Electroweak and Higgs Realization from a Premetric Response Atlas

Interaction Reconstruction and Target-Relative Closure This paper develops the electroweak–Higgs realization of the premetric bosonic response atlas established in BCRS-I. It studies how one Higgs carrier organizes electroweak fixation, residual charge, gauge response, scalar response, physical polarization, interaction structure, and source-attached continuation while preserving the distinction between carrier identity, response support, and physical particle realization. The construction begins with a common Higgs–gauge source on a licensed one-doublet branch. A nonzero fixation determines: a connected effective residual charge direction; a three-dimensional gauge-orbit tangent space; a one-dimensional scalar normal quotient; a rank-three gauge-response form; a canonical decomposition into electromagnetic, charged, neutral, and scalar response modules. The resulting four-module support lattice has one compatible module assignment. This is a classification of invariant response supports, not a count of primitive carriers or interacting particles. Electroweak labels are therefore recovered as structured consequences of the fixation geometry, residual action, kinetic form, and scalar quotient rather than inserted as an assumed particle inventory. The paper reconstructs the local gauge–Higgs interaction law from invariant response data. On the normalized positive family, four invariant coordinates determine the complete local interaction, with a fifth coordinate required when the vacuum value itself is part of the target. An explicit inverse proves completeness, while same-retained-data comparison pairs establish coordinate irredundancy. More generally, finite polynomial-jet tensors reconstruct the declared local law and its differential operations. The analysis then extends from local response to physical continuation. On admitted domains: complete analytic germs reconstruct meromorphic channel responses; bounded rational branches admit finite determining jets; joint source kernels reconstruct cyclic states, currents, and bounded continuations; supplied resolvents or complete closed graphs retain exact unbounded operator domains; mixed incoming, outgoing, and fixed-sibling attachments remain part of the comparison data. These constructions prevent marginal descriptions from being mistaken for complete physical interfaces. A gauge response, scalar response, polarization quotient, photon attachment, pole, or asymptotic channel is treated only on the domain where its necessary source, spectral, analytic, and boundary data are actually supplied. On a licensed Minkowski realization, the paper constructs the null and timelike polarization fibres and gives an explicit free-helicity realization. Source-attached photon and pole-transport results are developed on their independent spectral and asymptotic domains. Local radial–vector vertices and residual charge selection follow from the retained doublet kinetic and representation structure, while finite source-evaluated process families compose on their exact common domains. The native operations and incidence maps form a complete electroweak observation and continuation algebra. Whole-interface role occupation has one lawful assignment orbit over each reconstructed response point. This becomes terminal closure when the reconstruction data are detectable by the admitted observations; otherwise the correct terminal object is the explicitly defined native-readout quotient. The paper also establishes target-relative information minimality. Derived tensors, duplicated descriptions, and certified resolvent-generated data may be deleted when they are recoverable from retained information. Conversely, a deletion is ruled out when an admitted continuation separates two instances with identical retained data. This provides an exact no-repair criterion for determining which response information the target genuinely requires. Scope and realization boundary The paper establishes the electroweak–Higgs structure on its independently source-admitted, dependency-expanded one-doublet branches. It does not claim that the premetric construction alone supplies numerical coupling values, a numerical vacuum scale, interacting (W), (Z), photon, or Higgs pole data, complete asymptotic states, or a universal physical spectrum. The free-helicity, photon, resonance, analytic-continuation, and operator-domain results retain their own independent hypotheses. A physical object is not inferred merely from a response module, formal pole label, mass matrix, or marginal representation. The conclusions are therefore branchwise and target-relative: they classify what follows from the admitted source data and preserve unresolved physical domains rather than silently promoting them into structural conclusions. Role in the BCRS programme BCRS-2EWH supplies the electroweak and Higgs realization layer of the bosonic carrier–response–projection programme. It carries BCRS-I’s premetric distinctions into fixation geometry, residual charge, gauge and scalar response, local interaction reconstruction, polarization, photon realization, resonance transport, and physical continuation. Together with the color realization, it provides the sector-specific structures integrated by the broader BCRS atlas. Keywords electroweak–Higgs realization; premetric response atlas; Standard Model; Higgs fixation; residual charge; gauge response; invariant support lattice; one-doublet electroweak theory; local interaction reconstruction; polarization response; photon realization; analytic continuation; role-occupancy closure; information minimality; AASC