Explorative Thoughts

Since Pearl (2009), causal inference on DAGs has crystallized around a powerful but austere toolkit: boolean d-separation and do-calculus. Does evidence flow? Full stop. Does it flow after an intervention? Full stop. This framework is sufficient for causal identification—determining whether an effect is estimable from observed data. But it is curiously silent on a question that seems equally natural: how much flows, through which channels, and with what residual structure? ...

Reconstructing the Relay Channel: Modernizing the Cut-set Bound and Degraded Capacity Proofs When aiming to “extract dependencies and compress proof chains,” few starting points are as effective as the core results from Chapter 16 of El Gamal and Kim: the cut-set upper bound for general discrete memoryless relay channels and the capacity theorem for physically degraded relay channels. These results, originating from the landmark 1979 Cover–El Gamal paper, hold immense historical significance but carry a structural “debt” that allows for substantial modernization and simplification. ...