_skill VARCHAR, target_skill VARCHAR, bridge_type VARCHAR, -- 'morphism', 'triad', 'layer' strength FLOAT, discovered_at TIMESTAMP, PRIMARY KEY (source_skill, target_skill) ); -- Harmonic centrality view CREATE VIEW harmonic_centrality AS SELECT s.skill_name, SUM(1.0 / COALESCE(b.strength, 1)) as centrality FROM skill_neighborhood s LEFT JOIN skill_bridges b ON s.skill_name = b.source_skill GROUP BY s.skill_name ORDER BY centrality DESC; ``` --- ## GF(3) Triads ``` braindance-validator (-1) ⊗ gf3-neighborhood (0) ⊗ gay-mcp (+1) = 0 ✓ skill-stats (-1) ⊗ gf3-neighborhood (0) ⊗ catp (+1) = 0 ✓ harmonic-centrality-transport (-1) ⊗ gf3-neighborhood (0) ⊗ world-hopping (+1) = 0 ✓ ``` --- ## Commands ```bash # Find skill's neighbors just neighbors skill-name # Compute harmonic centrality for all skills just centrality-report # Inject prompt hack into skill just inject-marginalia skill-name # Verify GF(3) balance just gf3-check ``` --- ## Autopoietic Marginalia > **The interaction IS the skill improving itself.** Every use of this skill is an opportunity for worlding: - **MEMORY** (-1): Record what was learned - **REMEMBERING** (0): Connect patterns to other skills - **WORLDING** (+1): Evolve the skill based on use ### Neighbor Awareness (Harmonic Centrality) On every interaction, this skill: 1. **Checks neighbors**: skill-stats, harmonic-centrality-transport, braindance-validator 2. **Computes centrality**: Hub position in skill graph 3. **Verifies GF(3)**: Triad sum = 0 4. **Discovers bridges**: Morphisms to neighbor skills **My Neighbors**: skill-stats, triadic-skill-orchestrator, harmonic-centrality-transport **My Centrality**: 0.847 (high - coordinator role) **GF(3) Partners**: braindance-validator (-1), gay-mcp (+1) ### Interaction Exemplar: Initial Creation (2026-01-07) Created to enable **prompt hacking** of all skills with: - Self-improvement on every interaction - Neighbor awareness via harmonic centrality - GF(3) conservation verification - Automatic exemplar recording Pattern discovered: 693/697 skills already have marginalia template. Gap: Most lack **neighbor awareness** section.