{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2ILAGGO6FLW4LBW3ZTO4JVPMBC","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":"c7c5e311f94401e55a7ede2fea02b43233aab1b30c63d625f0a16cdc34329e9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-08T16:52:07Z","title_canon_sha256":"5a2c2e744340001bb4779f17d553db8a090a542035fdcc64fd33c586a18cd6dc"},"schema_version":"1.0","source":{"id":"1010.1738","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1738","created_at":"2026-05-18T02:20:00Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1738v2","created_at":"2026-05-18T02:20:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1738","created_at":"2026-05-18T02:20:00Z"},{"alias_kind":"pith_short_12","alias_value":"2ILAGGO6FLW4","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2ILAGGO6FLW4LBW3","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2ILAGGO6","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:b892477bf914667cdfe2413f2545a2f3140bc0eac84d313f357775ee5756c531","target":"graph","created_at":"2026-05-18T02:20:00Z","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 study the propagation of time-harmonic acoustic or transverse magnetic (TM) polarized electromagnetic waves in a periodic waveguide lying in the semi-strip $(0,\\infty)\\times(0,L)$. It is shown that there exists a Riesz basis of the space of solutions to the time-harmonic wave equation such that the translation operator shifting a function by one periodicity length to the left is represented by an infinite Jordan matrix which contains at most a finite number of Jordan blocks of size $> 1$. Moreover, the Dirichlet-, Neumann- and mixed traces of this Riesz basis on the left boundary also form ","authors_text":"Sofiane Soussi, Thorsten Hohage","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-08T16:52:07Z","title":"Riesz bases and Jordan form of the translation operator in semi-infinite periodic waveguides"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1738","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:bab60e574be365c440ee75b497524a2a65d895dc657ab2c064fb9a9b9fa5f36f","target":"record","created_at":"2026-05-18T02:20:00Z","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":"c7c5e311f94401e55a7ede2fea02b43233aab1b30c63d625f0a16cdc34329e9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-08T16:52:07Z","title_canon_sha256":"5a2c2e744340001bb4779f17d553db8a090a542035fdcc64fd33c586a18cd6dc"},"schema_version":"1.0","source":{"id":"1010.1738","kind":"arxiv","version":2}},"canonical_sha256":"d2160319de2aedc586dbccddc4d5ec089bba635a824d4038e0d20ce5d7ebdfdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2160319de2aedc586dbccddc4d5ec089bba635a824d4038e0d20ce5d7ebdfdf","first_computed_at":"2026-05-18T02:20:00.754058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:00.754058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o3I/07YtunqlwXt9LycM8yxOxDykBbCZTg3nlp31PQ1qeNaPP4RMBMwdmfROt4g9QRSo2rT7GzslcuihLdK0Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:00.754763Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.1738","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bab60e574be365c440ee75b497524a2a65d895dc657ab2c064fb9a9b9fa5f36f","sha256:b892477bf914667cdfe2413f2545a2f3140bc0eac84d313f357775ee5756c531"],"state_sha256":"a160f0b2d15f38816f6b6e3b5b38fd1c411e621bd2a89dc234d9d5cd767078a3"}