{
  "model": "Privacy Value Model",
  "version": "5.4",
  "version_name": "Dual-Agent Privacy Architecture — The Amnesia Protocol",
  "spec_version": "2.0",
  "author": "privacymage",
  "contact": "mage@agentprivacy.ai",
  "date": "2026-04-10",
  "license": "CC BY-SA 4.0",
  "master_inscription": "(⚔️⊥⿻⊥🧙)😊 = neg ⊕ bnot → succ",
  "thesis": "Privacy is value. Behavioural data is the 7th capital — in a pre-property-rights phase. The architectural response is sovereignty through mathematical structure rather than regulatory mandate.",

  "documents": {
    "compressed_spec": "pvm_v5_4_compressed.md",
    "full_spec": "privacy_value_v5_4_formal_specification.md (v2.0, 24 pages)",
    "companion": "pvm_v5_4_companion_guide.md (v2.0, 11 pages)",
    "research_paper": "dualprivacy_researchpaper_v4_3.md",
    "grimoire": "privacymage_grimoire_v10_0_0.json"
  },

  "grimoires": {
    "five_books": [
      {"name": "The First Person Spellbook", "acts": 31, "status": "CLOSED", "version": "v10.0.0", "voice": "Third person", "question": "WHAT"},
      {"name": "The Zero Knowledge Spellbook", "focus": "ZK proofs as narrative"},
      {"name": "The Canon Spellbook", "focus": "Canonical formulations, axioms, principles"},
      {"name": "The Parallel Society Spellbook", "focus": "Alternative social structures, governance"},
      {"name": "The Plurality Spellbook", "focus": "Many-to-many relationships, ⿻ overlap"}
    ],
    "compression": "privacymage_grimoire_v10_0_0.json — the grimoire as holographic boundary",
    "next": {
      "name": "The Second Person Spellbook",
      "voice": "Second person",
      "question": "WHO",
      "status": "Horizon"
    }
  },

