{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SBKVL4VG7WQV2SULOENF47TREW","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":"4f4f84146f35f112b502a56d3a93cfae619ec24e17703284a1b5305275dd6d7d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-01-10T19:07:14Z","title_canon_sha256":"9ae1f55d0b40ebc3344f07eab5955e3fd85b70717ad876c65d82a4f7e367830a"},"schema_version":"1.0","source":{"id":"1201.2142","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.2142","created_at":"2026-05-18T00:50:24Z"},{"alias_kind":"arxiv_version","alias_value":"1201.2142v1","created_at":"2026-05-18T00:50:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2142","created_at":"2026-05-18T00:50:24Z"},{"alias_kind":"pith_short_12","alias_value":"SBKVL4VG7WQV","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SBKVL4VG7WQV2SUL","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SBKVL4VG","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:3653b36937d6d753d231c9cbefb7c16175937657fcd2f694335271fa535d5b80","target":"graph","created_at":"2026-05-18T00:50:24Z","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":"Let $M$ be a compact real-analytic manifold, equipped with a real-analytic Riemannian metric $g,$ and let $\\beta$ be a closed real-analytic 2-form on $M$, interpreted as a magnetic field. Consider the Hamiltonian flow on $T^*M$ that describes a charged particle moving in the magnetic field $\\beta$. Following an idea of T. Thiemann, we construct a complex structure on a tube inside $T^*M$ by pushing forward the vertical polarization by the Hamiltonian flow \"evaluated at time $i$.\" This complex structure fits together with $\\omega-\\pi^*\\beta$ to give a Kaehler structure on a tube inside $T^*M$. ","authors_text":"Brian C. Hall, William D. Kirwin","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-01-10T19:07:14Z","title":"Complex structures adapted to magnetic flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2142","kind":"arxiv","version":1},"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:a38a393f71ad4dcc4458bbe2dac998b494f90997ab5659fbbc510d1c03bf1d10","target":"record","created_at":"2026-05-18T00:50:24Z","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":"4f4f84146f35f112b502a56d3a93cfae619ec24e17703284a1b5305275dd6d7d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-01-10T19:07:14Z","title_canon_sha256":"9ae1f55d0b40ebc3344f07eab5955e3fd85b70717ad876c65d82a4f7e367830a"},"schema_version":"1.0","source":{"id":"1201.2142","kind":"arxiv","version":1}},"canonical_sha256":"905555f2a6fda15d4a8b711a5e7e7125b2776695d5c057c40bccf55ac6b163bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"905555f2a6fda15d4a8b711a5e7e7125b2776695d5c057c40bccf55ac6b163bc","first_computed_at":"2026-05-18T00:50:24.002833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:24.002833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2ILKo1moncQW/bWsrXKsgsAB7xjeMbBPkqkpflpTMrRn2S9K2NqMVS7qxqIU0oAflLkEX3x4OyTM3FtfjoLyAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:24.003556Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.2142","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a38a393f71ad4dcc4458bbe2dac998b494f90997ab5659fbbc510d1c03bf1d10","sha256:3653b36937d6d753d231c9cbefb7c16175937657fcd2f694335271fa535d5b80"],"state_sha256":"f6a72806d4e0344f66edc5d5d6c097688d9e248868388c8f87f72379b9a278ab"}