Special Relativity from AASC The Necessary Kernel of Physical Objecthood and Its Lorentzian Realization

Special Relativity from AASC The Necessary Kernel of Physical Objecthood and Its Lorentzian Realization This paper develops a source-preserving derivation of special-relativistic structure from the necessary conditions of determinate physical objecthood. It begins with the AASC kernel K = (Adm, Stand, Ref, Irr) comprising admissibility, standing, reference, and irreversibility. These roles are shown to be necessary whenever physical objects, states, records, comparisons, selectors, calibrations, source maps, or realized laws are treated as determinate physical content. The paper then carries this kernel through a sequence of increasingly rich physical constructions. Premetric comparison, persistence, transport, clocks, endpoints, signal protocols, inertia, and metric realization are not introduced as independent formal overlays. They are constructed as source-preserving refinements whose domains, original records, applicability conditions, and failure modes remain attached throughout the derivation. Central result On the explicitly occupied comparison branch, the paper constructs the physical conditions required for a Lorentzian realization: a regular characteristic source and its physical record descent; stable comparison and persistence witnesses; homogeneous displacement composition; an affine receiving carrier; completed causal order and strict clock separation; finite propagation and intrinsic isotropy; a spatial quadratic form and Lorentz cone; common rest calibration; composable frame comparisons; comparison-preserving transport; complete invariant source and response protocols. These constructions produce the calibrated Lorentz law on the declared target. The resulting frame transformations are proper orthochronous Lorentz transformations, with the full Poincaré group available when the additional frame and translation supply is present. The paper’s main theorem establishes that every non-degenerate determinate physical domain necessarily instantiates the AASC kernel, and that every coherent occupied AASC construction datum satisfying the stated branch conditions yields a source-preserving chain to the familiar special-relativistic laws. Physical realization of the relativistic effects Using the same retained physical source, the paper derives the standard operational consequences of the Lorentzian structure: time dilation; length contraction; relativity of simultaneity; radar synchronization on its executed two-way signal domain; proper duration for the stated ideal-clock class; Lorentz covariance of attached source responses; the associated Ward identity on the closed invariant-source branch. The derivation preserves the identity of the physical bearer, its clocks, endpoints, rods, signal protocols, response records, and continuation data. These effects therefore arise as measurements on an occupied source rather than as detached coordinate identities. Inertia and mass–energy equivalence On the attached total-source, stable active-rest-orbit, and controlled-pulse target, the paper constructs the operational inertia relation M = (E₀ / c²) I₃ and obtains the scalar mass–energy relation E₀ = mᵢ c². The corresponding energy, momentum, and invariant mass shell are derived afterward from the controlled response protocols. The paper distinguishes the physical conditions required for kernel necessity, metric licensing, operational inertia, and numerical calibration; none of these roles is silently substituted for another. Common-source realization An explicit fixed-background model supplies a nonempty occupied realization containing: a regular characteristic source; an energetic internal clock; finite balanced signal protocols; a driven Hamiltonian control; the complete boosted clock phase; the original marked records and source projections. A common-history refinement then verifies the compatible Einstein and Schrödinger projections, exact metric matching, and Lorentz-path continuation on the declared domain. The positive laboratory response and the vacuum gravitational source remain distinct physical queries. The paper proves an obstruction to identifying them as one complete source on unchanged flat geometry. Scope and realization boundary The results are exact relative to the declared physical source, comparison class, branch conditions, occupied targets, source-preserving refinements, and calibration data. The paper does not claim: that every physical system realizes the stated Lorentzian branch; that the derivation supplies spacetime dimension without its explicit source conditions; that all microscopic realizations with the same admitted records are identical; that the result is a uniqueness theorem across different physical seeds, source systems, spectra, or initial data; that a finite-dimensional regular source is the only possible underlying realization; that the common-source construction identifies laboratory and gravitational sources without further certification. Instead, it establishes a disciplined dependency order: determinate physical objecthood incurs the necessary kernel; completed comparison and persistence support the affine and causal structures; physical conditions license metric realization; calibration and controlled response fix the numerical representatives. Role in the AASC programme This paper provides the Lorentzian realization layer of the AASC corpus. It exposes the necessary kernel beneath physical objecthood and carries that kernel through premetric comparison, persistence, causal geometry, clocks, transport, source response, and inertia. Its principal contribution is to show how the familiar special-relativistic laws arise on an explicitly inhabited, source-preserving target while retaining a strict boundary between: kernel necessity; physical occupation; comparison and metric licensing; numerical calibration; dynamical source identification. The resulting construction supplies exact reception interfaces for the Wheeler–DeWitt, symmetry, and Standard Model carrier programmes. Keywords AASC; special relativity; necessary kernel; physical objecthood; admissibility; standing; reference; irreversibility; premetric comparison; persistence and transport; Lorentzian realization; causal geometry; time dilation; mass–energy equivalence; source-preserving construction