{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JGZCRYZQGP3NEF23SGAUWAOSZ3","short_pith_number":"pith:JGZCRYZQ","canonical_record":{"source":{"id":"1610.09203","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-28T13:26:20Z","cross_cats_sorted":[],"title_canon_sha256":"37fa7834981517aa7eb49d45407b251ba7cc5cf65ba3c9fd792dac568d3d1c33","abstract_canon_sha256":"9573ccec5611656caa5a916a471d41288d8b2896d8617cefff0bb1d98f9c6c76"},"schema_version":"1.0"},"canonical_sha256":"49b228e33033f6d2175b91814b01d2cec6a1a8ff8d67e32ddfeae89123903b55","source":{"kind":"arxiv","id":"1610.09203","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09203","created_at":"2026-05-18T01:00:58Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09203v1","created_at":"2026-05-18T01:00:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09203","created_at":"2026-05-18T01:00:58Z"},{"alias_kind":"pith_short_12","alias_value":"JGZCRYZQGP3N","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JGZCRYZQGP3NEF23","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JGZCRYZQ","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JGZCRYZQGP3NEF23SGAUWAOSZ3","target":"record","payload":{"canonical_record":{"source":{"id":"1610.09203","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-28T13:26:20Z","cross_cats_sorted":[],"title_canon_sha256":"37fa7834981517aa7eb49d45407b251ba7cc5cf65ba3c9fd792dac568d3d1c33","abstract_canon_sha256":"9573ccec5611656caa5a916a471d41288d8b2896d8617cefff0bb1d98f9c6c76"},"schema_version":"1.0"},"canonical_sha256":"49b228e33033f6d2175b91814b01d2cec6a1a8ff8d67e32ddfeae89123903b55","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:58.816741Z","signature_b64":"67LH1v1pr+3Kwsf7IFS5bhMN62Dz4VqAPe+xPDxpwyUHTBllRfRsCd5RCRHN9FCELXTwZaR2nrR0stIuBmlGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49b228e33033f6d2175b91814b01d2cec6a1a8ff8d67e32ddfeae89123903b55","last_reissued_at":"2026-05-18T01:00:58.816071Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:58.816071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.09203","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:00:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BXrLFm7B7IT3IUIOCTgcusgKWTSCVocbmT/XbensE4EM3rH9/y3IX7nixbHbkFAru1GTRRek1E2GCYfgFMehDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:28:42.383129Z"},"content_sha256":"d0be08d85229b7b03b5f84089f179c9b53a350a8402358fc4054748bbd39e0a9","schema_version":"1.0","event_id":"sha256:d0be08d85229b7b03b5f84089f179c9b53a350a8402358fc4054748bbd39e0a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JGZCRYZQGP3NEF23SGAUWAOSZ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A breather construction for a semilinear curl-curl wave equation with radially symmetric coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michael Plum, Wolfgang Reichel","submitted_at":"2016-10-28T13:26:20Z","abstract_excerpt":"We consider the semilinear curl-curl wave equation $s(x) \\partial_t^2 U +\\nabla\\times\\nabla\\times U + q(x) U \\pm V(x) |U|^{p-1} U = 0 \\mbox{ for } (x,t)\\in \\mathbb{R}^3\\times\\mathbb{R}$. For any $p>1$ we prove the existence of time-periodic spatially localized real-valued solutions (breathers) both for the $+$ and the $-$ case under slightly different hypotheses. Our solutions are classical solutions that are radially symmetric in space and decay exponentially to $0$ as $|x|\\to \\infty$. Our method is based on the fact that gradient fields of radially symmetric functions are annihilated by the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09203","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:00:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tD8z7bC+MdC7mqkUPZP0iVLYppirpvb51dPoifpVetXocy8NcSBQukuKDrUcn9sntG1eEFh1ptTjjWKzFtDFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:28:42.383804Z"},"content_sha256":"56da19342e4c42bd816fa7c2045dcae105d7816928cc1d61c81e213f947f543a","schema_version":"1.0","event_id":"sha256:56da19342e4c42bd816fa7c2045dcae105d7816928cc1d61c81e213f947f543a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JGZCRYZQGP3NEF23SGAUWAOSZ3/bundle.json","state_url":"https://pith.science/