The Invariant Interval: Compositional Structure in Temporal Experience

Organizational psychology has produced numerous theories of workplace experience -- engagement, burnout, flow, self-determination, job demands-resources, leader-member exchange -- that are consistently intercorrelated in meta-analyses. Le et al. (2010) found that job satisfaction, engagement, commitment, and involvement share so much variance as to question their discriminant validity. Harter et al. (2002) reported meta-analytic correlations between employee satisfaction and engagement composites exceeding .90 at the business-unit level. The standard interpretation is that these constructs are related but distinct. This paper proposes a more parsimonious account: they are downstream measurements of a single unrecognized mediating variable -- spacetime sentiment (TS²), defined as the subjective perception of time's passage relative to the organism's concurrent sentiment toward its present activity. The theory is grounded in established psychophysics (Weber's Law, Scalar Expectancy Theory, arousal-driven temporal distortion; Wittmann, 2009), formalized using compositional mathematics (total and partial function composition; Spivak, 2014), and tested against four publicly available datasets (combined N > 245,000 observations). No existing dataset measures TS² directly. We test structural predictions using publicly available datasets. The original formulation is partially falsified: the transfer function is not universally logarithmic, and composition is not universally multiplicative. But the data reveal something sharper. What is invariant is not the functional form but the condition under which composition operates. Multiplicative composition of time and sentiment appears at moment-level granularity under imposed temporal boundaries (Stroop trial-level: p < 10⁻⁵) and is systematically destroyed by aggregation -- same data, same task, same participants, only the grain of analysis changes, and the signal goes from p < 10⁻⁵ to nonsignificance. The boundary condition is the respondent-operant distinction from behavioral science (Skinner, 1938): imposed contingencies maintain the organism in the environment, preserving the interval at which T and S compose; operant contingencies permit the organism to exit, truncating the multiplicative product. A formal mediation analysis using the ATUS Well-Being Module (N = 6,524 work-leisure episodes) confirms the boundary condition: sentiment robustly mediates the activity-type to well-being path (ACME = -0.22, 95% CI -0.27, -0.17), but the multiplicative interaction of duration and sentiment is non-significant (p = .81) and adds zero explanatory power beyond its components -- consistent with the aggregation gradient and the theory's prediction that compositional structure is destroyed when time and sentiment are measured separately at aggregate scales. Implications for organizational measurement, experience sampling methodology, and the discriminant validity problem are discussed.