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, metri