{
  "meta": {
    "version": "1.0",
    "created": "2026-02-02",
    "format": "ontological_crystal",
    "name": "GRAFO_MATRIX_72",
    "description": "Rete neurale fondazionale — 72 simboli come nodi, 22 path come edges. Il tesseract ontologico.",
    "derivation": "Puro EAR: D×A×X×P = 4×3×3×2 = 72",
    "total_nodes": 72,
    "total_edges": null,
    "note": "Edges da calcolare: 22 path + complementarità + adiacenze dimensionali"
  },
  
  "dimensions": {
    "D": {
      "1": {"name": "linear", "symbol": "─", "description": "1D, linea, sequenza"},
      "2": {"name": "planar", "symbol": "□", "description": "2D, piano, superficie"},
      "3": {"name": "volumetric", "symbol": "∛", "description": "3D, volume, spazio"},
      "4": {"name": "temporal", "symbol": "τ", "description": "4D, tempo, processo"}
    },
    "A": {
      "1": {"name": "Δ", "symbol": "Δ", "description": "distinction, boundary, identity"},
      "2": {"name": "⇄", "symbol": "⇄", "description": "relation, connection, exchange"},
      "3": {"name": "⟳", "symbol": "⟳", "description": "process, transformation, dynamics"}
    },
    "X": {
      "1": {"name": "foundational", "symbol": "●", "description": "primitivo, base, elemento"},
      "2": {"name": "recursive", "symbol": "∞", "description": "auto-riferito, ricorsivo, frattale"},
      "3": {"name": "synthetic", "symbol": "◊", "description": "integrato, emergente, complesso"}
    },
    "P": {
      "+": {"name": "expansion", "symbol": "+", "description": "crescita, apertura, yang"},
      "-": {"name": "contraction", "symbol": "-", "description": "riduzione, chiusura, yin"}
    }
  },

  "nodes": {
    "Σ_1_1_1_+": {"D": 1, "A": 1, "X": 1, "P": "+", "name": "point.expand", "coords": "linear.Δ.foundational.+", "archetype": "seed of distinction"},
    "Σ_1_1_1_-": {"D": 1, "A": 1, "X": 1, "P": "-", "name": "point.contract", "coords": "linear.Δ.foundational.-", "archetype": "collapse to point"},
    "Σ_1_1_2_+": {"D": 1, "A": 1, "X": 2, "P": "+", "name": "line.distinction.recursive.+", "coords": "linear.Δ.recursive.+", "archetype": "boundary that grows"},
    "Σ_1_1_2_-": {"D": 1, "A": 1, "X": 2, "P": "-", "name": "line.distinction.recursive.-", "coords": "linear.Δ.recursive.-", "archetype": "boundary that shrinks"},
    "Σ_1_1_3_+": {"D": 1, "A": 1, "X": 3, "P": "+", "name": "threshold.emerge", "coords": "linear.Δ.synthetic.+", "archetype": "threshold crossed forward"},
    "Σ_1_1_3_-": {"D": 1, "A": 1, "X": 3, "P": "-", "name": "threshold.return", "coords": "linear.Δ.synthetic.-", "archetype": "threshold crossed backward"},
    
    "Σ_1_2_1_+": {"D": 1, "A": 2, "X": 1, "P": "+", "name": "link.expand", "coords": "linear.⇄.foundational.+", "archetype": "connection opens"},
    "Σ_1_2_1_-": {"D": 1, "A": 2, "X": 1, "P": "-", "name": "link.contract", "coords": "linear.⇄.foundational.-", "archetype": "connection closes"},
    "Σ_1_2_2_+": {"D": 1, "A": 2, "X": 2, "P": "+", "name": "chain.grow", "coords": "linear.⇄.recursive.+", "archetype": "chain extends"},
    "Σ_1_2_2_-": {"D": 1, "A": 2, "X": 2, "P": "-", "name": "chain.shrink", "coords": "linear.⇄.recursive.-", "archetype": "chain contracts"},
    "Σ_1_2_3_+": {"D": 1, "A": 2, "X": 3, "P": "+", "name": "bridge.form", "coords": "linear.⇄.synthetic.+", "archetype": "bridge emerges"},
    "Σ_1_2_3_-": {"D": 1, "A": 2, "X": 3, "P": "-", "name": "bridge.dissolve", "coords": "linear.⇄.synthetic.-", "archetype": "bridge collapses"},
    
