A Conditional Theorem for Environmental Role Anchoring This paper studies how a specified constructional role can be fixed to one token when the complete licensed internal and indexical input does not itself determine a unique occupant. The analysis begins with the AASC kernel: admissibility, standing, reference, and irreversibility. These roles preserve the original bearer, the conditions under which it qualifies, the identity of the use being evaluated, and the original occurrence against substitution or retroactive repair. The central question is not whether a token exists, has an intelligible description, or produces a confirming outcome. It is whether that token was originally qualified for the specified role under the complete original conditions. The boundary-trace fixation theorem For a fixed role ℓ, candidate fibre Sℓ, and fixed background assignment R, the paper defines the complete original eligibility relation Fℓ(d) = {s ∈ Sℓ : Jℓ(d, s)} where Jℓ records the conjunction of all original role requirements, including candidate eligibility, channel incidence, compatibility with other assignments, reporting, continuation, transport, historical, and application-domain conditions. The main theorem applies when: the internal and outcome interfaces are specified on their claimed domains; the environmental input includes the identified environment and joint channel package; the trace is independently sound, complete, lawfully transported, and outcome-independent; the positive trace set is exactly one token, Pd = {s*}. Under these conditions: the trace returns s*; the assignment Rs* is admissible; every other candidate fails the original complete role requirements; s* is the unique original occupant of the role on the fixed background; the fixation is stable under lawful presentations and covariant transport; downstream confirmation does not supply the role’s first warrant. The result is therefore stronger than uniqueness of a displayed rule value. It establishes uniqueness of the originally qualified role occupant when the trace is role-exact. Structural selection and environmental determination The paper separates three related but distinct problems. First, it proves an exact stabilizer criterion for structural selection. For a lawful group action with eligible family F(z), a unique equivariant selector exists exactly when Kz = F(z) ∩ FixS(Gz) is a singleton at every input in the selector domain. This distinguishes genuine structural selection from a merely named preference, a preferred representative, or a non-singleton trace. Symmetry alone blocks an equivariant selector only when the complete input stabilizer moves every eligible candidate. Second, it proves a fibre criterion for environmental determination. If two complete inputs have the same internal-plus-indexical reduct but require different original role answers, then the answer cannot factor through that reduct. The determining distinction is carried by the retained boundary or channel data. Third, it proves a descent-and-lift distinction between class fixation and token fixation. A trace may uniquely determine a role-equivalence class without selecting a raw token representative. Conversely, a token-level result requires an independently licensed lift that preserves the original identity-bearing role. Sound, complete, and role-exact traces The paper carefully distinguishes several levels of positive result. A sound singleton trace establishes one originally qualified assignment and the unique value of that trace rule. It does not, by itself, exclude other originally admissible candidates. A complete role-exact trace establishes equality between the trace-positive set and the full original eligibility set: Pd = Fℓ(d). Only then does singleton positivity prove that the original role itself has exactly one admissible occupant. When the original role already requires the specified channel incidence, necessity of that incidence together with faithful trace reporting supplies the stronger completeness bridge. In that case, the receiving obligation is derived from the original role rather than added as an independent postulate. Environmental forcing after source exhaustion The paper proves an asymmetry-exhaustion result. Once the complete licensed internal, indexical, provenance, and non-boundary input has been accounted for, every warranted role-fixing rule must either: factor through that complete non-boundary input; or essentially use licensed boundary information or boundary grounds. If the non-boundary input is exhausted without producing a warranted singular answer, the environmental route is conditionally forced. This means that any remaining same-domain fixation requires boundary data or boundary warrant. The conclusion is deliberately conditional. The theorem does not infer that a qualifying boundary channel exists merely because the non-boundary route fails. The channel, its original incidence, its interpretation, its transport law, and its authority must still be independently established. Irreversibility and non-retroactive repair The paper distinguishes later discovery from later alteration. Later evidence may establish that an unchanged original channel already satisfied its original qualification conditions. It may improve knowledge of the original act without changing its truth. By contrast, changing the channel, adding a missing condition, calibrating a previously failed relation, or succeeding in a later act produces a different input or occurrence. Such a later construction cannot retroactively repair the qualification of the unchanged original incidence. This preserves the direction of authority from original incidence to faithful role use. A downstream confirmation cannot be used as the first warrant for the role whose interpretation is required to obtain that confirmation. Class-valued reception The paper also exports the result to quotient and class-valued receivers. A singleton trace may fix a unique role class without selecting a privileged raw representative, provided the original consumers factor through that class and lawful descent is established. This prevents several distinct conclusions from being conflated: unique trace value; unique selected assignment; unique role-equivalence class; unique raw token occupant; complete exclusion of every other original admissible assignment. Each requires its own receiving conditions. Scope and non-claims The results are conditional on the stated target domain, complete original role requirements, independently warranted channel or boundary data, lawful transport, and outcome-independent authority. The paper does not claim: that every role has a unique occupant; that every environmental channel exists physically; that a detector identifier or calibration record creates an incidence by itself; that a singleton predicate automatically excludes all other admissible candidates; that non-singleton trace data prove universal impossibility of selection; that a mathematical witness constructs a laboratory mechanism; that later evidence can alter an unchanged historical qualification; that failure to prove a channel is itself proof that no licensed channel exists; that class fixation and token fixation are interchangeable. A missing proof, a false condition, an empty trace, multiple positive traces, an unwarranted application, and ignorance of a pre-existing relation have different evidential status. Role in the AASC programme This paper provides the boundary-and-fixation layer of the AASC corpus. It formalizes how environmental information can anchor a role without becoming an arbitrary label, how singleton traces acquire authority, how structural selectors are constrained by stabilizers, and how role answers descend through lawful quotients. Its principal contribution is a precise boundary between: internal non-selection and environmental determination; dependence of an answer and dependence of its warrant; sound partial certification and complete role fixation; class-valued identity and token-valued identity; later discovery and retroactive repair. The resulting theorem is a conditional but exact rule for when a boundary trace genuinely fixes an original role under admissibility. Keywords boundary-trace fixation; admissibility; AASC; environmental role anchoring; role-qualified token; original incidence; singleton trace; structural selection; stabilizer criterion; fibre factorization; lawful transport; irreversibility; provenance and channel authority; class-valued quotient; no retroactive repair