{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:T7QMTCO46V5D2QMHD3RRJP6USK","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":"491dacc66553875185ffe9155fc4136456342efa323ef47c0706067de4e3791c","cross_cats_sorted":["math-ph","math.AP","math.MP","physics.plasm-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-25T16:51:02Z","title_canon_sha256":"d763e218c1c510abcd7431b73a5b128c480905c5501976291c6f0cd72687cf92"},"schema_version":"1.0","source":{"id":"1308.5425","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5425","created_at":"2026-05-18T03:15:04Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5425v1","created_at":"2026-05-18T03:15:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5425","created_at":"2026-05-18T03:15:04Z"},{"alias_kind":"pith_short_12","alias_value":"T7QMTCO46V5D","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T7QMTCO46V5D2QMH","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T7QMTCO4","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:f148798667bb9e88070b0215a160482c0a22c0597719aafd6ef73f07909e9522","target":"graph","created_at":"2026-05-18T03:15:04Z","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":"The Debye source representation for solutions to the time harmonic Maxwell equations is extended to bounded domains with finitely many smooth boundary components. A strong uniqueness result is proved for this representation. Natural complex structures are identified on the vector spaces of time-harmonic Maxwell fields. It is shown that in terms of Debye source data, these complex structures are uniformized, that is, represented by a fixed linear map on a fixed vector space, independent of the frequency. This complex structure relates time-harmonic Maxwell fields to constant-k Beltrami fields, ","authors_text":"Charles L. Epstein, Leslie Greengard, Michael O'Neil","cross_cats":["math-ph","math.AP","math.MP","physics.plasm-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-25T16:51:02Z","title":"Debye Sources, Beltrami Fields, and a Complex Structure on Maxwell Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5425","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:c8ccaf25c99d957c04f2aeca5a9bd4439ee4aaa51ea9c7f7f6db6c5536534042","target":"record","created_at":"2026-05-18T03:15:04Z","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":"491dacc66553875185ffe9155fc4136456342efa323ef47c0706067de4e3791c","cross_cats_sorted":["math-ph","math.AP","math.MP","physics.plasm-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-25T16:51:02Z","title_canon_sha256":"d763e218c1c510abcd7431b73a5b128c480905c5501976291c6f0cd72687cf92"},"schema_version":"1.0","source":{"id":"1308.5425","kind":"arxiv","version":1}},"canonical_sha256":"9fe0c989dcf57a3d41871ee314bfd492866a3b7d5c7a82212e8f9aaf107ed2e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fe0c989dcf57a3d41871ee314bfd492866a3b7d5c7a82212e8f9aaf107ed2e5","first_computed_at":"2026-05-18T03:15:04.693184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:04.693184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2VuNr/BJr9HuwxfaeOqIHXjRAYxPgXCUAWu68+SRxKQoJ04b3rsU975wgLoeldCOHzNioh5UoEpbDx+H2dWYBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:04.694062Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5425","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8ccaf25c99d957c04f2aeca5a9bd4439ee4aaa51ea9c7f7f6db6c5536534042","sha256:f148798667bb9e88070b0215a160482c0a22c0597719aafd6ef73f07909e9522"],"state_sha256":"b247584d1f6add9e2d8cacb909abd3794994f608a6a1896e5ec48584b3ae975c"}