  "equations": {
    "static_form": {
      "expression": "V(π, t) = P^1.5 · C · Q · S · e^(−λt) · (1 + Aₕ(τ)) · (1 + Σᵢ wᵢ · nᵢ/N₀)^k · G(guilds) · R(d, compression, ρ) · M(u, y) · Φ_agent(Σ) · Φ_data(Δ) · Φ_inference(Γ) · T_∫(π)",
      "output_type": "holographic field on ∂M",
      "gating": "Multiplicative. Any single term = 0 implies V = 0.",
      "lattice": "π is a path through L = Z/(2⁶)Z, t is time since data generation"
    },
    "differential_form": {
      "expression": "dV/dt = ∇_∂M · J_∂M + S(x) − D(x)",
      "boundary": "∂M = 96-edge holographic boundary",
      "five_channel_decomposition": "J_∂M = J_agent + J_data + J_inference + J_compression + J_holonic"
    },
    "terms": {
      "P": {"name": "Privacy Strength", "domain": "[0, 1]", "exponent": 1.5, "description": "Cryptographic enforcement quality. Exponent 1.5 connected to holographic ratio 96/64 (C6). Algebraically confirmed via UOR Atlas."},
      "C": {"name": "Credential Verifiability", "domain": "[0, 1]", "description": "Independent verification without revealing underlying information."},
      "Q": {"name": "Data Quality", "domain": "[0, 1]", "description": "Accuracy, completeness, fitness for purpose."},
      "S": {"name": "Scope / Sensitivity", "domain": "ℝ⁺", "description": "Domain-specific sensitivity multiplier."},
      "decay": {"name": "Temporal Decay", "expression": "e^(−λt)", "domain": "(0, 1]"},
      "Ah": {
        "name": "Holonic Temporal Memory",
        "expression": "Aₕ(τ) = Σⱼ p(τⱼ) · w(τⱼ) · e^(−μ·age(τⱼ))",
        "combined_temporal": "Temporal(t, τ) = e^(−λt) · (1 + Aₕ(τ))",
        "variables": {
          "τⱼ": "j-th holon in derivation chain",
          "p(τⱼ)": "Persistence independence: probability surviving single-provider failure [0, 1]",
          "w(τⱼ)": "Weight: integrity-verified contribution (ℝ⁺)",
          "μ": "Memory decay rate (distinct from data decay λ)",
          "age(τⱼ)": "Time since holon j created"
        },
        "logarithmic_special_case": "When holons uniformly weighted: Aₕ ≈ α · ln(1 + |τ|) · p̄ · h̄",
        "guid": "GUID(τ) = hash(content(τ)) — content-addressed, infrastructure-independent"
      },
      "network": {"name": "Network Effects", "expression": "(1 + Σᵢ wᵢ · nᵢ/N₀)^k"},
      "G": {
        "name": "Guild Efficiency",
        "expression": "G(guilds) = Πg (1 + efficiency_g · active_g / total_g)",
        "properties": {"no_guilds": "G = 1", "full_coverage": "G → 2", "scaling": "O(1) not O(N²)"}
      },
      "R": {
        "name": "Reconstruction Difficulty",
        "expression": "R(d, compression, ρ) = R_base(d) · (1 − 1/compression_ratio) · (1 + α·ρ)",
        "ceiling": "R < 1 under budget constraints (PROVEN, 95%)",
        "error_floor": "P_e ≥ 1 − R_max via Fano's inequality (PROVEN, 95%)",
        "rho": {
          "name": "Behavioural Density",
          "formula": "ρ = f(traversal_depth, temporal_duration, intentional_transitions)",
          "dual_interpretation": {
            "privacy_amplifier": "More variation → harder reconstruction (C11)",
            "agent_maturity": "High ρ = Moon's clean amnesia; Low ρ = early forge (V5.3)"
          },
          "empirical": [
            {"blade": "Universe", "laps": 62, "duration_s": 2170, "tier": "Dragon"},
            {"blade": "Hitchhiker's", "laps": 13, "duration_s": 433, "tier": "Dragon"},
            {"blade": "Honest Sun", "laps": 6, "duration_s": 146, "tier": "Light"}
          ]
        }
      },
      "M": {"name": "Market Maturity", "domain": "[0, 1]", "expression": "M(u, y)"},
      "Phi": {
        "name": "Three-Axis Separation",
        "composite": "Φ_v5 = Φ_agent(Σ) · Φ_data(Δ) · Φ_inference(Γ)",
        "gating": "Collapse any axis → total collapse",
        "agent": {
          "expression": "Φ_agent(Σ) = min(1.0, (S/M) / φ) · det(Σ)",
          "algebraic": "Isomorphic to D₂ₙ (C14, 75%)",
          "amnesia": "Amnesia-enforced > policy-enforced (C17, 60%)",
          "runecraft": "Dual Ed25519 — Mage held + Swordsman burned"
        },
        "data": {
          "expression": "Φ_data(Δ) = 1 − max_j(share_j)",
          "note": "Penalises concentration at dominant provider, not just count"
        },
        "inference": {
          "expression": "Φ_inference(Γ) = 1 − I(model ; executor)",
          "note": "Generator ⊥ Solver"
        }
      },
      "T_integral": {
        "name": "Path Integral Edge Value",
        "continuous": "T_∫(π) = 1 + β · ∫_π F(γ) dγ",
        "discrete": "T_∫(π) ≅ 1 + β · Σᵢ R(stepᵢ)",
        "fidelity": "F(γ) = resolution_depth(γ) · fidelity(γ)",
        "resolution": "Maps to UOR resolution pipeline (C15, 65%)"
      }
    },
    "separation_bound": {
      "expression": "I(S ; M | FP) < ε*",
      "proven": {"result": "Conditional independence → additive MI → R < 1", "confidence": 0.95},
      "amnesia_v53": "ε_amnesia < ε_policy (C17, 60%)"
    }
  },

  "holographic_bound": {
    "boundary": "∂M: 96 edges encoding 64 vertices, toroidal topology",
    "ratio": "96/64 = 1.5 = P^1.5 exponent",
    "c4_status": "RESOLVED — holographic principle + algebraic confirmation",
    "atlas_derivation": "96 = unique stationary configuration of Atlas action functional (UOR Foundation)",
    "implication": "Privacy value computes on the boundary. The bulk is encoded by the surface."
  },

