Terminal Nonpromotion and Target-Relative Factorization in Charged and Colored Matter

Fully Abstract Signatures, Aggregate-Safe Colored Targets, and an Exact Evidence-Relative Disposition Atlas This paper develops the terminal-realization layer of the Fermion Carrier–Generation Structure programme. It receives the exact-three root object, four typed matter fibres, and one-Higgs rooted response structure from FCGS-I, then determines the additional conditions required for a rooted sector, relation, aggregate, or parent presentation to acquire terminal physical standing. The paper separates three questions that are often collapsed into a single particle table: which premetric roots and response incidences are structurally present; which presentations represent the same standing carrier at a frozen target; which carriers acquire terminal physical realization at a specified boundary and authority. A generation root is not automatically a terminal bearer. Nor can a generation count, mass, charge, decay process, matrix display, Higgs incidence, field name, or detector record replace the complete terminal factorization required by the target. For a frozen target, same-target carrier identity is defined semantically as equality under every licensed use. The paper constructs a codomain-typed continuation signature and proves full abstraction when: every signature coordinate is a licensed semantic use; every licensed use factors through the signature; exact domains, failure values, and continuation states are retained; all witness codomains and source attachments remain typed. Signature equality then characterizes semantic identity, remains stable under continuation, and induces a semantic carrier quotient with its universal factorization property. Terminal realization is stratified into distinct stages: candidate precertification; injective compatible preassignment; assignment-local live residue; compatible role-covering bijections; physical authority; a lawful assignment action; exactly one assignment orbit under Role-Occupancy Closure. This removes circularity from the terminal certificate. Positive terminal realization requires an actual singleton-ROC certificate; it cannot be inferred from a successful surface display or from the existence of a familiar physical label. The paper also establishes representative-independent descent for unary and joint terminal predicates. The resulting assignment and disposition structures are defined on quotient classes rather than on arbitrary presentations, and the surface-fibre criterion identifies precisely when surface information could determine the deeper precertification layer. Two target-relative applications are developed. Charged matter The charged-lepton branch is evaluated against a frozen target and finite, versioned evidence basis. Structural and mass-role results are retained, together with selector routes, mass-shape information, readouts, process data, and remaining authority gaps. Because neither the positive terminal packet nor the exhaustive-negative completion packet is activated, the exact charged disposition is This is not a claim that charged leptons do not exist. It records precisely which terminal premises remain unresolved at the declared target and evidence basis. Colored matter The colored branches are formulated on joint multi-parton configurations rather than through an oversimplified constituent-to-hadron map. A Set-valued profunctor connects upstream colored configurations to gauge-invariant singlet boundary records while preserving: (U/D) constituent provenance; multi-constituent configurations; antiparticle and gauge-field participation; channel multiplicity; physical boundary authority; continuation and failure data. The structural Yang–Mills extension contributes its theorem-scope nonlocal sector authority and extended-support results. These remain distinct from confinement, asymptotic authority, and complete channel coverage. At the evaluated evidence basis, the two marked colored branches have the exact dispositions The paper therefore preserves quark standing, color transport, sharp-local vacuum-gap results, and structurally established nonlocal sector information without converting them into an unrestricted confinement theorem. The terminal ROC objects remain unformed at full terminal strength, so no terminal cardinality is reported. Scope and realization boundary FCGS-II establishes the conditional terminal factorization theorem and evaluates the charged and colored targets relative to their frozen evidence bases. Its readiness values are exact outputs of the declared evidence calculus, each carrying its residual profile, successor rule, and counterexample criterion. “NotReady” is not a negative existence theorem. It means that the required positive terminal certificate or exhaustive-negative packet has not been activated at the stated target. The paper therefore does not claim that charged leptons or quarks do not exist, nor that no future terminal realization is possible. Likewise, a local Yang–Mills gap, structural sector theorem, color-neutral projection, isolated composite, or familiar particle display does not by itself establish unrestricted confinement, asymptotic completeness, or a universal hadron spectrum. Role in the FCGS programme FCGS-II extends FCGS-I from primitive roots and rooted response structure to terminal physical realization. It establishes the semantic quotient, terminal assignment-orbit factorization, nonpromotion theorem, aggregate-safe colored target architecture, and evidence-relative disposition atlas required by later physical completion. Its central result is that terminal identity and terminal cardinality are target-relative conclusions requiring complete source, role, assignment, authority, and evidence closure. Keywords terminal nonpromotion; target-relative factorization; fully abstract signatures; semantic carrier quotient; Role-Occupancy Closure; charged matter; colored matter; aggregate-safe confinement interface; quark color transport; evidence-relative disposition; physical authority; continuation congruence; Higgs response preservation; NotReady classification; AASC