{"paper":{"title":"Graphical Symplectic Algebra","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.CT","math.SG","quant-ph"],"primary_cat":"cs.LO","authors_text":"Cole Comfort, Robert I. Booth, Titouan Carette","submitted_at":"2024-01-15T19:07:33Z","abstract_excerpt":"We give complete presentations for the dagger-compact props of affine Lagrangian and coisotropic relations over an arbitrary field. This provides a unified family of graphical languages for both affinely constrained classical mechanical systems, as well as odd-prime-dimensional stabiliser quantum circuits. To this end, we present affine Lagrangian relations by a particular class of undirected coloured graphs. In order to reason about composite systems, we introduce a powerful scalable notation where the vertices of these graphs are themselves coloured by graphs. In the setting of stabiliser qu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.07914","kind":"arxiv","version":3},"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/2401.07914/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"}