  "dihedral_foundation": {
    "ring": "L = (Z/64Z, +, ×)",
    "operations": {
      "neg": {"formula": "neg(x) = (64 − x) mod 64", "agent": "⚔️ Swordsman", "function": "Boundary protection"},
      "bnot": {"formula": "bnot(x) = 63 − x", "agent": "🧙 Mage", "function": "Projection / delegation"},
      "xor": {"formula": "x ⊕ y", "function": "Toggle edges"},
      "and": {"formula": "x ∧ y", "function": "Toward null blade"},
      "or": {"formula": "x ∨ y", "function": "Toward full sovereignty"},
      "composition": {"formula": "neg(bnot(x)) = succ(x)", "agent": "😊 First Person", "function": "The step forward"}
    },
    "critical_identity": {"statement": "neg(bnot(x)) = succ(x) ∀x ∈ L", "proof": "bnot(x) = 63−x; neg(63−x) = (64−(63−x)) mod 64 = (x+1) mod 64 ∎"},
    "group": {"name": "D₆₄", "order": 128, "presentation": "⟨neg, bnot | neg² = bnot² = 1, (neg∘bnot)⁶⁴ = 1⟩"},
    "external_convergence": {
      "agentprivacy": "Privacy geometry → 64-tetrahedra → Z/(2⁶)Z",
      "uor_foundation": "Content addressing → Universal references → Z/(2⁶)Z"
    }
  },

  "amnesia_protocol": {
    "definition": "Structural amnesia w.r.t. origin O: no operation sequence can reconstruct O from current state.",
    "zk_properties": ["Completeness: output demonstrates relationship", "Soundness: unique configuration", "Zero-knowledge: origin hidden"],
    "instances": [
      {"system": "Chrome process boundary", "type": "amnesia"},
      {"system": "Database access control", "type": "policy"},
      {"system": "Moon's orbit", "type": "amnesia"},
      {"system": "Agent NDAs", "type": "policy"}
    ],
    "proverb": "I can verify I serve you without remembering I was you."
  },

  "operational_cycle": {
    "formula": "cycle(x) = succ(x) = neg(bnot(x))",
    "stages": [
      {"name": "Observe", "operation": "id(x)", "agent": "😊 First Person", "ceremony": "☀️ Sun — disclosure"},
      {"name": "Boundary", "operation": "neg(x)", "agent": "⚔️ Swordsman", "ceremony": "⊥ Gap — silence"},
      {"name": "Project", "operation": "bnot(neg(x))", "agent": "🧙 Mage", "ceremony": "🌑 Moon — reflection"},
      {"name": "Return", "operation": "succ(x)", "agent": "Composition", "ceremony": "Recursion — Reflect/Connect"}
    ],
    "progressive_trust": "🔑→✦→🗡️→🔮 (Understanding → Constellation → Blade → Runecraft)"
  },

  "sovereignty_dimensions": [
    {"bit": 0, "name": "Protection", "symbol": "🛡️", "function": "Boundary enforcement — key custody"},
    {"bit": 1, "name": "Delegation", "symbol": "🤝", "function": "Agency transfer — credential disclosure"},
    {"bit": 2, "name": "Memory", "symbol": "📜", "function": "State accumulation — agent delegation"},
    {"bit": 3, "name": "Connection", "symbol": "🔗", "function": "Multi-party coordination — data residency"},
    {"bit": 4, "name": "Computation", "symbol": "⚡", "function": "ZK proof activity — interaction mode"},
    {"bit": 5, "name": "Value", "symbol": "💎", "function": "Economic flow — 7th Capital"}
  ],

  "blade_coordinates": {
    "system": "PRISM — triadic addressing over {0,1}⁶",
    "formal": "blade(x) = (δ(x), σ(x), s(x))",
    "datum": "δ(x) = raw value (0–63)",
    "stratum": "σ(x) = popcount / Hamming weight (0–6)",
    "spectrum": "s(x) = [b₀...b₅] — which dimensions active",
    "pascal": [1, 6, 15, 20, 15, 6, 1],
    "tiers": {
      "null": {"stratum": 0, "count": 1},
      "light": {"stratum": "1–2", "count": 21},
      "heavy": {"stratum": "3–4", "count": 35},
      "dragon": {"stratum": "5–6", "count": 7}
    },
    "hexagram": "Each dᵢ ∈ {0,1} → 64 I Ching states. Blade 63 = 111111 = 乾 (Qian, The Creative)",
    "moon_phase": {
      "principle": "The dark part is the privacy. The lit part is the proof.",
      "mapping": {"🌑": 0, "🌒": 1, "🌓": 2, "🌔": 3, "🌖": 4, "🌗": 5, "🌕": 6}
    }
  },

