Temporal Structural Forecasting: Constructing and Validating the {4,5,6} Forecast

Forecasting exists to address the timing problem: when to act. Every published time series method identifies what the next value will be instead, because every one of them performs a Unidimensional Univariate (UU) Operation: the method discards the calendar coordinate attached to each historical observation, replaces that coordinate with a sequential index, and returns a value carrying no position in time. This paper defines a Forecast as a {4,5,6} object carrying a Dimension 4 value, a Dimension 5 calibrated probability distribution, and a Dimension 6 calendar coordinate, and establishes that no single UU Operation produces one. The paper then specifies a construction that does. Two UU Operations run along two structurally independent timelines, one sequential and one seasonal, and Orthogonal Projection combines their outputs to place a value at a calendar coordinate. A separate calibration procedure recovers the probability distribution at each position from the accuracy the corresponding season recorded in prior completed cycles, producing the Calibrated Probability Band (CPB). The complete set of bands across a forecast horizon constitutes the Map of Normal: a structural specification of what counts as normal at every position, committed before any actual value arrives. Because every input to a Forecast predates the position that Forecast describes, no pathway exists for an outcome to enter the computation that specified it, and the accumulated record of committed Forecasts admits direct verification. Equity forecasts serve as the worked instance in Section 7, because the specification is a price, the outcome resolves in currency, and every element is checkable against public market data.