Syntrometrie Framework (Conceptual Overview)

graph TB %% Global Styling (Included for consistency, Mermaid might override some) classDef foundation fill:#EAECEE,stroke:#AEB6BF,stroke-width:2px,color:black,font-size:14px classDef structure fill:#E8DAEF,stroke:#A569BD,stroke-width:2px,color:black,font-size:14px classDef geometry fill:#D6EAF8,stroke:#5DADE2,stroke-width:2px,color:black,font-size:14px classDef emergence fill:#D5F5E3,stroke:#58D68D,stroke-width:2px,color:black,font-size:14px classDef computation fill:#FCF3CF,stroke:#F4D03F,stroke-width:2px,color:black,font-size:14px %% Foundational Layer subgraph "A: Foundational Logic" A1["Primordial Exp.
(ästhetische Empirie)"]:::foundation --> A2["Reflection Synthesis
(Endo/Exo)"]:::foundation A2 --> A3["Subjective Aspect (S)
(Mental State)"]:::foundation A3 --> A4["Predicates P_n = [f_q]_n"]:::foundation A3 --> A5["Dialectics D_n = [d_q]_n"]:::foundation A3 --> A6["Coordination K_n = E_n F(ζ_n, z_n)"]:::foundation A4 --> A6 A5 --> A6 A7["Antagonismen
(Logical Tensions)"]:::foundation --> A5 A3 --> A8["Aspect Systems A = α(S)"]:::foundation A9["Categories γ
(Invariant Grounding)"]:::foundation --> A3 end %% Recursive Structure Layer subgraph "B: Recursive Hierarchy" B1["Metrophor a ≡ (a_i)_n
(Base Qualia)"]:::structure --> B2["Synkolator Functor F
Generates L_{k+1} from L_k"]:::structure B2 --> B3["Syntrix Levels L_k = F^k(L0)
(Hierarchical Constructs)"]:::structure B3 --> B4["Syntrix
(Union L_k)
⟨{, a, m⟩"]:::structure B5["Recursive Def.
a = ⟨{, a, m⟩"]:::structure --> B2 B6["Normalization
(Stabilizes Recursion)"]:::structure --> B2 B7["Hierarchical Coord.
K_Syntrix = ∏ K_n"]:::structure --> B4 A9 --> B1 end %% Geometric Layer subgraph "C: Geometric Structure" C1["12D Hyperspace (H12)
(Underlying Reality)"]:::geometry <-->|"Maps Onto"| B4 C2["N=6 Stability
(Physical Constraint)"]:::geometry --> C1 C1 --> C3["Metric Tensor
g_ik^γ(x) = sum f_q^i(x) f_q^k(x)"]:::geometry C3 --> C4["Connection
Γ^i_kl"]:::geometry C4 --> C5["Curvature
R^i_klm = sum (...)"]:::geometry C6["Quantized Change
δφ = φ(n) - φ(n-1)"]:::geometry --> C1 B3 --> C3 C2 --> C3 C7["Mass Formula
(Link to Physics)"]:::geometry <-- "Relates to" --> C3 end %% Emergence Layer subgraph "D: Reflexive Integration" D1["RIH
(Reflexive Integration Hypothesis)"]:::emergence C3 --> D2["Integration Measure
I(S) = sum MI_d(S) > τ(t)"]:::emergence C5 --> D2 B4 --> D3["Reflexivity Cond.
ρ: Id_S → F^n"]:::emergence B5 --> D3 C2 --> D4["Threshold
τ = τ_0(N=6) + Δτ(t)"]:::emergence C3 --> D4 D2 --> D1 D3 --> D1 D4 --> D1 D1 --> D5["Emergent Properties
(e.g., Consciousness)"]:::emergence A7 -- "Resolved By" --> D5 end %% Computational Layer subgraph "E: Computational Models" E1["Syntrometric Kripke Frame
(Worlds=S(x), R based on g_ik)"]:::computation -->|"Models"| A E1 -->|"Models"| C E1 -->|"Models"| D E2["Sequent Calculus
(S; Γ |- ϕ)"]:::computation -->|"Derives From"| A E2 -->|"Derives From"| B E1 -- "Interprets" --> E2 E3["GNN Implementation
(Agent Model)"]:::computation -->|"Approximates"| B E3 -->|"Approximates"| C E3 -->|"Approximates"| D3 E4["Metrics (att_score, value, ...)"]:::computation <-- "Calculated By" --> E3 E4 -- "Correspond To" --> D3 E4 -- "Correspond To" --> C3 E4 -- "Correspond To" --> D4 end