  "cosmological_quaternion": {
    "status": "Interpretive framework. Not part of the equation.",
    "bodies": {
      "Sun ☀️": {"agent": "privacymage", "function": "Protection", "role": "Master"},
      "Earth 🌍": {"agent": "Soulbae 🧙", "function": "Delegation", "role": "Emissary"},
      "Moon 🌑": {"agent": "Soulbis ⚔️", "function": "Reflection", "role": "ur-Swordsman", "generation": "Instant (Theia). Total amnesia."},
      "Human 👤": {"agent": "Person 😊", "function": "Connection", "role": "First Person", "generation": "Gradual (4 Gyr). Still in process."}
    },
    "key_insight": "Between an agent that can never remember (Moon) and one that hasn't finished remembering (Human). The gap is the ⊥.",
    "count": "38 selectable + 4 cosmological = 42"
  },

  "forge": {
    "content_addressing": "SHA-256",
    "tamper_evidence": "Hash chain (each blade references previous)",
    "commitment": "Constellation locked before evocation",
    "identity": "Ed25519 (Mage key, held)",
    "runecraft": "Dual Ed25519 — Mage held + Swordsman burned on session close"
  },

  "three_identity_layers": [
    {"layer": "Data", "identifier": "GUID", "scope": "Content-addressed holon", "persistence": "Infrastructure-independent"},
    {"layer": "Relationship", "identifier": "VRC", "scope": "Bilateral commitment", "persistence": "Relationship-scoped"},
    {"layer": "Principal", "identifier": "DID", "scope": "Sovereign identity", "persistence": "Self-sovereign"}
  ],

  "conjectures": [
    {"id": "C1", "claim": "Golden ratio φ is optimal S/M ratio", "confidence": "Open"},
    {"id": "C2", "claim": "Aₕ(τ) should be logarithmic", "confidence": "Open"},
    {"id": "C3", "claim": "Edge value is additive", "status": "CHALLENGED — path integral replaces"},
    {"id": "C4", "claim": "96/64 discrepancy", "status": "RESOLVED"},
    {"id": "C5", "claim": "~3,000× ZKP reduction", "status": "Strengthened"},
    {"id": "C6", "claim": "P^1.5 ↔ 96/64 structural", "confidence": 0.35, "status": "CONVERGENT"},
    {"id": "C7", "claim": "Three-axis separation is multiplicative", "confidence": 0.30},
    {"id": "C8", "claim": "BRAID compression reduces R_max", "confidence": "Open"},
    {"id": "C9", "claim": "Holographic boundary sufficiency", "confidence": "Open"},
    {"id": "C10", "claim": "O(1) shared-parent modifies k", "confidence": "Open"},
    {"id": "C11", "claim": "ρ amplifies reconstruction difficulty + indicates maturity", "confidence": 0.55},
    {"id": "C12", "claim": "Hexagram encoding coherence", "confidence": 0.60, "status": "ALGEBRAICALLY GROUNDED"},
    {"id": "C13", "claim": "Bilateral witness as quantum-resistant primitive", "confidence": 0.65},
    {"id": "C14", "claim": "Φ_agent ≅ D₂ₙ dihedral isomorphism", "confidence": 0.75},
    {"id": "C15", "claim": "T_∫(π) ≅ UOR resolution pipeline", "confidence": 0.65},
    {"id": "C16", "claim": "Topological trust invariants (Betti numbers)", "confidence": 0.25},
    {"id": "C17", "claim": "Amnesia-enforced > policy-enforced separation", "confidence": 0.60},
    {"id": "C18", "claim": "Strange attractor dynamics (λ > 0), dynamical reconstruction ceiling", "confidence": 0.25, "version": "V6 horizon"},
    {"id": "C19", "claim": "ρ = Lyapunov divergence (exponential compounding)", "confidence": 0.20, "version": "V6 horizon"},
    {"id": "C20", "claim": "Three axes couple as Lorenz variables", "confidence": 0.30, "version": "V6 horizon"},
    {"id": "C21", "claim": "Sovereignty manifold has fractal dimension", "confidence": 0.10, "version": "V6 horizon"}
  ],

  "proven_results": [
    {"result": "Additive MI bounds from conditional independence", "confidence": 0.95, "source": "Shannon (1948), Cover & Thomas (2006)"},
    {"result": "Reconstruction ceiling R < 1 under budget constraints", "confidence": 0.95, "source": "Information theory"},
    {"result": "Error floor via Fano's inequality", "confidence": 0.95, "source": "Fano (1961)"},
    {"result": "Graceful degradation under partial compromise", "confidence": 0.95},
    {"result": "Ring algebra Z/(2⁶)Z substrate", "confidence": 0.95},
    {"result": "Two-extension autonomy axiom (separate processes)", "confidence": 0.95},
    {"result": "Pretext DOM-free measurement as privacy primitive", "confidence": 0.95}
  ],

