IsomorphismDiscoveryTask

TaskExecutionConfig Fields

Field	Type	Description
source_domain *	String	Description of the source domain (e.g., 'Number Theory').
target_domain *	String	Description of the target domain (e.g., 'Geometry').
mapping_strictness	String	'loose' (homomorphism) or 'strict' (isomorphism). Default: strict.
verify_operations	Boolean	Whether to verify that operations are preserved across the map. Default: true.
input_files	List<String>	Optional files to provide domain context.
related_files	List<String>	Additional context files for structural analysis.

Task Process Lifecycle

1. Primitive Definition: Identify fundamental objects (atoms) and operations (verbs) in both domains.
2. Candidate Generation: Propose a mapping function (dictionary) between objects and operations.
3. Structure Verification: Verify preservation: f(A * B) = f(A) # f(B).
4. Refinement: Adjust mappings based on verification failures to find the most consistent fit.
5. Conclusion: Final assessment of validity, confidence score, and limitations.

Headless Execution (UnifiedHarness)

Invoke the discovery engine programmatically within CI/CD pipelines or automated research tools.

import com.simiacryptus.cognotik.apps.general.UnifiedHarness
import com.simiacryptus.cognotik.plan.tools.reasoning.IsomorphismDiscoveryTask
import com.simiacryptus.cognotik.plan.tools.reasoning.IsomorphismDiscoveryTask.IsomorphismDiscoveryTaskExecutionConfigData
import com.simiacryptus.cognotik.plan.tools.TaskTypeConfig
fun runDiscovery(projectDir: java.io.File) {
    val harness = UnifiedHarness(serverless = true, openBrowser = false)
    harness.start()
    val config = IsomorphismDiscoveryTaskExecutionConfigData(
        source_domain = "Relational Algebra",
        target_domain = "SQL Query Language",
        mapping_strictness = "strict",
        verify_operations = true
    )
    harness.runTask(
        taskType = IsomorphismDiscoveryTask.IsomorphismDiscovery,
        typeConfig = TaskTypeConfig(),
        executionConfig = config,
        workspace = projectDir
    )
    harness.stop()
}

Agentic Planning Integration

Add this task to an automated agent's plan to allow it to perform cross-domain reasoning.

harness.runPlan(
    prompt = "Analyze the codebase and find if the internal event system is isomorphic to the Observer Pattern.",
    cognitiveSettings = CognitiveModeConfig(type = CognitiveModeType.AdaptivePlanning),
    workspace = File("./src"),
    autoFix = true
)

Prompt Segment

The following logic is injected into the LLM context:

IsomorphismDiscovery - Search for and validate structural mappings between two distinct domains
  ** Specify source_domain and target_domain
  ** Set mapping_strictness ('loose' or 'strict')
  ** Enable verify_operations to check structural preservation
  ** The task will:
     - Identify primitives (objects and operations) in both domains
     - Generate candidate mapping rules
     - Verify if operations are preserved (f(A op B) = f(A) op' f(B))
     - Refine and assess the validity of the isomorphism
  ** Useful for theoretical physics, system architecture, cryptography, and abstract modeling