{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RAWYVAWZ72NSCCWHME2BQORCXU","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":"97830e5391ab52075c1ccd0c67c4f2d64c62b07f9934b9960c10adb24297e337","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-03-14T16:04:24Z","title_canon_sha256":"dc0cbcee29cbd871c3a2dfad7176e186bdd5b0a6f61eb4a808f446756d05955d"},"schema_version":"1.0","source":{"id":"2503.11539","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.11539","created_at":"2026-07-05T10:31:33Z"},{"alias_kind":"arxiv_version","alias_value":"2503.11539v1","created_at":"2026-07-05T10:31:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.11539","created_at":"2026-07-05T10:31:33Z"},{"alias_kind":"pith_short_12","alias_value":"RAWYVAWZ72NS","created_at":"2026-07-05T10:31:33Z"},{"alias_kind":"pith_short_16","alias_value":"RAWYVAWZ72NSCCWH","created_at":"2026-07-05T10:31:33Z"},{"alias_kind":"pith_short_8","alias_value":"RAWYVAWZ","created_at":"2026-07-05T10:31:33Z"}],"graph_snapshots":[{"event_id":"sha256:ab11696a3fd410bf7c17d356dd1d77de03e8f57f74e277a59bc65b479cf18c12","target":"graph","created_at":"2026-07-05T10:31:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2503.11539/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For Maxwell's equations with nonlinear polarization we prove the existence of time-periodic breather solutions travelling along slab or cylindrical waveguides. The solutions are TE-modes which are localized in space directions orthogonal to the direction of propagation. We assume a magnetically inactive and electrically nonlinear material law with a linear $\\chi^{(1)}$- and a cubic $\\chi^{(3)}$-contribution to the polarization. The $\\chi^{(1)}$-contribution may be retarded in time or instantaneous whereas the $\\chi^{(3)}$-contribution is always assumed to be retarded in time. We consider two d","authors_text":"Sebastian Ohrem, Wolfgang Reichel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-03-14T16:04:24Z","title":"Travelling breather solutions in waveguides for cubic nonlinear Maxwell equations with retarded material laws"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.11539","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:ea1b29070c54ef777e9c52249f50758f8b357e5de728b0c9f382312672ca33dc","target":"record","created_at":"2026-07-05T10:31:33Z","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":"97830e5391ab52075c1ccd0c67c4f2d64c62b07f9934b9960c10adb24297e337","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-03-14T16:04:24Z","title_canon_sha256":"dc0cbcee29cbd871c3a2dfad7176e186bdd5b0a6f61eb4a808f446756d05955d"},"schema_version":"1.0","source":{"id":"2503.11539","kind":"arxiv","version":1}},"canonical_sha256":"882d8a82d9fe9b210ac76134183a22bd3cb5e5613356a0092135cbf679de1ebe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"882d8a82d9fe9b210ac76134183a22bd3cb5e5613356a0092135cbf679de1ebe","first_computed_at":"2026-07-05T10:31:33.914069Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:31:33.914069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FWCAVd2juxqSTuRA1xqAAMEQCH7Q+RrkKo9xdbc5Q2ovjEZiy4ZyjKmGB6vAt92+LFC6BpEN44xyHEmHQGThAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:31:33.914585Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.11539","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea1b29070c54ef777e9c52249f50758f8b357e5de728b0c9f382312672ca33dc","sha256:ab11696a3fd410bf7c17d356dd1d77de03e8f57f74e277a59bc65b479cf18c12"],"state_sha256":"dfe4e4b9074b6fb1b0d001190170989ea9973fb158b2f8ac286b9452c4b44d44"}