This article assembles the physical dictionary and the fundamental V*P structure as the passage from stratified time and package geometry to the physical node of the theory.
In NAPG 2.0 the physical picture appears as the next layer after the logical-geometric foundation: V*P defines the path from temporal primacy to reduced classical regimes.
From the physical side the construction begins not with a ready-made spacetime but with two upstream inputs.
The first input is the MTF layer, from which one imports temporal primacy, stratified time, nonlocal temporal support, and the distinction between fundamental time and its downstream observable reductions.
The second input is the NAPG layer, from which one imports package data, package morphisms, the associator-defect regime, the quadratic object R ⋆ R, the obstruction layer, the cohomological layer, and the differential/Hodge–Laplace bridge.
Within this part MTF supplies the ontological thesis of the primacy of time, whereas NAPG supplies the rigorous package-geometric language in which that primacy becomes formalizable. The fundamental physical structure V * P is introduced precisely from this synthesis.
In the physical language of the program, time is not treated as an external one-dimensional parameter attached to a pre-existing spatial geometry. It is treated instead as a stratified primary support from which downstream observable temporal parameters may later be extracted.
The stratification of time is interpreted as an internal multilayer organization of the temporal support. Physically, it encodes not only order but also compatibility, separation, and transition between distinct temporal layers.
Space, by contrast, is not taken as an ontologically primary object. It is interpreted as a layer, a section, or a realized geometric regime over a temporally primary support.
The symbol V * P (Time*Space) denotes the fundamental physical structure of the program. At the present stage it is understood as a temporally primary, package-controlled, non-metric-first structure whose classical spacetime content appears only after reduction.
A package is a coherent family of mutually dependent structures that cannot be faithfully replaced by a single isolated field without loss of essential information.
A layer is an admissible realized regime of a more fundamental structure. A section is an observable extraction inside a richer package-controlled structure. In particular, classical spacetime is understood here not as primitive ontology but as a sectional reduction.
Nonassociativity is read not as a merely formal algebraic defect but as a structural signal that the composition of fundamental objects does not reduce to ordinary associative kinematics. At the present stage the associator defect is not yet identified with matter, energy, or classical curvature; it is treated only as an internal source-like indicator of the full theory.
Four negative rules are fixed for the physical layer:
the object R ⋆ R is not identified with the energy–momentum tensor;
obstruction data are not identified with ordinary matter;
the Hodge–Laplace bridge is not identified with the full field dynamics;
classical spacetime does not exhaust the ontology of the theory.
Let Tstr be the stratified temporal carrier imported from the MTF layer, and let PNAPG be the frozen package-geometric datum imported from NAPG.
A spatial-layer family over stratified time is a surjective map πlay: LoTstr, where L is the total layered support and each fibre Lt := πlay−1(t), t ∈ Tstr, is interpreted as the corresponding admissible spatial layer.
A package-compatibility assignment for πlay: LoTstr is a rule CV * P assigning to each admissible temporal domain U ⊆ Tstr a package-geometric realization on LU := πlay−1(U) subject to the following conditions:
the realization is controlled by the imported datum PNAPG;
the associator, obstruction, cohomological, and differential/Hodge–Laplace layers remain available on LU;
restriction to smaller admissible temporal domains is compatible with restriction of the realization;
no classical spacetime structure is inserted as primary input.
A pre-fundamental V * P structure is a sextuple V = (Tstr, πlay: LoTstr, PNAPG, CV * P, Σcl, Rcl), consisting of a stratified temporal carrier, a spatial-layer family, the imported frozen package datum, a package-compatibility assignment, a nonempty distinguished class Σcl of admissible classical candidate sections, and a classical reduction rule Rcl: ΣcloClassicalData.
The pre-fundamental structure is called fundamental if the following hold:
temporal primacy: every admissible realization is organized over Tstr, and no classical spacetime datum appears before the reduction step;
layered spatial realization: every admissible spatial regime is realized as a fibre or compatible union of fibres;
package control: the admissible realization is controlled by the imported package datum;
defect retention: the associator sector, the quadratic object R ⋆ R, the obstruction package, and the cohomological package survive as genuine internal sectors of the theory;
classical reducibility: there exists at least one admissible section whose reduction produces a classical spacetime-type datum;
non-metric-first architecture: metric data, when they appear after reduction, are derived observables rather than the primary definition of the theory.
A classical section of a fundamental V * P structure is an admissible section s: UoL, U ⊆ Tstr, belonging to the distinguished class Σcl. Its effective classical content is the reduced datum Rcl(s).
A classical section s ∈ Σcl is called a Minkowski–Einstein type section if Rcl(s) carries the standard status of classical spacetime geometry, namely a Lorentzian spacetime structure and a classically admissible connection regime. If, in addition, the reduced connection is the Levi–Civita connection of the reduced Lorentzian metric, then the section is called an Einstein-type section.
The intrinsic source-like sector of a fundamental structure is the internal sector generated, through the compatibility assignment CV * P, by the nonassociative and obstruction data imported from NAPG. It is denoted abstractly by Ssrc(V).
At the present stage Ssrc(V) must not be identified with ordinary matter, dark matter, or dark energy. It is only a candidate internal source sector from which later effective contributions may arise.
Physical applications of NAPRLK should be understood as limiting, reduced, or sectional regimes of a more general package architecture. The claim that the theory applies to classical physics therefore means not direct substitution but controlled degeneration of structure.
If the set of states collapses to one stratum and the internal package dynamics is frozen, then a classical physical limit arises that is compatible with the ordinary apparatus of differential geometry.