Pre-loaded AI directives for dimensional programming. These directives provide the governing rules and algebraic transformations that keep AI systems stable and deterministic.
Structured Prompt
The core directive structure: a clear prompt plus governing rules that define allowed transformations. This prevents drift, hallucination, and brittle failure modes.
directive: {
prompt: "Clear task description",
rules: [
"No destructive updates",
"Maintain identity",
"Use manifold operations",
"Validate outputs"
]
}Algebraic Transformations
Allowed transformations using the manifold operation z derived from x and y. These transformations preserve the identity of the original content while allowing flexible extraction through modifier application.
transformations: {
manifold: "derived z from x and y",
identity: "x preserved in z",
invertibility: "x = z / y",
russian_doll: "z contains history"
}Determination Graphs
DAG-based decision structures that independently route nodes through the manifold. Each node represents a computation that can be resolved through manifold operations.
determination_graph: {
nodes: [
{ id: 1, operation: "manifold" },
{ id: 2, operation: "extract" },
{ id: 3, operation: "validate" }
],
edges: [(1,2), (2,3)]
}Truth Table Constraints
Hard constraints enforced through truth tables. These provide mathematical guarantees that certain conditions will always be satisfied, preventing LLMs from returning invalid outputs.
truth_table: {
inputs: [A, B, C],
outputs: [valid],
constraints: [
"A ∧ B → valid",
"¬A ∧ ¬B → invalid"
]
}Decision Trees
Tree-based decision structures that provide shortcuts through the manifold. Decision trees allow efficient routing by pruning unnecessary computation paths.
decision_tree: {
root: condition_1,
branches: {
true: node_2,
false: node_3
},
leaf: final_output
}Logic Gates
Boolean logic operations that can be applied to manifold states. These provide the fundamental logical operations needed for complex decision-making.
logic_gates: {
AND: (a, b) => a && b,
OR: (a, b) => a || b,
NOT: (a) => !a,
XOR: (a, b) => a ^ b
}Regex Pre-Filters
Regular expression filters applied before manifold operations. These provide pattern-based filtering to reduce the search space and improve efficiency.
regex_filters: [
/^[a-zA-Z0-9]+$/,
/\d{4}-\d{2}-\d{2}/,
/^[a-z]+@[a-z]+\.[a-z]+$/
]Complex-Valued Mode
Extended manifold operations using complex numbers. This mode allows representation of phase and magnitude, enabling more sophisticated transformations.
complex_mode: {
z = (a + bi) * (c + di),
magnitude: |z|,
phase: arg(z),
applications: ["phase_space", "quantum_ops"]
}Schwarz Diamond Manifold
Minimal surface decision boundaries using the Schwarz Diamond TPMS. This provides optimal routing through cost-quality tradeoff space.
schwarz_diamond: {
surface: "TPMS minimal",
boundary: "cost_quality",
optimization: "minimal_surface",
porosity: 0.5
}