The Bosonic Carrier–Response–Projection Atlas

Common-Source Reconstruction, Gauge–Higgs Coherence, and Physical Realization under Structural Constraints This paper presents the capstone integration of the Bosonic Carrier–Response–Projection Series (BCRS). It combines the premetric bosonic source architecture of BCRS-I with the color realization of BCRS-2C and the electroweak–Higgs realization of BCRS-2EWH, establishing a common framework in which carrier identity, response structure, and physical projection remain distinct but coherently related. The central problem is that the electromagnetic, weak, color, and Higgs sectors do not operate as unrelated marginal systems. Their joint responses contain relative attachment, global-form, matter-incidence, metric, and continuation information that cannot always be recovered from separate sector descriptions. The atlas therefore reconstructs the coupled structure from one common source, retaining the actual interfaces through which the sectors act together. The paper develops a mechanism-preserving boson-kind atlas for electromagnetic, weak, color, and Higgs response. Cross-kind interactions are represented as typed multi-input incidences rather than as identifications of their participating carriers. This allows a covariant derivative, matter current, Higgs interaction, color response, or metric exchange to combine several sector inputs without collapsing their distinct source identities. A complete mixed observation algebra is constructed before quotienting. Its exact observational quotient records the joint signatures generated by mixed operations, domains, failure values, and relative attachments. The difference between a marginal quotient and the integrated quotient is identified precisely as the mixed-signature kernel. This establishes when separate sector descriptions are insufficient and what additional relational information is required for joint reconstruction. The shared gauge–Higgs source then yields: a common global-form structure; one Higgs bridge with distinct response incidences; a color-correlated electromagnetic stabilizer; a nonzero minimal single-doublet branch; a graded joint reducing-support lattice with five atoms; dimensions ((8,1,2,1;1)), with gauge and scalar grading preserved. The five response coordinates of the integrated local branch reconstruct the complete stipulated joint gauge–Higgs interaction law. A sixth coordinate is required when the vacuum contribution is itself observed. Complete mixed polynomial-jet data extend the reconstruction to independently admitted higher-operator targets. The result is an explicit inverse and a target-relative minimality criterion: information is essential precisely when its deletion produces an admitted native distinction that cannot be recovered from what remains. The atlas also constructs a populated simultaneous classical gauge–Higgs–gravity branch on a fixed Wheeler–DeWitt matter sector. The branch includes a retained massive scalar clock, exact coupled constraints, a proper local quotient, and local covariant development. Gauge and Higgs energy therefore participate in one coupled metric history rather than being appended to an independently solved sector description. This classical realization is supplemented by source-specific physical projection layers. Polarization spaces, photon channels, physical poles, neutral-composite channels, confinement-qualified color responses, typed processes, joint state kernels, and metric exchange are incorporated only on their actual authority domains. Their source requirements remain explicit, and the atlas distinguishes a constructed physical projection from a formal response coordinate or particle label. The integrated framework establishes: naturality under lawful common-source redescription; preservation of mixed operation domains and failure records; reconstruction of actual relative attachments; common-source existence and incompatibility criteria; complete joint local-law reconstruction; simultaneous classical gauge–Higgs–gravity realization; exact process composition and coupled metric exchange; joint state-kernel and operator-domain reconstruction; target-relative minimal identity; a global no-backflow theorem preventing downstream particle labels, numerical fits, or detector records from revising earlier carrier or whole-law classifications. A central conclusion is that law rigidity and response diversity are compatible. One complete law may support multiple marked responses, histories, physical channels, and realization branches. Conversely, a unique response at one complete source datum does not select one coupling, history, global branch, or physical state across the entire source family. The atlas therefore provides a unified structural map from premetric source laws through sector responses, common classical realization, and independently authorized physical projections. Scope and realization boundary The paper establishes the integrated bosonic structure on its actual common-source domains. It does not claim that every formal parameter tuple has a physical realization, that every marginal sector can be jointly lifted, or that every response coordinate is a numerical mass, width, lifetime, or cross section. The populated classical branch is not a pure Standard Model vacuum and does not by itself provide an unrestricted quantum, spectral, scattering, asymptotic, or global gravitational realization. Photon, pole, confinement, neutral-composite, and detector-level claims retain their own source, state, boundary, and authority requirements. The final disposition preserves positive constructions, proved obstructions, inactive or inapplicable mechanisms, and unresolved premises as distinct statuses. An unsupplied physical authority is recorded as NotReady rather than converted into either a negative result or an assumed realization. Role in the BCRS programme BCRS-III is the integrating capstone of the bosonic arc. BCRS-I establishes the premetric carrier–response foundation; BCRS-2C realizes the color branch; BCRS-2EWH realizes the electroweak–Higgs branch; and this atlas reconstructs their common-source interfaces, joint response algebra, classical coupled realization, and physical projection boundaries. Its principal contribution is a disciplined passage from carrier identity to response structure and finally to physical realization without allowing information from a later projection to flow backward and alter an earlier structural result. Keywords bosonic carrier–response–projection atlas; AASC; Standard Model; common-source reconstruction; mixed observational quotient; carrier identity; electroweak–Higgs structure; color response; gauge–Higgs interaction; Wheeler–DeWitt branch; classical gauge–Higgs realization; physical projection; response reconstruction; minimal identity; no-backflow theorem