{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JXJNFOJR7SQUODEZVLKY4VUNN4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ed048a3e6cb597b4893159d61475a7ce4f87a92a926e8752e1d89cfe6818392d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-05-09T16:31:45Z","title_canon_sha256":"506fb018be943df65ad7418846c49df610e1193549f87b51deeae8d190d251a4"},"schema_version":"1.0","source":{"id":"1405.2283","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2283","created_at":"2026-05-18T01:37:44Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2283v3","created_at":"2026-05-18T01:37:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2283","created_at":"2026-05-18T01:37:44Z"},{"alias_kind":"pith_short_12","alias_value":"JXJNFOJR7SQU","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JXJNFOJR7SQUODEZ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JXJNFOJR","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:c5ea1c48047b24d5ad5339d586f9cacdd4d363bc606653b48f3305a7a0f87e6b","target":"graph","created_at":"2026-05-18T01:37:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We use a T-duality invariant action to investigate the behaviour of a string in non-geometric backgrounds, where there is a non-trivial global $O(D,D)$ patching or monodromy. This action leads to a set of Dirac brackets describing the dynamics of the doubled string, with these brackets determined only by the monodromy. This allows for a simple derivation of non-commutativity and non-associativity in backgrounds which are (even locally) non-geometric. We focus here on the example of the three-torus with H-flux, finding non-commutativity but not non-associativity, and also comment on the relatio","authors_text":"Chris D. A. Blair","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-05-09T16:31:45Z","title":"Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2283","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d53c61d27e492486bd053034feaffa2581d5d0998a3db37235f4dcf757877ba3","target":"record","created_at":"2026-05-18T01:37:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ed048a3e6cb597b4893159d61475a7ce4f87a92a926e8752e1d89cfe6818392d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-05-09T16:31:45Z","title_canon_sha256":"506fb018be943df65ad7418846c49df610e1193549f87b51deeae8d190d251a4"},"schema_version":"1.0","source":{"id":"1405.2283","kind":"arxiv","version":3}},"canonical_sha256":"4dd2d2b931fca1470c99aad58e568d6f0d847ed4cdd16c42b62625035370dcde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4dd2d2b931fca1470c99aad58e568d6f0d847ed4cdd16c42b62625035370dcde","first_computed_at":"2026-05-18T01:37:44.792876Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:44.792876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RdGUxdyOFMU8fdwXpuAxrhE/2brsYf6EMOhmul0kIe0zmX8tQ/N48dGTGBX9lWYNJbyfC4BgHYpiKyIJINjeCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:44.793536Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2283","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d53c61d27e492486bd053034feaffa2581d5d0998a3db37235f4dcf757877ba3","sha256:c5ea1c48047b24d5ad5339d586f9cacdd4d363bc606653b48f3305a7a0f87e6b"],"state_sha256":"f42f3efcff5378f4010e7bc8db58c55c361d9417fad42897877640a8e8caa8ea"}