Sparklet Framework

Sparklet Space

Mathematical Definition:

S = {(x,y,z,w) ∈ ℝ⁴ | x² + y² + z² + w² = 1}

w ∈ [w₀, w₁, w₂, ..., w₁₅] # 16-fold multiplexed aspect vector

Probability Quantization: - Default: q = 137 probability multitudes - Distribution: Balanced Ternary 68-1-68 across [-1, 0, +1]

Sparklet Topology

Invariant Structure: - 16 Spark vertices: {0,1,2,3,4,5,6,7,8,9,a,b,c,d,e,f} - 35 Arc edges with 3 morphism types: {IN, OUT, REC} - Fixed relational patterns

Template:

strict digraph Sparklet {
    style = filled;
    color = lightgray;
    node [shape = circle; style = filled; color = lightgreen;];
    edge [color = darkgray;];
    label = "{{Name}}";
    comment = "{{descriptions}}";
    
    spark_0_t [label = "{{Name}}.meta({{meta}})";comment = "Abstract: {{descriptions}}";shape = doublecircle;color = darkgray;];
    spark_1_t [label = "{{Name}}.r1({{title}})";comment = "Initiation: {{descriptions}}";color = darkgreen;];
    spark_2_t [label = "{{Name}}.r2({{title}})";comment = "Response: {{descriptions}}";color = darkgreen;];
    spark_4_t [label = "{{Name}}.r4({{title}})";comment = "Integration: {{descriptions}}";color = darkgreen;];
    spark_8_t [label = "{{Name}}.r8({{title}})";comment = "Reflection: {{descriptions}}";color = darkgreen;];
    spark_7_t [label = "{{Name}}.r7({{title}})";comment = "Consolidation: {{descriptions}}";color = darkgreen;];
    spark_5_t [label = "{{Name}}.r5({{title}})";comment = "Propagation: {{descriptions}}";color = darkgreen;];
    spark_3_t [label = "{{Name}}.r3({{title}})";comment = "Thesis: {{descriptions}}";color = darkblue;];
    spark_6_t [label = "{{Name}}.r6({{title}})";comment = "Antithesis: {{descriptions}}";color = darkblue;];
    spark_9_t [label = "{{Name}}.r9({{title}})";comment = "Synthesis: {{descriptions}}";color = darkblue;];
    spark_a_t [label = "{{Name}}.receive({{title}})";comment = "Potential: {{descriptions}}";shape = invtriangle;color = darkred;];
    spark_b_t [label = "{{Name}}.send({{title}})";comment = "Manifest: {{descriptions}}";shape = triangle;color = darkred;];
    spark_c_t [label = "{{Name}}.dispatch({{title}})";comment = "Why-Who: {{descriptions}}";shape = doublecircle;color = darkred;];
    spark_d_t [label = "{{Name}}.commit({{title}})";comment = "What-How: {{descriptions}}";shape = doublecircle;color = darkgreen;];
    spark_e_t [label = "{{Name}}.serve({{title}})";comment = "When-Where: {{descriptions}}";shape = doublecircle;color = darkblue;];
    spark_f_t [label = "{{Name}}.exec({{title}})";comment = "Which-Closure: {{descriptions}}";shape = doublecircle;color = lightgray;];
    
    spark_a_t -> spark_0_t [label = "IN"; comment = "{{descriptions}}"; color = darkred; constraint = false;];
    spark_0_t -> spark_b_t [label = "OUT"; comment = "{{descriptions}}"; color = darkred;];
    spark_0_t -> spark_3_t [label = "REC"; comment = "{{descriptions}}"; color = darkblue; dir = both;];
    spark_0_t -> spark_6_t [label = "REC"; comment = "{{descriptions}}"; color = darkblue; dir = both;];
    spark_0_t -> spark_9_t [label = "REC"; comment = "{{descriptions}}"; color = darkblue; dir = both;];
    spark_0_t -> spark_1_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both;];
    spark_0_t -> spark_2_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both;];
    spark_0_t -> spark_4_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both;];
    spark_0_t -> spark_8_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both;];
    spark_0_t -> spark_7_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both;];
    spark_0_t -> spark_5_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both;];
    
    spark_a_t -> spark_c_t [label = "REC"; comment = "{{descriptions}}"; color = darkred; dir = both;];
    spark_b_t -> spark_c_t [label = "REC"; comment = "{{descriptions}}"; color = darkred; dir = both;];
    spark_1_t -> spark_d_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both;];
    spark_2_t -> spark_d_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both;];
    spark_4_t -> spark_d_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both;];
    spark_8_t -> spark_d_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both;];
    spark_7_t -> spark_d_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both;];
    spark_5_t -> spark_d_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both;];
    spark_3_t -> spark_e_t [label = "REC"; comment = "{{descriptions}}"; color = darkblue; dir = both;];
    spark_6_t -> spark_e_t [label = "REC"; comment = "{{descriptions}}"; color = darkblue; dir = both;];
    spark_9_t -> spark_e_t [label = "REC"; comment = "{{descriptions}}"; color = darkblue; dir = both;];
    
    spark_1_t -> spark_2_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both; style = dashed; constraint = false;];
    spark_2_t -> spark_4_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both; style = dashed; constraint = false;];
    spark_4_t -> spark_8_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both; style = dashed; constraint = false;];
    spark_8_t -> spark_7_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both; style = dashed; constraint = false;];
    spark_7_t -> spark_5_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both; style = dashed; constraint = false;];
    spark_5_t -> spark_1_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both; style = dashed; constraint = false;];
    spark_3_t -> spark_6_t [label = "REC"; comment = "{{descriptions}}"; color = darkblue; dir = both; style = dashed; constraint = false;];
    spark_6_t -> spark_9_t [label = "REC"; comment = "{{descriptions}}"; color = darkblue; dir = both; style = dashed; constraint = false;];
    spark_9_t -> spark_3_t [label = "REC"; comment = "{{descriptions}}"; color = darkblue; dir = both; style = dashed; constraint = false;];
    spark_a_t -> spark_b_t [label = "REC"; comment = "{{descriptions}}"; color = darkred; dir = both; style = dashed; constraint = false;];
    
    spark_c_t -> spark_f_t [label = "REC"; comment = "{{descriptions}}"; color = darkred; dir = both;];
    spark_d_t -> spark_f_t [label = "REC"; comment = "{{descriptions}}"; color = darkgreen; dir = both;];
    spark_e_t -> spark_f_t [label = "REC"; comment = "{{descriptions}}"; color = darkblue; dir = both;];
}

What I meant is that there is this Sphere that have r=1; since it's 3D it has x,y,z axis. So, the w-axis is twisted into (x,y,z); and the w-axis itself also has 16 Aspects.

Then, each axis can have Probability Multitudes that expressed in Balanced Ternary, it's happens I liked 137 that can be expressed as 68-1-68 throughout [-1,0,+1]

I've tried my best to express it; I only have High School Grade formal education.

I'm using Sparklet Framework to develop MythOS (a Fictional Cosmology) at:

https://github.com/cilang/mythos