Intent as Directed Selection: Mainstream Biological Evidence for the Irreducibility of the Triadic Invariant's Second Factor

A persistent objection to the triadic invariant R = P × I × Pr ≠ 0 targets its second factor: Intent, critics argue, is a psychological property of conscious agents and therefore cannot be a fundamental structural feature of reality. This objection rests on a folk definition contradicted by the philosophical record (Brentano 1874; Stanford Encyclopedia of Philosophy; Cambridge University Press) and now contradicted by mainstream experimental biology. We trace the corruption of Brentano's original concept through Chisholm, Quine, Searle, and Dennett, establish that the triadic invariant's canonical definition — directed selection — is a strict refinement of Brentano's genus, and demonstrate that recent peer-reviewed work from Tufts University and the Harvard Wyss Institute (Hartl & Levin, Trends in Genetics 2025; Levin, BioEssays 2024; Buckley et al., Entropy 2024) provides independent institutional confirmation that biological systems at every scale exhibit goal-directed selection among alternatives, active interpretation, and context-sensitive decision-making. Six independent closure layers — philosophical authority, self-refutation, mathematical formalization, thermodynamic grounding, empirical confirmation, and exhaustive uniqueness — establish the irreducibility of Intent as directed selection. The justification demand is closed.