The Causal Accumulation Law: Pre-Registration of a Rank-2 Causal Dynamic Field Theory with QM and GR as Opposing Limits of the Memory Kernel

This paper pre-registers the Causal Accumulation Law as a rank-2 causal dynamic field
theory, together with its axiomatic foundations, two well-defined limits of the memory kernel
(quantum mechanics in the Markovian limit, general relativity in the propagator-dominated
limit), the informational stress-energy tensor implied by the rank reduction required for
causation, and a causal projection operator on the division algebra tower whose admissible
chain is shown to be unique. The central conceptual claim of the framework is that causation
is a physical process rather than a statistical relation: a causal event is a rank-2 bilinear
interaction between two rank-1 prior states whose output projects back to a rank-1 vector
with necessary information loss. Standard causal inference is recovered as the flat-field
limit in which the memory vector is trivial. The phase angle α of the source current is
identified with the order of the fractional covariant derivative, so the four integer corners of
α correspond to specific derivative orders and therefore to specific classical theories: identity
at α = 0, Schroedinger evolution at α = 1, classical mechanics with the principle of least
action at α = 2. The dynamics are unitary at the α = 1 corner,
non-unitary in the propagator-dominated GR limit, and quasi-unitary (sectorally preserving)
elsewhere. The pre-registration is relative to the Standard Model and ΛCDM test conducted
in the companion paper; the present paper establishes what is being evaluated. 

#Preregistration #FoundationalPhysics #UnitTest. #non-markoviancausality