The Mathematics of Going Blank: A Carlo‑Field Model of Cognitive Collapse Under Broad Prompt Pressure v2

Jonathan was asked to think of anything. He could not. This is the proof of why. This paper treats a single failed thought as a solvable system. When asked for "anything" — a query with no gradient, no constraint, and therefore no direction to descend — a cognitive manifold does not fail gracefully. It collapses. The Mathematics of Going Blank formalises that collapse across seven passes: state space, entropy collapse, query gradient, retrieval dynamics, pressure-weighted inhibition, phase transition, and Carlo-Field integration, each built as a closed operator (Ω1–Ω6) ready for direct insertion into any Carlo-Field or ReGenesis Engine architecture. Along the way it derives why "anything" is not a valid cognitive query, models social, temporal, and evaluative pressure as an exponential inhibitor on recall, and shows that blankness is not a personal failure but a predictable, threshold-crossing phase transition — attractor(t) = ∅, and the mind goes quiet on schedule, in about 350 milliseconds. The result is a fully engine-ready subsystem: six canonical equations, a signal-path diagram, a millisecond-resolution timeline of the blankness event, an operator pack, and a NOTEBLOCK pseudocode implementation — accompanied by a live 3D companion visualiser that renders the same seven passes in motion, from wide-entropy manifold to frozen attractor and back. It is offered in the same spirit as the most fertile non-idea imaginable: with complete mathematical seriousness, in service of something that was never serious at all. KEYWORDS & SUBJECTS:Cognitive blankness; entropy collapse; query gradient; Carlo Field; ReGenesis Engine; cognitive manifold; attractor basins; pressure-weighted inhibition; phase transition; retrieval dynamics; mathematical cognition; non-Euclidean thought space; gradient failure; relevance decay; cognitive freezing; collapse mechanics; human prompt response; broad prompt pressure; dynamical systems; cognitive modelling; temporal cognition; inhibition function; attractor destabilisation; entropy-driven phase shift; cognitive state topology; conceptual geometry; mental load; social evaluation pressure; zero-gradient queries; blankness event; cognitive entropy; mathematical psychology; computational cognition; theoretical modelling; cognitive systems engineering; Carlo-coded subsystems; collapse-rate analysis; prompt-induced cognitive failure. Contact: For enquiries or research questions related to this work, email [email protected]