Executable Capability Percolation Theory (ECPT) is a mathematical framework for studying how execution-available capability packets can accumulate, combine, and propagate through constrained directed hypergraphs. The theory models ASI-proxy phase approach as a typed phase-control problem rather than as an absolute claim about artificial superintelligence. It separates settled, provisional, and speculative target claims, and represents capability growth through stochastic relaxation quotients, global Gibbs activation, speculative RAF-like closure, liquidity-debt settlement, reachable-mass recursion, and intervention-identified mean-field envelopes. This version emphasizes operability and machine readability. It introduces constructed path-law response policies, log-linked generator identification, finite-sample quotient certification, self-normalized risk margins, AND-support activation thresholds, and protocol-relative checker soundness. The TeX source also embeds a machine-readable manifest, claim registry, citation metadata, CodeMeta JSON-LD, and BibTeX mirror, making the artifact suitable for reproducible mathematical review and metadata indexing.