Status audit and model limits of the framework page: primitive data, adopted assumptions, derived objects and what is not claimed

This remark records the status of the notions of the framework page. It is bookkeeping: it asserts no law and no empirical claim, and every mathematical statement it repeats is proved in the item cited.

Primitive data of a model. The spacetime data $(V,\tau ,g,A,\text{orientation of }K)$ of Adopted Newtonian spacetime structure: absolute time, Euclidean spatial slices and their smooth structure: the affine event space, the surjective absolute-time covector, the Euclidean spatial metric on the three-dimensional kernel and the fixed spatial orientation. These are the primitive geometric data; no equation constrains them. The particle labels, their worldlines and their positive masses $m_1,\dots ,m_N$ are the primitive material data of Particle labels, worldlines, the frame-time parameter condition and fixed inertial masses. The class of inertial frames is fixed by Inertial frames, stationary observers and the adopted Galilean transformations between frames as the adapted charts of the spacetime data, with the adopted Galilean transformations between them.

Adopted assumptions on this page. That the primitive data are the spacetime of a physical model, with absolute simultaneity, Euclidean distance within slices and no Lorentzian structure, is the postulate Adopted Newtonian spacetime structure: absolute time, Euclidean spatial slices and their smooth structure. That the model's frames are its adapted charts, that the changes between them are the Galilean transformations, and that a frame's stationary congruence is derived from it, is the postulate Inertial frames, stationary observers and the adopted Galilean transformations between frames. That particles are labels with twice continuously differentiable worldlines parametrized by frame time and fixed positive masses is the postulate Particle labels, worldlines, the frame-time parameter condition and fixed inertial masses. The unit and dimension conventions of Dimensions and SI unit conventions of the non-relativistic classical mechanics framework are part of the formulation and assert no measured value.

Constructed or proved on this page. The adapted coordinates and the affine structure of the simultaneous slices, with existence and uniqueness of coordinates, are mathematics: Affine time space with Euclidean simultaneous slices and adapted charts, Existence and uniqueness of adapted coordinates, and the affine structure of simultaneous slices. The transformation law between adapted charts and its kinematic consequences are the mathematical lemma Transformation between adapted charts and its kinematic consequences; the rotation group and its group properties are The orthogonal group $O(3)$ and the rotation group $SO(3)$ and $SO(3)$ is a subgroup of the general linear group, with $R^{-1}=R^{\mathsf{T}}$. The coordinate velocity and acceleration and their frame dependence are the definition Coordinate velocity and acceleration of a worldline in an inertial frame, and the spatial velocity and acceleration vectors. The configuration domain, its collision exclusion, its constrained branch with the dimension count and the mass operator are the definition Configuration domain of $N$ labeled particles: open admissible sets, regular holonomic constraints and the mass operator, whose dimension statement rests on the established regular-level theorem and whose mass data are those of Constrained configurations, the mass matrix and the mass metric. The frame change laws $w^{\mathrm{\prime }}=Rw+v$, $a^{\mathrm{\prime }}=Ra$, the frame-independence of vanishing coordinate acceleration and the group structure of the Galilean transformations are the physics theorem Galilean transformation of worldlines: velocity and acceleration laws, frame-independence of zero coordinate acceleration, and the group of frame changes, a conditional deduction from the postulates and the cited mathematics.

Explicitly not claimed on this page. No force law and no equation of motion: nothing here determines the acceleration of any particle, and the identification of the acceleration term with a force is made on the pages that introduce dynamics. No conservation law and no selected potential for a concrete system. Kinetic energy is already defined: for a tangent velocity $v\in T_{q}Q$, Constrained configurations, the mass matrix and the mass metric gives $T_q(v)=\frac{1}{2}{G}_q(v,v)$, and Dimensions and SI unit conventions of the non-relativistic classical mechanics framework gives the Cartesian construction $T=\frac{1}{2}{\sum }_i{m}_i\mid x_i^{\mathrm{\prime }}{\mid }^2$ with dimension $\mu {\mathrm{\ell }}^2{\tau }^{-2}$. Its value along a motion requires a specified curve. The conditional mechanical-energy construction $E=T+U$ in the unit conventions also requires a specified potential $U$; it selects no such potential, supplies no conserved energy and asserts no measured energy. No gravitational interaction; gravitation is an optional force model adopted later with its own coupling parameters. No electromagnetic coupling and no electromagnetic field: coupling the framework to classical electromagnetism would require that framework's fields, sources and coupling assumptions and is not a premise or a consequence here. No relativity: the model contains no Lorentzian metric, no light cone and no invariant speed; the Galilean transformations of Inertial frames, stationary observers and the adopted Galilean transformations between frames are not derived as a limit of any other theory and no Lorentz transformation appears. No quantum correspondence: replacing a classical coordinate or velocity by an operator is not a derivation, and no such replacement is made or promised. No thermodynamic or statistical-mechanical statement: equilibrium, entropy and coarse graining are not consequences of the kinematic framework. No measured value of any mass, length, duration or constant, and no observation.

• Conditional content. Every physical conclusion of this pair is conditional on the postulates of Adopted Newtonian spacetime structure: absolute time, Euclidean spatial slices and their smooth structure, Inertial frames, stationary observers and the adopted Galilean transformations between frames and Particle labels, worldlines, the frame-time parameter condition and fixed inertial masses and on the stated mathematical hypotheses of the cited suppliers. The kinematic theorem Galilean transformation of worldlines: velocity and acceleration laws, frame-independence of zero coordinate acceleration, and the group of frame changes establishes what follows from the model; it does not establish that the model describes nature, and it does not by itself identify the class $a\equiv 0$ with the motion of a physically free particle; that identification is the content of a dynamics postulate stated on a later page with its own force hypotheses.

• Regime. The intended regime is non-relativistic: speeds small compared with the speed of light, classical scales, apparatus describable by a classical continuum. The framework sets no numerical cutoffs; each application states the regime in which the point-particle idealization, the chosen frame description and the eventual force law are adequate.

• Evidence. This pair records no experiment and no measurement. Any later comparison of model predictions with reported observations is evidence about a fully specified model, its apparatus assumptions and its analysis; agreement is not a proof of these postulates, and disagreement can expose the model, an auxiliary assumption, the apparatus description or the analysis. Reviewer confidence is not an empirical uncertainty estimate.