trureturingGitHub MATHEMATICAL ATLAS

ConceptDynamics / CONCEPT

Conditional factorization and shared ancestors

Complete responses factorize under coordinatewise independent-source evaluation. Sharing a random ancestor changes that premise, even when every equation has independent local noise.

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DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH7
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THEOREM

Average the conditional products

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Joint benefit from four interventional marginalsJoint benefit from fourinterventional marginalsConditional factorization and shared ancestorsConditional factorization andshared ancestors
Proof dependencyStructural affinityDocument link

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Certified topology / DOWNSTREAM

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Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.