Tier-1 Source-Readout Non-Identity: An Admission-Presentation Non-Identity Theorem

This paper develops a formal support theorem for Shadow Theory by distinguishing Tier-1 admitted/readout reality from the admission-side carrier of structure required for its appearance as measurable, recordable, representable, and operationally stable content. The paper introduces an admission presentation for a readout domain: a structured closure presentation, a readout domain, a partial admission/readout map, status annotations, and a typed active-separation profile. It then proves an admission-presentation non-identity theorem: when the active-separation profile is non-empty, the readout domain is not identical to the admission-side presentation in the relevant structural sense. Applied to Tier-1, the paper treats ordinary physical reality as the record-mediated readout domain of admitted content. The key operational premise is non-exhaustive candidate presentation: distinct candidate-side states may be collapsed or left unresolved by the admitted record protocol. Under this condition, the Tier-1 admission/readout map has a nontrivial non-injective register, which establishes Tier-1 source-readout non-identity as an admission-presentation result. The paper does not claim to replace existing physics, derive a completed source theory, or identify the admission-side carrier with source reality by notation alone. Instead, it supplies a typed formal foundation for the later Shadow Theory support papers on reflective mathematics and physics-as-readout, and it reinforces the main Shadow Theory architecture by showing why Tier-1 mathematics and physics require disciplined source/readout status handling.