{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XG63V65BZXZCXMHB2WSSJ2LWSM","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":"2ffcd8ced06d10200895b6b8b0995469e58d75536e6c66e8ee4fea05349c3ab8","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-07-25T16:05:58Z","title_canon_sha256":"8544b5d6fd6797a76349ce5ea947724d40f56e0d3021f96f3604b1f9e7fc9bea"},"schema_version":"1.0","source":{"id":"1307.6802","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6802","created_at":"2026-05-17T23:51:56Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6802v2","created_at":"2026-05-17T23:51:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6802","created_at":"2026-05-17T23:51:56Z"},{"alias_kind":"pith_short_12","alias_value":"XG63V65BZXZC","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XG63V65BZXZCXMHB","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XG63V65B","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:c62d4339e1eae7be9defdb6680f9604a96896f361df1b8bf7ec6e5ab52083f5d","target":"graph","created_at":"2026-05-17T23:51:56Z","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":"Using the Weil-Brezin-Zak transform of solid state physics, we describe line bundles over elliptic curves in terms of Weyl operators. We then discuss the connection with finitely-generated projective modules over the algebra $A_\\theta$ of the noncommutative torus. We show that such $A_\\theta$-modules have a natural interpretation as Moyal deformations of vector bundles over an elliptic curve $E_\\tau$, under the condition that the deformation parameter $\\theta$ and the modular parameter $\\tau$ satisfy a non-trivial relation.","authors_text":"Davide Franco, Francesco D'Andrea, Gaetano Fiore","cross_cats":["math-ph","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-07-25T16:05:58Z","title":"Modules over the Noncommutative Torus and Elliptic Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6802","kind":"arxiv","version":2},"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:f404a88a7db7e6feba83e24df1bc31cd78d6bcad3a607d557b5bb3760ea82080","target":"record","created_at":"2026-05-17T23:51:56Z","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":"2ffcd8ced06d10200895b6b8b0995469e58d75536e6c66e8ee4fea05349c3ab8","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-07-25T16:05:58Z","title_canon_sha256":"8544b5d6fd6797a76349ce5ea947724d40f56e0d3021f96f3604b1f9e7fc9bea"},"schema_version":"1.0","source":{"id":"1307.6802","kind":"arxiv","version":2}},"canonical_sha256":"b9bdbafba1cdf22bb0e1d5a524e97693240d555d8222ecbe7f772c940faec89e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9bdbafba1cdf22bb0e1d5a524e97693240d555d8222ecbe7f772c940faec89e","first_computed_at":"2026-05-17T23:51:56.194696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:56.194696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p1lNzGIRTK8/jJ4/ueO9FdCJIcH1X2t0+Vj+GkDvcpxHWpX/FU6cDnaxLErLNAVK0I9O9FK+HvE6kAgX84/xDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:56.195375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.6802","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f404a88a7db7e6feba83e24df1bc31cd78d6bcad3a607d557b5bb3760ea82080","sha256:c62d4339e1eae7be9defdb6680f9604a96896f361df1b8bf7ec6e5ab52083f5d"],"state_sha256":"1f8598c5fd808ccb4a775e8eb9ead6694fbb6858516d036e973c89a2368eae9c"}