Residual Trajectories as Primary Epistemic Objects: Drift-Slew Decomposition of Laplacian Relaxation and the Spectral Fingerprint of Graph Structure

We propose that the residual trajectory of Tutte's spring embedding, when analyzed through the drift-slew decomposition of the Drift-Slew Fusion Bootstrap (DSFB) framework, carries structural spectral information about the graph Laplacian that is discarded by classical convergence-oriented treatments - and argue that this trajectory, not the fixed-point embedding, is the epistemically primary object of the problem. This paper is a conceptual and theoretical contribution: no numerical experiments are reported and no empirical claims are made. The core argument proceeds from a spectral identity established in Section 3, relating the residual sequence to the Laplacian eigendecomposition, which is mathematically…