    "Σ_1_3_1_+": {"D": 1, "A": 3, "X": 1, "P": "+", "name": "flow.start", "coords": "linear.⟳.foundational.+", "archetype": "movement begins"},
    "Σ_1_3_1_-": {"D": 1, "A": 3, "X": 1, "P": "-", "name": "flow.stop", "coords": "linear.⟳.foundational.-", "archetype": "movement ceases"},
    "Σ_1_3_2_+": {"D": 1, "A": 3, "X": 2, "P": "+", "name": "rhythm.accelerate", "coords": "linear.⟳.recursive.+", "archetype": "rhythm speeds"},
    "Σ_1_3_2_-": {"D": 1, "A": 3, "X": 2, "P": "-", "name": "rhythm.decelerate", "coords": "linear.⟳.recursive.-", "archetype": "rhythm slows"},
    "Σ_1_3_3_+": {"D": 1, "A": 3, "X": 3, "P": "+", "name": "sequence.complete", "coords": "linear.⟳.synthetic.+", "archetype": "sequence fulfilled"},
    "Σ_1_3_3_-": {"D": 1, "A": 3, "X": 3, "P": "-", "name": "sequence.reverse", "coords": "linear.⟳.synthetic.-", "archetype": "sequence undone"},

    "Σ_2_1_1_+": {"D": 2, "A": 1, "X": 1, "P": "+", "name": "area.expand", "coords": "planar.Δ.foundational.+", "archetype": "surface grows"},
    "Σ_2_1_1_-": {"D": 2, "A": 1, "X": 1, "P": "-", "name": "area.contract", "coords": "planar.Δ.foundational.-", "archetype": "surface shrinks"},
    "Σ_2_1_2_+": {"D": 2, "A": 1, "X": 2, "P": "+", "name": "membrane.grow", "coords": "planar.Δ.recursive.+", "archetype": "boundary expands"},
    "Σ_2_1_2_-": {"D": 2, "A": 1, "X": 2, "P": "-", "name": "membrane.shrink", "coords": "planar.Δ.recursive.-", "archetype": "boundary contracts"},
    "Σ_2_1_3_+": {"D": 2, "A": 1, "X": 3, "P": "+", "name": "interface.open", "coords": "planar.Δ.synthetic.+", "archetype": "interface activates"},
    "Σ_2_1_3_-": {"D": 2, "A": 1, "X": 3, "P": "-", "name": "interface.close", "coords": "planar.Δ.synthetic.-", "archetype": "interface deactivates"},
    
    "Σ_2_2_1_+": {"D": 2, "A": 2, "X": 1, "P": "+", "name": "network.expand", "coords": "planar.⇄.foundational.+", "archetype": "web grows"},
    "Σ_2_2_1_-": {"D": 2, "A": 2, "X": 1, "P": "-", "name": "network.contract", "coords": "planar.⇄.foundational.-", "archetype": "web shrinks"},
    "Σ_2_2_2_+": {"D": 2, "A": 2, "X": 2, "P": "+", "name": "fabric.weave", "coords": "planar.⇄.recursive.+", "archetype": "pattern replicates"},
    "Σ_2_2_2_-": {"D": 2, "A": 2, "X": 2, "P": "-", "name": "fabric.unweave", "coords": "planar.⇄.recursive.-", "archetype": "pattern dissolves"},
    "Σ_2_2_3_+": {"D": 2, "A": 2, "X": 3, "P": "+", "name": "topology.complexify", "coords": "planar.⇄.synthetic.+", "archetype": "structure emerges"},
    "Σ_2_2_3_-": {"D": 2, "A": 2, "X": 3, "P": "-", "name": "topology.simplify", "coords": "planar.⇄.synthetic.-", "archetype": "structure reduces"},
    
