Causal Reconciliation of Quantum-Like and Relativity-Like Organization from Strictly Retarded Classical Dynamics

This study formulates a deterministic finite memory extension of classical Newtonian mechanics in which every interaction is evaluated strictly from realized past history over explicit memory horizons. Within this past only causal structure, we show that two familiar phenomenological organizations can emerge from one unified law on internally certified coherent segments, quantum type behavior in push pull interaction channels and relativistic type bookkeeping in attraction only specializations. In the quantum type regime, a structured comparison of past anchored interaction imprints across a nonzero coherence horizon together with an inertial memory horizon produces a reproducible two scale phase organization under repeated deterministic preparations. From these preparation ensembles we construct a complex spatial wavefield and a minimal rotation invariant quadratic intensity as derived diagnostics, while enforcing a strict audit boundary that prevents any ensemble based construction from entering force evaluation. Numerical experiments exhibit robust interference like hit density fringes in a double slit geometry and tunneling like under barrier transmission trends with systematic dependence on barrier shape. In the relativistic type regime, attraction only inward transport consumption on coherent increments yields operational time dilation and an emergent quadratic invariant remainder, and Lorentz type symmetry appears as a derived consequence of this invariance rather than an imposed spacetime axiom. Coherence and closure conditions serve as regime selection and remainder control devices, enabling controlled extraction of Kepler range reductions and secular drift while predicting failure modes when coherence breaks. Overall, the framework supplies explicit causal content for both quantum like and relativistic like phenomena within one strictly past only finite memory mechanics.