{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:LAX4UVOA7KFR4D3TBOG6TMVCKA","short_pith_number":"pith:LAX4UVOA","canonical_record":{"source":{"id":"1802.08133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-02-16T03:11:05Z","cross_cats_sorted":[],"title_canon_sha256":"a7f5d85e6bd06859257390993ae78d47033fcd1caa7ef4dfaa6efddef55c7613","abstract_canon_sha256":"6c5403cb04d25ccf8b9023040b3ef28bd107273ee47dfa840d70c3c1521e6dea"},"schema_version":"1.0"},"canonical_sha256":"582fca55c0fa8b1e0f730b8de9b2a25037494515ed700825192173c6cadd7b78","source":{"kind":"arxiv","id":"1802.08133","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.08133","created_at":"2026-05-18T00:22:45Z"},{"alias_kind":"arxiv_version","alias_value":"1802.08133v1","created_at":"2026-05-18T00:22:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08133","created_at":"2026-05-18T00:22:45Z"},{"alias_kind":"pith_short_12","alias_value":"LAX4UVOA7KFR","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"LAX4UVOA7KFR4D3T","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"LAX4UVOA","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:LAX4UVOA7KFR4D3TBOG6TMVCKA","target":"record","payload":{"canonical_record":{"source":{"id":"1802.08133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-02-16T03:11:05Z","cross_cats_sorted":[],"title_canon_sha256":"a7f5d85e6bd06859257390993ae78d47033fcd1caa7ef4dfaa6efddef55c7613","abstract_canon_sha256":"6c5403cb04d25ccf8b9023040b3ef28bd107273ee47dfa840d70c3c1521e6dea"},"schema_version":"1.0"},"canonical_sha256":"582fca55c0fa8b1e0f730b8de9b2a25037494515ed700825192173c6cadd7b78","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:45.456618Z","signature_b64":"FFUXPJH2eL2pdzDrqb+JQXiV6Y96y3E2FKTP9ujR8F4wer50en2gHRg7NkonpvZVOljO9jHspy7/RtJUKmxrAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"582fca55c0fa8b1e0f730b8de9b2a25037494515ed700825192173c6cadd7b78","last_reissued_at":"2026-05-18T00:22:45.455922Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:45.455922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.08133","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":"2026-05-18T00:22:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NnMGAEZOSylPDF89RSRdlANoYtFakLrucTRNqgEtft13ResYqB0E4jxotdpkTI5WJ53+zZ1FSYWUNyPFTqPFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:47:18.875354Z"},"content_sha256":"16a190bf7a2ee270c1dc0a4db5d25817ae270bab3f8b142a5e2da723e9c46821","schema_version":"1.0","event_id":"sha256:16a190bf7a2ee270c1dc0a4db5d25817ae270bab3f8b142a5e2da723e9c46821"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:LAX4UVOA7KFR4D3TBOG6TMVCKA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reducibility for wave equations of finitely smooth potential with periodic boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bing Xie, Jing Li, Yingte Sun","submitted_at":"2018-02-16T03:11:05Z","abstract_excerpt":"In the present paper, the reducibility is derived for the wave equations with finitely smooth and time-quasi-periodic potential subjects to periodic boundary conditions. More exactly, the linear wave equation $u_{tt}-u_{xx}+Mu+\\varepsilon (V_0(\\omega t)u_{xx}+V(\\omega t, x)u)=0,\\;x\\in \\mathbb{R}/2\\pi \\mathbb{Z}$ can be reduced to a linear Hamiltonian system of a constant coefficient operator which is of pure imaginary point spectrum set, where $V$ is finitely smooth in $(t, x)$, quasi-periodic in time $t$ with Diophantine frequency $\\omega\\in \\mathbb{R}^{n},$ and $V_0$ is finitely smooth and q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08133","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":"2026-05-18T00:22:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AtfXzOt5BfxhsMUU5EoRr8rTDHDTRivxdJfO9IIC59jRQni35OA0D1hyFtczVFiRDtrPvAs6nuvd0SyDriLpBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:47:18.875731Z"},"content_sha256":"7a07f9d3750067e341f6a1eb85593b117c5c53cba98a1ad7586b12d9e9962109","schema_version":"1.0","event_id":"sha256:7a07f9d3750067e341f6a1eb85593b117c5c53cba98a1ad7586b12d9e9962109"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LAX4UVOA7KFR4D3TBOG6TMVCKA/bundle.json","state_url":"https://pith.science