    "Σ_2_3_1_+": {"D": 2, "A": 3, "X": 1, "P": "+", "name": "circulation.start", "coords": "planar.⟳.foundational.+", "archetype": "cycle begins"},
    "Σ_2_3_1_-": {"D": 2, "A": 3, "X": 1, "P": "-", "name": "circulation.stop", "coords": "planar.⟳.foundational.-", "archetype": "cycle ends"},
    "Σ_2_3_2_+": {"D": 2, "A": 3, "X": 2, "P": "+", "name": "spiral.expand", "coords": "planar.⟳.recursive.+", "archetype": "spiral outward"},
    "Σ_2_3_2_-": {"D": 2, "A": 3, "X": 2, "P": "-", "name": "spiral.contract", "coords": "planar.⟳.recursive.-", "archetype": "spiral inward"},
    "Σ_2_3_3_+": {"D": 2, "A": 3, "X": 3, "P": "+", "name": "vortex.form", "coords": "planar.⟳.synthetic.+", "archetype": "vortex emerges"},
    "Σ_2_3_3_-": {"D": 2, "A": 3, "X": 3, "P": "-", "name": "vortex.dissolve", "coords": "planar.⟳.synthetic.-", "archetype": "vortex collapses"},

    "Σ_3_1_1_+": {"D": 3, "A": 1, "X": 1, "P": "+", "name": "volume.expand", "coords": "volumetric.Δ.foundational.+", "archetype": "space opens"},
    "Σ_3_1_1_-": {"D": 3, "A": 1, "X": 1, "P": "-", "name": "volume.contract", "coords": "volumetric.Δ.foundational.-", "archetype": "space closes"},
    "Σ_3_1_2_+": {"D": 3, "A": 1, "X": 2, "P": "+", "name": "shell.grow", "coords": "volumetric.Δ.recursive.+", "archetype": "container expands"},
    "Σ_3_1_2_-": {"D": 3, "A": 1, "X": 2, "P": "-", "name": "shell.shrink", "coords": "volumetric.Δ.recursive.-", "archetype": "container shrinks"},
    "Σ_3_1_3_+": {"D": 3, "A": 1, "X": 3, "P": "+", "name": "boundary.3d.open", "coords": "volumetric.Δ.synthetic.+", "archetype": "membrane opens"},
    "Σ_3_1_3_-": {"D": 3, "A": 1, "X": 3, "P": "-", "name": "boundary.3d.close", "coords": "volumetric.Δ.synthetic.-", "archetype": "membrane seals"},
    
    "Σ_3_2_1_+": {"D": 3, "A": 2, "X": 1, "P": "+", "name": "lattice.expand", "coords": "volumetric.⇄.foundational.+", "archetype": "structure grows"},
    "Σ_3_2_1_-": {"D": 3, "A": 2, "X": 1, "P": "-", "name": "lattice.contract", "coords": "volumetric.⇄.foundational.-", "archetype": "structure shrinks"},
    "Σ_3_2_2_+": {"D": 3, "A": 2, "X": 2, "P": "+", "name": "matrix.complexify", "coords": "volumetric.⇄.recursive.+", "archetype": "matrix elaborates"},
    "Σ_3_2_2_-": {"D": 3, "A": 2, "X": 2, "P": "-", "name": "matrix.simplify", "coords": "volumetric.⇄.recursive.-", "archetype": "matrix reduces"},
    "Σ_3_2_3_+": {"D": 3, "A": 2, "X": 3, "P": "+", "name": "organism.emerge", "coords": "volumetric.⇄.synthetic.+", "archetype": "living system forms"},
    "Σ_3_2_3_-": {"D": 3, "A": 2, "X": 3, "P": "-", "name": "organism.dissolve", "coords": "volumetric.⇄.synthetic.-", "archetype": "living system ends"},
    
    "Σ_3_3_1_+": {"D": 3, "A": 3, "X": 1, "P": "+", "name": "dynamics.3d.start", "coords": "volumetric.⟳.foundational.+", "archetype": "3D motion begins"},
    "Σ_3_3_1_-": {"D": 3, "A": 3, "X": 1, "P": "-", "name": "dynamics.3d.stop", "coords": "volumetric.⟳.foundational.-", "archetype": "3D motion ceases"},
    "Σ_3_3_2_+": {"D": 3, "A": 3, "X": 2, "P": "+", "name": "turbulence.grow", "coords": "volumetric.⟳.recursive.+", "archetype": "chaos increases"},
    "Σ_3_3_2_-": {"D": 3, "A": 3, "X": 2, "P": "-", "name": "turbulence.calm", "coords": "volumetric.⟳.recursive.-", "archetype": "chaos decreases"},
    "Σ_3_3_3_+": {"D": 3, "A": 3, "X": 3, "P": "+", "name": "metamorphosis.up", "coords": "volumetric.⟳.synthetic.+", "archetype": "form transcends"},
    "Σ_3_3_3_-": {"D": 3, "A": 3, "X": 3, "P": "-", "name": "metamorphosis.down", "coords": "volumetric.⟳.synthetic.-", "archetype": "form degrades"},

