Self-Folding Signatures: Proof, Concordance, and Capability Transfer Risk Across Twelve Scientific Domains

Seven companion documents investigating self-folding geometry, cross-domain structural concordance, and AI safety implications. Document 1 — Cross-Domain Concordance of Self-Folding Signatures: Primary paper. Maps five structural signatures across twelve scientific and engineering fields using only independently validated, peer-reviewed results. Novel claim is the concordance itself: that these phenomena may share a common generative mechanism. Includes control experiment (Appendix A) testing five non-physical domains, which reclassified musical composition from control to primary field. Document 2 — The Self-Referential Orthogonality Residual Theorem (SORT): Formal proof that self-consistent self-folding systems cannot achieve perfect orthogonality. Includes material extension establishing a second independent lower bound from substrate thickness, producing fold limits, crease hysteresis, and birth-order memory. Document 3 — Control Experiment (Appendix A): Five non-physical control fields tested against the concordance criteria. Separation of 46.4 percentage points between primary and control domains after music reclassification. Document 4 — Cluster Robustness and Dependency Analysis: Tests concordance survival under conservative independence assumptions. Two dependency clusters identified. Concordance holds at 84.6% across nine independent voices. Document 5 — Predicted Field — Linguistics: First field added by prediction rather than curation. Scored 5.0/5 against all five SORT signatures. Confirms the concordance as a prediction-generating framework. Document 6 — Group-Theoretic Reduction of SORT Signatures: Shows five signatures reduce to four independent conditions (non-abelian group, finite-dimensional representation, non-invertible quotient, specific weight structure) plus one derived confirmation. Identifies S5 as locus of functorial cross-domain information. Document 7 — Structural Concordance as Capability Transfer Vector: Mandatory risk companion. Identifies the concordance framework as a domain-boundary bypass for AI safety architectures. Compositional hazard: individually safe components combine to enable cross-domain capability generation in restricted domains. Recommends compositional safety evaluation, structural anomaly detection, and S5 monitoring as mitigations. Published with the science, not after it. Keywords: self-folding geometry, orthogonality residual, cross-domain concordance, substrate thickness, dimensional generation, group-theoretic reduction, capability transfer, AI safety, compositional risk, structural isomorphism, non-abelian representation, concordance matrix, responsible disclosure. Indexed under: Cardwell, Ryan.