The AMetric Boundary

Pre-Fixational Authority, Non-Transmissivity, and Complete Interfaces This paper develops the AMetric boundary as a foundational constraint on what distinctions, selections, and qualifications a determinate construction can legitimately support. The argument begins from the necessary kernel of non-degenerate determinate objecthood: Any construction that preserves an identifiable subject, supports a warranted use, retains an attributable original occurrence, and continues under identity-preserving transformation already performs the work represented by these four roles. The AMetric boundary describes what follows before additional target-fixing structure has been independently licensed. Foundational Result The paper proves that a pre-fixational admissibility-bearing interface cannot acquire additional standing-bearing discrimination merely by changing representation, introducing a bare label, or borrowing authority from a structure whose own use depends on the disputed qualification. The resulting boundary is: binary at each fixed complete qualification question; non-eventful in its constitutive order; non-parameterized with respect to arbitrary crossing or indexing; non-transmissive from later or richer structure back to an unchanged source interface; regime-invariant across lawful identity-preserving realizations of the same constructional conditions. The boundary does not prohibit richer structure. It requires that any additional distinction be supplied by independently warranted data, a lawful comparison, or a proved connection to the original bearer and question. The paper’s constructed Axiom 6 states the complete result: a claimed source of target-specific authority must either already determine the answer with an independently established original-incidence warrant, receive additional fixing data with a warranted connection to that answer, or fail to establish the claimed authority. A bare name, canonicalization rule, metric, rank, probability, selector, threshold, or provisional designation cannot supply a missing discriminator merely by being introduced. Minimal Regime Qualification The regime-invariance theorem applies to constructions possessing evaluated acts or states, bivalent admissibility or standing, lawful identity-preserving transformation, irreversible same-lineage commitment, same-scope continuation, and no undeclared boundary discriminator. The conditions above are not definitional restatements of the present framework. They specify the minimal structural requirements under which proposition-bearing, identity-preserving construction with irreversible commitment is well-typed. Any system failing to satisfy these conditions does not constitute a counterexample, as it fails to instantiate the target phenomenon. Mathematical Boundary The paper gives exact mathematical classifications for the information and selection available under lawful transformations. Key results include: invariant information factors uniquely through the corresponding orbit quotient; an equivariant selector exists precisely when eligible stabilizer-fixed outputs are available on the relevant input orbits; selection is unique exactly when every eligible stabilizer-fixed set is a singleton; the equality-only interface reduces finite-tuple information to equality patterns; an unanchored equality-only carrier admits no invariant strict ordering or privileged atom selection; a complete observation family determines a unique maximal comparison-respecting quotient; an interface is sufficient exactly when its fibres do not identify inputs requiring different warranted answers; additional queries refine the interface precisely when they distinguish points previously identified by the existing quotient. The paper also formulates the results for different presentation types through a groupoid treatment of lawful transport. Non-Transmissivity and Grounding A central theorem gives the exact criterion for backward determination. If a richer presentation is reduced to retained source data through a forgetting map, a target answer descends to the source precisely when it is constant on the fibres of that map. Therefore, if two richer realizations share the same retained source data but require different warranted answers, the source interface cannot determine both answers. The missing distinction must be supplied as additional independently warranted structure. A separate grounding theorem excludes circular self-authorization. A family of mutually presupposing licenses cannot establish itself when every rule entering the family already requires a member of that same family. The theorem allows genuine grounded entrances, sound cyclic systems with independently proved semantics, and new constructions with their own warrants. It excludes only the attempted use of an asserted license as its own first ground. Complete Interfaces and Construction The paper develops a complete interface theory for admissibility-bearing construction. It distinguishes: preserving an original result; identifying a lawful equivalence class; selecting a representative; proving that the selected representative is a warranted realization. These are separate achievements with separate proof obligations. The construction results include exact descent criteria for partial operations, preservation of definedness and output classes, finite composition of compatible operations, maximal continuation congruences, and universal assembly from independently warranted components. Existence, coverage, compatibility, and realization are kept distinct from uniqueness. Historical fixation is treated separately through retained-history conservation. A later positive endpoint does not erase a failed earlier stage, and a new construction cannot retroactively change the result or conditions of the original construction. Scope and Boundaries This paper presents a structural and mathematical theorem for admissibility-bearing construction. It does not claim: that every formal or physical system satisfies the regime assumptions; that the AMetric boundary is an empirical measurement or dynamical mechanism; that all possible systems have one unique physical realization; that bivalence alone proves existence, coverage, or computability; that every richer structure is forbidden; that a quotient theorem replaces a domain-specific realization or physical existence proof. The result is strongest where the bearer, complete question, lawful transformation, original incidence, and intended use family are independently specified. Within that fixed domain, the AMetric boundary is not an optional interpretive overlay. It is the unique regime-invariant constraint governing what admissibility-bearing construction can warrant. Role in the AASC Programme This paper supplies the foundational boundary theorem used by subsequent AASC work. It connects kernel necessity to exact limits on discrimination, selection, representation, transport, and historical continuity. Its central contribution is to show how a determinate construction can acquire additional structure without allowing that structure to manufacture its own missing authority. Every legitimate refinement must identify its new data, its lawful relation to the original construction, and the conditions under which its conclusions stand. Keywords AASC; Admissibility And Standing Constraint; AMetric boundary; admissibility-bearing construction; regime invariance; pre-fixational authority; non-transmissivity; bivalent standing; identity-preserving transformation; irreversible commitment; equivariant selection; orbit quotient; observation quotient; complete interface; historical fixation