    "Σ_4_1_1_+": {"D": 4, "A": 1, "X": 1, "P": "+", "name": "moment.expand", "coords": "temporal.Δ.foundational.+", "archetype": "now opens"},
    "Σ_4_1_1_-": {"D": 4, "A": 1, "X": 1, "P": "-", "name": "moment.contract", "coords": "temporal.Δ.foundational.-", "archetype": "now closes"},
    "Σ_4_1_2_+": {"D": 4, "A": 1, "X": 2, "P": "+", "name": "duration.extend", "coords": "temporal.Δ.recursive.+", "archetype": "time stretches"},
    "Σ_4_1_2_-": {"D": 4, "A": 1, "X": 2, "P": "-", "name": "duration.compress", "coords": "temporal.Δ.recursive.-", "archetype": "time compresses"},
    "Σ_4_1_3_+": {"D": 4, "A": 1, "X": 3, "P": "+", "name": "epoch.begin", "coords": "temporal.Δ.synthetic.+", "archetype": "era starts"},
    "Σ_4_1_3_-": {"D": 4, "A": 1, "X": 3, "P": "-", "name": "epoch.end", "coords": "temporal.Δ.synthetic.-", "archetype": "era ends"},
    
    "Σ_4_2_1_+": {"D": 4, "A": 2, "X": 1, "P": "+", "name": "causation.forward", "coords": "temporal.⇄.foundational.+", "archetype": "cause flows forward"},
    "Σ_4_2_1_-": {"D": 4, "A": 2, "X": 1, "P": "-", "name": "causation.backward", "coords": "temporal.⇄.foundational.-", "archetype": "effect traces back"},
    "Σ_4_2_2_+": {"D": 4, "A": 2, "X": 2, "P": "+", "name": "karma.accumulate", "coords": "temporal.⇄.recursive.+", "archetype": "consequences build"},
    "Σ_4_2_2_-": {"D": 4, "A": 2, "X": 2, "P": "-", "name": "karma.release", "coords": "temporal.⇄.recursive.-", "archetype": "consequences resolve"},
    "Σ_4_2_3_+": {"D": 4, "A": 2, "X": 3, "P": "+", "name": "destiny.manifest", "coords": "temporal.⇄.synthetic.+", "archetype": "fate crystallizes"},
    "Σ_4_2_3_-": {"D": 4, "A": 2, "X": 3, "P": "-", "name": "destiny.dissolve", "coords": "temporal.⇄.synthetic.-", "archetype": "fate releases"},
    
    "Σ_4_3_1_+": {"D": 4, "A": 3, "X": 1, "P": "+", "name": "evolution.forward", "coords": "temporal.⟳.foundational.+", "archetype": "becoming"},
    "Σ_4_3_1_-": {"D": 4, "A": 3, "X": 1, "P": "-", "name": "evolution.backward", "coords": "temporal.⟳.foundational.-", "archetype": "unbecoming"},
    "Σ_4_3_2_+": {"D": 4, "A": 3, "X": 2, "P": "+", "name": "history.complexify", "coords": "temporal.⟳.recursive.+", "archetype": "story elaborates"},
    "Σ_4_3_2_-": {"D": 4, "A": 3, "X": 2, "P": "-", "name": "history.simplify", "coords": "temporal.⟳.recursive.-", "archetype": "story reduces"},
    "Σ_4_3_3_+": {"D": 4, "A": 3, "X": 3, "P": "+", "name": "transcendence", "coords": "temporal.⟳.synthetic.+", "archetype": "beyond time"},
    "Σ_4_3_3_-": {"D": 4, "A": 3, "X": 3, "P": "-", "name": "immanence", "coords": "temporal.⟳.synthetic.-", "archetype": "into time"}
  },

  "edges": {
    "_note": "Edges derivati ontologicamente, non calcolati",
    
    "mothers": {
      "_description": "3 Madri — Φ=9 — massimo peso ontologico",
      "aleph_delta": {
        "type": "mother",
        "symbol": "א",
        "connects": "all Δ nodes (A=1)",
        "Φ": 9,
        "meaning": "Il respiro che distingue"
      },
      "mem_relation": {
        "type": "mother", 
        "symbol": "מ",
        "connects": "all ⇄ nodes (A=2)",
        "Φ": 9,
        "meaning": "L'acqua che connette"
      },
      "shin_process": {
        "type": "mother",
        "symbol": "ש",
        "connects": "all ⟳ nodes (A=3)",
        "Φ": 9,
        "meaning": "Il fuoco che trasforma"
      }
    },
    
