Endpoint on Higgs Structural Identity: Bridge-Carrier Occupation and No Fifth Identity Ground

This manuscript proves the second paper in the Higgs structural endpoint arc. Paper 1 established the Higgs bridge/fixation carrier CH := Hbr/fix as the standing-bearing carrier forced by a neutral Higgs-domain order-to-deformation and massresponse target. The present paper asks the next question: what fixes Higgs identity once the carrier has been admitted? The answer is an endpoint theorem, not a definition by stipulation. In a same-scope Higgs-domain regime preserving the inherited target DH, the inherited role bundle Hrole, admissible redescription, and the Paper-1 normal form RH, every admissible Higgs identity claim must factor through CH. Scalarity, vev-status, potential-minimum status, pole-mass status, RG-running status, Yukawa-form status, mass-matrix status, vacuum-branch status, thermaltransition status, and metric-comparison status are identity representatives or downstream route statuses; none supplies primitive Higgs identity by itself. The proof proceeds by separating identity grounds from descriptions, then exhausting the same-scope identity alternatives. A Higgs identity claim is a claim that purports to determine what counts as the Higgs in DH, rather than merely describing, measuring, coordinating, or routing Higgs-associated structure. The representative catalogue is admitted as useful physics language, but each entry fails as primitive identity ground unless it presupposes or factors through the bridge carrier. The identity normal form Rid H = (DH,CH,Hrole,RH,∼id H, ρid H) records that admissible identity-bearing use must preserve the same target, the same carrier occupation, the same role bundle, and the same admissibility boundary. The ordered fail-closed identity classifier places every identity candidate into one of six classes: CarrierIdentical, RepresentativeOnly, RouteStatus, StandingSmuggling, RoleIncomplete, or TargetUpdate. Carrier-identical candidates are the same identity role under licensed redescription; representative and route candidates do not ground identity; standing-smuggling is blocked by the no-generator/no-transfer/no-repair discipline; role-incomplete candidates fail the target; target updates leave the same-scope identity theorem. The main theorem is the Higgs Structural Identity Theorem: IdH = unique admissible occupation of CH inside DH. Equivalently, any same-scope occupant satisfying the full Higgs identity role is not a second primitive identity ground but the same bridge/fixation carrier up to role-preserving redescription. No fifth identity ground remains outside carrier occupation, representatives, downstream routes, standing smuggling, role incompletion, and target update. The result preserves ordinary Standard Model Higgs language as representative language while denying its promotion into primitive identity authority.