{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5752HDQSM64P3WDI27SPYEPV47","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":"c9dccdefb44da91c9605ad7f4378418243409352001ccbc6b97af779c3a15562","cross_cats_sorted":["math-ph","math.DG","math.MP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-20T14:00:34Z","title_canon_sha256":"e76db26d280bc5fcca262be71609b0c9c21e931b634396b4953993c6f0c05f53"},"schema_version":"1.0","source":{"id":"1105.4095","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4095","created_at":"2026-05-18T04:21:42Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4095v1","created_at":"2026-05-18T04:21:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4095","created_at":"2026-05-18T04:21:42Z"},{"alias_kind":"pith_short_12","alias_value":"5752HDQSM64P","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5752HDQSM64P3WDI","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5752HDQS","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:d2166efd1d4b3790a495961e815b832dc5a79a971fb84bf40765878459e9fd4e","target":"graph","created_at":"2026-05-18T04:21:42Z","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 present both, theory and an algorithm for solving time-harmonic wave problems in a general setting. The time-harmonic solutions will be achieved by computing time-periodic solutions of the original wave equations. Thus, an exact controllability technique is proposed to solve the time-dependent wave equations. We discuss a first order Maxwell type system, which will be formulated in the framework of alternating differential forms. This enables us to investigate different kinds of classical wave problems in one fell swoop, such as acoustic, electro-magnetic or elastic wave problems. After a s","authors_text":"Dirk Pauly, Tuomo Rossi","cross_cats":["math-ph","math.DG","math.MP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-20T14:00:34Z","title":"Theoretical Considerations on the Computation of Generalized Time-Periodic Waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4095","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:caf034b71f32b7a8ad5095bf3d157fc053e793cff97ec4ed57af0a547761b2bc","target":"record","created_at":"2026-05-18T04:21:42Z","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":"c9dccdefb44da91c9605ad7f4378418243409352001ccbc6b97af779c3a15562","cross_cats_sorted":["math-ph","math.DG","math.MP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-20T14:00:34Z","title_canon_sha256":"e76db26d280bc5fcca262be71609b0c9c21e931b634396b4953993c6f0c05f53"},"schema_version":"1.0","source":{"id":"1105.4095","kind":"arxiv","version":1}},"canonical_sha256":"effba38e1267b8fdd868d7e4fc11f5e7dbf42282848f841d8f71f69c0b7a5559","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"effba38e1267b8fdd868d7e4fc11f5e7dbf42282848f841d8f71f69c0b7a5559","first_computed_at":"2026-05-18T04:21:42.952350Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:42.952350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KKI+nXKN/SE7fMUzXLeS3euhoSHHKYA36b94UjnAglrNJltuXnClWOwo3ZAuDhthoNgV6ZdnBvKpe4dUmMnpAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:42.953430Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4095","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caf034b71f32b7a8ad5095bf3d157fc053e793cff97ec4ed57af0a547761b2bc","sha256:d2166efd1d4b3790a495961e815b832dc5a79a971fb84bf40765878459e9fd4e"],"state_sha256":"b8baedc63db4dab59ddb9ad69092030671cf3bb9f35a4b04f5bee156789f5325"}