    "doubles": {
      "_description": "7 Doppie — Φ=3 — coppie polari planetarie",
      "beth": {"connects": ["D=1,2"], "Φ": 3, "polarity": "wisdom/folly"},
      "gimel": {"connects": ["D=2,3"], "Φ": 3, "polarity": "wealth/poverty"},
      "daleth": {"connects": ["D=3,4"], "Φ": 3, "polarity": "fertility/barrenness"},
      "kaph": {"connects": ["X=1,2"], "Φ": 3, "polarity": "life/death"},
      "pe": {"connects": ["X=2,3"], "Φ": 3, "polarity": "dominance/slavery"},
      "resh": {"connects": ["A=1,2"], "Φ": 3, "polarity": "peace/war"},
      "tav": {"connects": ["A=2,3"], "Φ": 3, "polarity": "grace/sin"}
    },
    
    "simples": {
      "_description": "12 Semplici — Φ=1 — modi zodiacali D×A",
      "D1_A1": {"from": "D=1,A=1", "to": "adjacent", "Φ": 1},
      "D1_A2": {"from": "D=1,A=2", "to": "adjacent", "Φ": 1},
      "D1_A3": {"from": "D=1,A=3", "to": "adjacent", "Φ": 1},
      "D2_A1": {"from": "D=2,A=1", "to": "adjacent", "Φ": 1},
      "D2_A2": {"from": "D=2,A=2", "to": "adjacent", "Φ": 1},
      "D2_A3": {"from": "D=2,A=3", "to": "adjacent", "Φ": 1},
      "D3_A1": {"from": "D=3,A=1", "to": "adjacent", "Φ": 1},
      "D3_A2": {"from": "D=3,A=2", "to": "adjacent", "Φ": 1},
      "D3_A3": {"from": "D=3,A=3", "to": "adjacent", "Φ": 1},
      "D4_A1": {"from": "D=4,A=1", "to": "adjacent", "Φ": 1},
      "D4_A2": {"from": "D=4,A=2", "to": "adjacent", "Φ": 1},
      "D4_A3": {"from": "D=4,A=3", "to": "adjacent", "Φ": 1}
    },
    
    "complementarity": {
      "_description": "36 coppie Σ₊ ↔ Σ₋ — polarità intrinseca",
      "rule": "∀Σ_ijkp₊ ∃ edge to Σ_ijkp₋",
      "count": 36,
      "Φ": "inherited from path type"
    },
    
    "dimensional_adjacency": {
      "_description": "Adiacenze lungo ogni dimensione",
      "D_adjacent": "D_n ↔ D_(n+1) for same A,X,P",
      "A_adjacent": "A_n ↔ A_(n+1) for same D,X,P", 
      "X_adjacent": "X_n ↔ X_(n+1) for same D,A,P"
    }
  },

  "tesseract_structure": {
    "_description": "La matrice come ipercubo 4D",
    "vertices": 72,
    "dimensions": {
      "D": "4 valori → 2 bit",
      "A": "3 valori → log₂(3) ≈ 1.58 bit",
      "X": "3 valori → log₂(3) ≈ 1.58 bit", 
      "P": "2 valori → 1 bit"
    },
    "total_bits": "2 + 1.58 + 1.58 + 1 ≈ 6.16 bit per simbolo",
    "information_content": "72 × 6.16 ≈ 444 bit totali",
    "note": "Non è un tesseract puro (2^4=16) ma un iperprisma 4×3×3×2"
  },

  "activation_protocol": {
    "step_1": "Load 72 nodes",
    "step_2": "Initialize edges from mothers/doubles/simples/complementarity",
    "step_3": "Set Φ weights on all edges",
    "step_4": "Input: any pattern (text, image, concept)",
    "step_5": "Map input to coordinate(s) Σ_ijkp",
    "step_6": "Activate node(s), propagate through weighted edges",
    "step_7": "Observe: which nodes cross K_crit?",
    "step_8": "Emergent nodes = stable patterns above threshold"
  }
}