Conventions, provenance and scope

An internal resolution means a mathematically closed assumption-to-prediction chain inside an explicitly declared physical constitution. In the pilot theory the Bell law is a controlled effective limit, with the material programme included in the same ordinary configuration graph. This usage makes no claim of empirical confirmation, universal preparation of equilibrium, or deduction of P1–P4 from the older source/readout premise. The massive alternative has its own postulated guidance and equilibrium laws. No theorem exchanges axioms between them.

A constitutive assumption specifies an interaction, an ontology or a statistical resource. A theorem derives consequences under named assumptions. A comparison transfers only the outputs that its common measurable space includes. Counts are random atomic measures; their expectations and predictable compensators are different objects. Reduced population evolution does not itself select an actual event generator. At a coarse aperture the directed traffic is a sum of positive microscopic currents; taking the positive part after summation requires a separate directional-alignment condition.

Throughout the discrete chapters, $J_{nm}$ is current into configuration $n$ from $m$, $w_m$ is its coherent weight, and $N_{nm}$ denotes an event count when supplied with these indices. The scalar $N$ in the pilot construction is the number of carriers. Normalized service intensities are denoted by $\Phi$, while $\lambda$ denotes a conditional event intensity. The incidence matrix $B$ is not an apparatus operator in those chapters. In the massive chapters $q$ and $Q_t$ are continuous material coordinates and their actual path; internal coherent keys are not additional discrete actual occupancies. Symbols local to an apparatus are defined again at that apparatus. The pilot clock's integer position and the massive controller's continuous position are distinct variables in distinct theories.

For probability laws, $\TV(P,Q)=\sup_A|P(A)-Q(A)|$; for density operators, $D(\rho,\sigma)=\tfrac12\|\rho-\sigma\|_1$. Four conclusions must be kept separate: complete state distance, endpoint distribution distance, faithfulness to a specified actual past label, and total variation on entire physical-time paths. The first two do not imply the latter two. Whenever conditional laws are compared, both conditioning probabilities are positive. In particular, $\TV(P,Q)<P(E)$ with $P(E)>0$ guarantees $Q(E)>0$ and permits Lemma 2.1; taking a minimum with one cannot define a conditional law on a null event.

An inaccessible reference remains in the joint state. Any memory, classical key, loss product or reset receiver that can return belongs to the complete experiment. The complete post-interaction joint state is retained; an imperfect operation does not insert an ideal daughter. General statements fix the graph, input class, programme and physical horizon before resource limits are taken. Uniformity over growing programmes requires additional estimates.

References M01–M30 and C01–C03 identify the inherited manuscripts and checkpoints; F01–F07 identify their foundation sources. Their substantive results retain their assumptions. The two resolution papers' essential arguments are integrated below. The supplied AI-generated audit was used as working material, after verifying its manuscript hashes, and supplies no external validation authority. Established constructions are attributed to primary literature; no historical-priority claim is made.