What the Whole Adds Without Erasing Its Parts: Local Persistence, Overlap, and Relational Completion in Structural Accounts of Experience

What can a whole add while its constituent processes continue, and what evidence identifies that addition? We distinguish process persistence, complete structural preservation, and equality of a local observation. A finite overlap contract separates shared physical occurrences, admissibility of a joint description, and relations left undetermined by local descriptions. Exact overlap requires more than commuting maps. Under the explicitly assumed structural identity of Unified Consciousness Theory (UCT), grounded embeddings and their exact intersections transport coherently into experiential descriptions; this does not establish subjective unity. The main dynamical construction extends an explicitly credited parity-memory precedent to two overlapping, individually memoryful processes. With memoryless joint innovations, it gives a sharp interval of collective retention coefficients and a local-asymmetry bound on exponential correlation time. Two scope results substantially qualify that frontier. A lag-wise binary compatibility bound survives without Markov assumptions, whereas a fixed positive transition floor removes the unbounded-lifetime limit. More decisively, a fully positive hidden-mediator construction preserves both complete local trajectory laws and the entire observed one-step transition matrix, yet produces an arbitrarily slow collective correlation tail. A two-step semigroup defect distinguishes it from its memoryless observational twin. Fresh relation preparation also separates persistent background correlation from storage of a newly written bit. Matched-local-distribution preparations and marginal-preserving innovation interventions yield an explicit relation-sensitive test without treating a readout as experience. Exact rational verification accompanies all finite constructions. Classical completion, coupling, Markov projection, and common-drive ideas are credited. The contribution is a reproducible composition-and-inference contract with positive examples and explicit failure witnesses, not a new consciousness threshold or an empirical refutation of competing theories. Scientific status: Open theoretical/mathematical preprint; no independent peer review. The finite exact models do not demonstrate biological or artificial consciousness, a specific feeling, or refutation of IIT. Contributor statement: Hongju Liu is the human author of record and responsible depositor. ChatGPT/GPT-6 substantially assisted literature analysis, modeling, code, critical revision, and drafting under user direction. Separate human line-by-line review and journal acceptance are not claimed. Version and rights: PDF, Markdown and ZIP retain exact v1.1.0 author-directed review bytes; no DOI has been inserted into the frozen assets. The present record identifies them. CC BY 4.0 applies to original material to the extent the author holds rights; cited third-party works retain their terms.