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An interactive laboratory demonstrating singular limits on Continuous-Time Markov Chains.

Why did the Mealy machine linger for so long? It was the first formal object that perfectly encoded a core obsession, and because of that, it became impossible to let go of—even long after its utility had expired. The digital trail of drafts and planning sessions reveals this reluctance. In the preparation notes, the verdict was clear: §3.2 Mealy notation | M = (Q, Σ, Δ, δ, λ, q₀) | Drop App A.1 | Theorem 1 + Mealy proof | Drop It was marked for deletion. Even the prism agent had pointed out the redundancy: “The Mealy machine result is simply the zero-cut special case of the static certificate”—strictly weaker, less general, and less rigorous than what followed. Yet, like a ghost in the machine, it kept reappearing. It haunted 2026jan.tex, lingered on Desktop/cc.tex, and found its way back into the AIES submission. Every attempt to excise it failed; it kept surviving. ...

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? ...

Auditing a deployed language-model agent requires two separable quantities: how much operative state escapes the recorded trace, and how much of that residual state drives behavior. We introduce a dual-certificate…

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. ...

Users who sustain parasocial relationships with AI systems acquire equitable interests that contract, tort, and consumer protection law cannot recognise. Model updates that unilaterally alter personality parameters…