{"paper":{"title":"Causality from the spectrum: Emergence of causal order from process-matrix mereology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alexei Grinbaum, Nicolas Loizeau, Oliver Friedrich, Varun Kushwaha","submitted_at":"2026-07-16T18:00:31Z","abstract_excerpt":"In Hamiltonian systems, the only basis-independent quantity is the spectrum. Given a spectrum, quantum mereology seeks preferred tensor-product decompositions into local subsystems, leading to the emergence of locality. Causal order, however, remains fixed by the Hamiltonian time evolution. In contrast, higher-order quantum theory permits more general processes that need not possess a definite global causal order. In the process-matrix framework, specifying a process requires a choice of subsystems corresponding to the input and output Hilbert spaces of each agent. A change of basis redefines "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.15345","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.15345/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}