pith/JGZCRYZQGP3NEF23SGAUWAOSZ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JGZCRYZQGP3NEF23SGAUWAOSZ3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T20:28:42Z","links":{"resolver":"https://pith.science/pith/JGZCRYZQGP3NEF23SGAUWAOSZ3","bundle":"https://pith.science/pith/JGZCRYZQGP3NEF23SGAUWAOSZ3/bundle.json","state":"https://pith.science/pith/JGZCRYZQGP3NEF23SGAUWAOSZ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JGZCRYZQGP3NEF23SGAUWAOSZ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JGZCRYZQGP3NEF23SGAUWAOSZ3","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":"9573ccec5611656caa5a916a471d41288d8b2896d8617cefff0bb1d98f9c6c76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-28T13:26:20Z","title_canon_sha256":"37fa7834981517aa7eb49d45407b251ba7cc5cf65ba3c9fd792dac568d3d1c33"},"schema_version":"1.0","source":{"id":"1610.09203","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09203","created_at":"2026-05-18T01:00:58Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09203v1","created_at":"2026-05-18T01:00:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09203","created_at":"2026-05-18T01:00:58Z"},{"alias_kind":"pith_short_12","alias_value":"JGZCRYZQGP3N","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JGZCRYZQGP3NEF23","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JGZCRYZQ","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:56da19342e4c42bd816fa7c2045dcae105d7816928cc1d61c81e213f947f543a","target":"graph","created_at":"2026-05-18T01:00:58Z","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 consider the semilinear curl-curl wave equation $s(x) \\partial_t^2 U +\\nabla\\times\\nabla\\times U + q(x) U \\pm V(x) |U|^{p-1} U = 0 \\mbox{ for } (x,t)\\in \\mathbb{R}^3\\times\\mathbb{R}$. For any $p>1$ we prove the existence of time-periodic spatially localized real-valued solutions (breathers) both for the $+$ and the $-$ case under slightly different hypotheses. Our solutions are classical solutions that are radially symmetric in space and decay exponentially to $0$ as $|x|\\to \\infty$. Our method is based on the fact that gradient fields of radially symmetric functions are annihilated by the ","authors_text":"Michael Plum, Wolfgang Reichel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-28T13:26:20Z","title":"A breather construction for a semilinear curl-curl wave equation with radially symmetric coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09203","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:d0be08d85229b7b03b5f84089f179c9b53a350a8402358fc4054748bbd39e0a9","target":"record","created_at":"2026-05-18T01:00:58Z","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":"9573ccec5611656caa5a916a471d41288d8b2896d8617cefff0bb1d98f9c6c76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-28T13:26:20Z","title_canon_sha256":"37fa7834981517aa7eb49d45407b251ba7cc5cf65ba3c9fd792dac568d3d1c33"},"schema_version":"1.0","source":{"id":"1610.09203","kind":"arxiv","version":1}},"canonical_sha256":"49b228e33033f6d2175b91814b01d2cec6a1a8ff8d67e32ddfeae89123903b55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49b228e33033f6d2175b91814b01d2cec6a1a8ff8d67e32ddfeae89123903b55","first_computed_at":"2026-05-18T01:00:58.816071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:58.816071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"67LH1v1pr+3Kwsf7IFS5bhMN62Dz4VqAPe+xPDxpwyUHTBllRfRsCd5RCRHN9FCELXTwZaR2nrR0stIuBmlGBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:58.816741Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09203","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0be08d85229b7b03b5f84089f179c9b53a350a8402358fc4054748bbd39e0a9","sha256:56da19342e4c42bd816fa7c2045dcae105d7816928cc1d61c81e213f947f543a"],"state_sha256":"6a7374b0606be2ff1804042d36ae541a2db6747cce9ea61ec4a1d00c23996697"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R/DPPXwiBYnFCgrC0m+LOqaoyDrB9dg4KoJrvU6GoM9tKC038/koZnzne3CrlxjNu36BFt1XLPLzvA/YEcFCBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:28:42.387178Z","bundle_sha256":"23d27f8c48b5c9cf688af53d6f6eb24d103b0ea4d9d543b95720435ba29b65ad"}}