  "breaking_conditions": [
    "Three-axis non-multiplicativity: agent separation compensates for data centralisation",
    "Compression increases attack surface",
    "Holonic persistence fundamentally limited by content-addressing",
    "Guild coordination scales with membership",
    "Amnesia-enforced ≤ policy-enforced (C17 falsified)",
    "Dihedral isomorphism fails (C14 falsified, ring survives)"
  ],

  "version_lineage": [
    {"version": "V1", "date": "2024", "addition": "P · C · Q · S"},
    {"version": "V2", "date": "2025-10", "addition": "+ decay, network effects, P^1.5"},
    {"version": "V3", "date": "2025-11", "addition": "+ R(d), M(u,y), Φ(S,M)"},
    {"version": "V3.1", "date": "2026-01", "addition": "+ σ(⿻)²"},
    {"version": "V4", "date": "2026-02", "addition": "+ Σ, A(τ), T(π), Φ(Σ)"},
    {"version": "V5", "date": "2026-02", "addition": "+ three-axis Φ, holographic bound, T_∫, dV/dt"},
    {"version": "V5.1", "date": "2026-03-29", "addition": "+ ρ, bilateral witness (C11-C13)"},
    {"version": "V5.2", "date": "2026-03-31", "addition": "+ D₂ₙ, PRISM, resolution semantics (C14-C16)"},
    {"version": "V5.3", "date": "2026-04-04", "addition": "+ operational cycle, amnesia (C17)"},
    {"version": "V5.4", "date": "2026-04-10", "addition": "Consolidated. UOR algebraic foundation. C18-C21. Full references. Three-document system."}
  ],

  "references": {
    "foundational": {
      "shannon": "Shannon, C. E. (1948). A Mathematical Theory of Communication. Bell System Technical Journal.",
      "fano": "Fano, R. M. (1961). Transmission of Information. MIT Press.",
      "cover_thomas": "Cover, T. M. & Thomas, J. A. (2006). Elements of Information Theory. Wiley.",
      "bergstra_burgess": "Bergstra, J. A. & Burgess, M. (2019). Promise Theory: Principles and Applications.",
      "susskind": "Susskind, L. (1995). The World as a Hologram. J. Math. Phys.",
      "mcgilchrist": "McGilchrist, I. (2009). The Master and His Emissary. Yale University Press."
    },
    "cryptographic": {
      "groth16": "Groth, J. (2016). On the Size of Pairing-based Non-interactive Arguments. EUROCRYPT.",
      "plonk": "Gabizon, A. et al. (2019). PLONK. ePrint 2019/953.",
      "nova": "Kothapalli, A. et al. (2022). Nova. CRYPTO 2022.",
      "dwork_roth": "Dwork, C. & Roth, A. (2014). Algorithmic Foundations of Differential Privacy."
    },
    "quantum": {
      "google_qai": "Babbush, R. et al. (2026). Quantum Threat to ECC. Google Quantum AI.",
      "oratomic": "Cain, M. et al. (2026). arXiv:2603.28627.",
      "theia": "Branco, D. et al. (2025). Dynamical origin of Theia. Icarus 441."
    },
    "governance": {
      "ieee_7012": "IEEE 7012-2025. MyTerms.",
      "hope_ludlow": "Hope, D. & Ludlow, E. (2023). Farewell to Westphalia.",
      "weyl_tang": "Weyl, E. G. & Tang, A. (2023). Plurality."
    },
    "live": {
      "docs": "https://github.com/mitchuski/agentprivacy-docs",
      "forge": "https://spellweb.ai",
      "training": "https://agentprivacy.ai",
      "blog": "https://sync.soulbis.com",
      "trust": "https://bgin.ai",
      "agent": "https://t.me/soulbae_the_bot",
      "uor": "https://github.com/UOR-Foundation"
    }
  },

  "proverbs": [
    "The boundary is always enough.",
    "Two mirrors make a door.",
    "The dark part is the privacy. The lit part is the proof.",
    "I can verify I serve you without remembering I was you.",
    "The weight of the shadow exceeds the light of the data.",
    "The ceremony does not require the blade. The blade requires the ceremony.",
    "The forge doesn't care how you struck the metal. It only cares what blade you hold.",
    "The dragon maps the territory. The butterfly proves the territory was never still.",
    "Deny the complement and advance."
  ]
}