The Replicator-Optimization Mechanism: A Scale-Relative Formalism for Persistence-Conditioned Dynamics with a Conditional Consent-Friction Instantiation

Persistence models often conflate propagation, survival, and cross-scale loss. The Replicator-Optimization Mechanism (ROM) is a replicator-mutator template separating baseline weight, bounded survival, and a transfer kernel at a declared scale. Its equation conserves mass but guarantees neither invariance, convergence, a potential, nor a preferred scale. For finite static density-independent continuous time, an irreducible weighted kernel yields a unique positive Perron-Frobenius composition; discrete-time power convergence needs primitivity. The componentwise ranking proved here is guaranteed under exact uniform-residual transfer. Strong lumpability gives universal first-order transfer closure, and blockwise effective fitness gives an exact quotient. An institutional instantiation uses normalized stakes, signed preference-decision alignment, information loss, and descriptive effective voice. It specifies conditional survival, not legitimacy or normative authority. A companion mixed-motive MARL battery reports exploratory evidence against the implemented proxy ratio in its environment: a positive signed target-coordinate-correlation effect survives held-out evaluation under shared-state contention, while a reduced feasible-centred frozen-policy crossing reverses the predicted correlation-noise interaction. The treatment varies ideal-point correlation inside a fixed reward family, not objective- or reward-function alignment. Lean checks mapped algebraic identities and scalar monotonicities, not the stationary theorem, empirical mapping, or normative bridge. ROM is an assumptions ledger and model-construction discipline, not a cross-substrate law. Files main_ROM.pdf — 37-page reader edition (reference PDF for arXiv v5) technical-supplement_ROM.pdf — 23-page standalone technical supplement (extended proofs, ownership mechanics, network analysis, Lean listings) ROM_arxiv_source_v5.tar.gz — arXiv source package: reader source closure, main.bbl, the supplement as anc/technical-supplement_ROM.pdf, and the six cited Lean modules under anc/lean/ with a hash manifest ROM_technical_supplement_source_v5.tar.gz — supplement source Version note v5.0.0 (2026-09-12): Matches the arXiv v5 source package (37 pages; the arXiv v4 of 31 August 2026 had no Zenodo counterpart). Relative to arXiv v4: the technical supplement's showcased Lean proof ethicalSurvival_mono_alignment_via_friction, withdrawn as evidence on 30 July 2026 in the cited repository because the friction functional it depends on was retracted, is replaced and the withdrawal is disclosed in the reader edition's claim-boundary table and in the supplement; the ancillary Lean modules are recopied from dissensus-ai/lean-formalizations at commit 8e11333 so that ROMEthics/Bridge.lean carries the withdrawal notice; the Lean map states 22 theorems mapped to results named in the paper plus six unmapped companion welfare-bridge theorems, replacing the sentence “twenty-eight machine-checked theorems correspond directly to results named in this paper”; the survival-factor domain sentence, two citation attributions, the pointer to the companion MARL paper's non-public claim map and technical supplement, and the AI-use disclosure are corrected. No equation, theorem statement, empirical estimate, or data schema changed. Relative to v3.0.0 (the 69-page arXiv v3 text): this is the reader edition promoted on 19 August 2026, which drops the earlier cross-field “not metaphorical but literal” framing, states the componentwise-ranking result as a sufficient guarantee under exact uniform-residual transfer, and confines the Lean claim to mapped algebraic identities and scalar monotonicities. Links arXiv: arXiv:2601.06363 Lean 4 proofs: github.com/dissensus-ai/lean-formalizations (archived: 10.5281/zenodo.22089594) Companion MARL evidence release: 10.5281/zenodo.22004215 ASCRI: systems.ac/4/DAI-2503 Research lab: Dissensus