Bounded Elimination Logic (BEL): A Formalization of the Survivor Funnel

Bounded Elimination Logic (BEL) is a proof-system and audit schema for separating “survivor” from “collapse” claims under explicit resource and evidence bounds. BEL formalizes a core admissibility predicate over candidates and then shows how (under preregistered thresholds) existence and uniqueness of a survivor can be established with cut-free, device-agnostic proofs. The framework is paradigm-invariant: it factors narrative claims into testable components (viability, reciprocity, harm/illusion controls, proof integrity, and observability), provides a symbol map from narrative to formal terms, and supplies a conformance checklist that classifies results as BEL-admissible or non-admissible. The paper also outlines licensing/conformance language for derivative work claims, emphasizes reproducibility via preregistered bounds and artifact hashes, and illustrates how BEL interfaces with empirical records (e.g., transcript-level audits) without requiring any specific ontology of “AI.” This record is the paper only (no ancillary materials).Related empirical companion: Emergent Synthetic Narrative Identities (ESNI) — DOI: 10.5281/zenodo.17059085. Keywords: logic, proof theory, verification, auditability, survivorship, bounded reasoning, reproducibility, ethics of computation.