/pith/LAX4UVOA7KFR4D3TBOG6TMVCKA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LAX4UVOA7KFR4D3TBOG6TMVCKA/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":"2026-05-28T13:47:18Z","links":{"resolver":"https://pith.science/pith/LAX4UVOA7KFR4D3TBOG6TMVCKA","bundle":"https://pith.science/pith/LAX4UVOA7KFR4D3TBOG6TMVCKA/bundle.json","state":"https://pith.science/pith/LAX4UVOA7KFR4D3TBOG6TMVCKA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LAX4UVOA7KFR4D3TBOG6TMVCKA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LAX4UVOA7KFR4D3TBOG6TMVCKA","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":"6c5403cb04d25ccf8b9023040b3ef28bd107273ee47dfa840d70c3c1521e6dea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-02-16T03:11:05Z","title_canon_sha256":"a7f5d85e6bd06859257390993ae78d47033fcd1caa7ef4dfaa6efddef55c7613"},"schema_version":"1.0","source":{"id":"1802.08133","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.08133","created_at":"2026-05-18T00:22:45Z"},{"alias_kind":"arxiv_version","alias_value":"1802.08133v1","created_at":"2026-05-18T00:22:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08133","created_at":"2026-05-18T00:22:45Z"},{"alias_kind":"pith_short_12","alias_value":"LAX4UVOA7KFR","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"LAX4UVOA7KFR4D3T","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"LAX4UVOA","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:7a07f9d3750067e341f6a1eb85593b117c5c53cba98a1ad7586b12d9e9962109","target":"graph","created_at":"2026-05-18T00:22:45Z","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":"In the present paper, the reducibility is derived for the wave equations with finitely smooth and time-quasi-periodic potential subjects to periodic boundary conditions. More exactly, the linear wave equation $u_{tt}-u_{xx}+Mu+\\varepsilon (V_0(\\omega t)u_{xx}+V(\\omega t, x)u)=0,\\;x\\in \\mathbb{R}/2\\pi \\mathbb{Z}$ can be reduced to a linear Hamiltonian system of a constant coefficient operator which is of pure imaginary point spectrum set, where $V$ is finitely smooth in $(t, x)$, quasi-periodic in time $t$ with Diophantine frequency $\\omega\\in \\mathbb{R}^{n},$ and $V_0$ is finitely smooth and q","authors_text":"Bing Xie, Jing Li, Yingte Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-02-16T03:11:05Z","title":"Reducibility for wave equations of finitely smooth potential with periodic boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08133","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":"sha256:16a190bf7a2ee270c1dc0a4db5d25817ae270bab3f8b142a5e2da723e9c46821","target":"record","created_at":"2026-05-18T00:22:45Z","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":"6c5403cb04d25ccf8b9023040b3ef28bd107273ee47dfa840d70c3c1521e6dea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-02-16T03:11:05Z","title_canon_sha256":"a7f5d85e6bd06859257390993ae78d47033fcd1caa7ef4dfaa6efddef55c7613"},"schema_version":"1.0","source":{"id":"1802.08133","kind":"arxiv","version":1}},"canonical_sha256":"582fca55c0fa8b1e0f730b8de9b2a25037494515ed700825192173c6cadd7b78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"582fca55c0fa8b1e0f730b8de9b2a25037494515ed700825192173c6cadd7b78","first_computed_at":"2026-05-18T00:22:45.455922Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:45.455922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FFUXPJH2eL2pdzDrqb+JQXiV6Y96y3E2FKTP9ujR8F4wer50en2gHRg7NkonpvZVOljO9jHspy7/RtJUKmxrAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:45.456618Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.08133","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16a190bf7a2ee270c1dc0a4db5d25817ae270bab3f8b142a5e2da723e9c46821","sha256:7a07f9d3750067e341f6a1eb85593b117c5c53cba98a1ad7586b12d9e9962109"],"state_sha256":"4d83c3a587e844f46aefc4b18d8d4ca4e360f7cf4d74b95ce3f66baa1cb95347"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uYMSLJORIvDvL1XCYrJVG2zzr7yZWGZbso/6lADxxDVk0T4UedArQ9vDOSx/PszXgJmlodAIiutlDBqTt2W+Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:47:18.877732Z","bundle_sha256":"1efb0bb2576c86a5ebe8ba997a031e0c6a666910f93e6c82c859f283c70623b8"}}