{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:N5HITW4UOEVUA2Z6WSBEK3BBDG","short_pith_number":"pith:N5HITW4U","canonical_record":{"source":{"id":"1607.00105","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-01T03:58:37Z","cross_cats_sorted":[],"title_canon_sha256":"567aea95fb52924b4e8a9f66c680f905b5829bbb06a6dc184941641603480734","abstract_canon_sha256":"d2404720b39277c245281a60d00e00abe9870a85771ddf7143bec45464167d80"},"schema_version":"1.0"},"canonical_sha256":"6f4e89db94712b406b3eb482456c2119a6f0a94b75449d5e2ce19495078b1580","source":{"kind":"arxiv","id":"1607.00105","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00105","created_at":"2026-07-05T00:39:07Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00105v2","created_at":"2026-07-05T00:39:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00105","created_at":"2026-07-05T00:39:07Z"},{"alias_kind":"pith_short_12","alias_value":"N5HITW4UOEVU","created_at":"2026-07-05T00:39:07Z"},{"alias_kind":"pith_short_16","alias_value":"N5HITW4UOEVUA2Z6","created_at":"2026-07-05T00:39:07Z"},{"alias_kind":"pith_short_8","alias_value":"N5HITW4U","created_at":"2026-07-05T00:39:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:N5HITW4UOEVUA2Z6WSBEK3BBDG","target":"record","payload":{"canonical_record":{"source":{"id":"1607.00105","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-01T03:58:37Z","cross_cats_sorted":[],"title_canon_sha256":"567aea95fb52924b4e8a9f66c680f905b5829bbb06a6dc184941641603480734","abstract_canon_sha256":"d2404720b39277c245281a60d00e00abe9870a85771ddf7143bec45464167d80"},"schema_version":"1.0"},"canonical_sha256":"6f4e89db94712b406b3eb482456c2119a6f0a94b75449d5e2ce19495078b1580","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:39:07.162443Z","signature_b64":"Y36obL7sXdi6V1wmYSnXDrD0W2oxIKCMZu61Ag4XQc4NyhCwJltmIlmds5JrgocuNrj4gQCraI+j41hE6s7aAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f4e89db94712b406b3eb482456c2119a6f0a94b75449d5e2ce19495078b1580","last_reissued_at":"2026-07-05T00:39:07.161925Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:39:07.161925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.00105","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:39:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LKHNXJT5Ohnz7UtNIjlwKN9ngVmbneXrTpXjHeLFLQ2i3WRV96T8HAJUOngaZuhwLKpkAlGH1AeFeb/OpLMNAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T09:28:27.237435Z"},"content_sha256":"c5257dd4fe9a5bb31644fc0573d9a0984b4df7d4897708d573dd01746699f8c7","schema_version":"1.0","event_id":"sha256:c5257dd4fe9a5bb31644fc0573d9a0984b4df7d4897708d573dd01746699f8c7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:N5HITW4UOEVUA2Z6WSBEK3BBDG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Unified Analysis of Linear Quaternion Dynamic Equations on Time Scales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dong Cheng, Kit Ian Kou, Yong Hui Xia","submitted_at":"2016-07-01T03:58:37Z","abstract_excerpt":"Over the last years, considerable attention has been paid to the role of the quaternion differential equations (QDEs) which extend the ordinary differential equations. The theory of QDEs was recently well established and it has wide applications in physics and life science. This paper establishes a systematic frame work for the theory of linear quaternion dynamic equations on time scales (QDETS), which can be applied to wave phenomena modeling, fluid dynamics and filter design. The algebraic structure of the solutions to the QDETS is actually a left- or right- module, not a linear vector space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00105","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1607.00105/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:39:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tRfovEelSwICRUT3NSaB/QPXz29F4nwuVCzIq59VrUpsBmuD+bqElKZ/E9vLfnLevFZTJXTQWAwqOXCxgSi+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T09:28:27.237947Z"},"content_sha256":"727d8f62a473b8dd2466d992aaac13202e897d21dc887cb2ea4ef15c2babad82","schema_version":"1.0","event_id":"sha256:727d8f62a473b8dd2466d992aaac13202e897d21dc887cb2ea4ef15c2babad82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N5HITW4UOEVUA2Z6WSBEK3BBDG/bundle.json","state_url":"https://pith.science/pith/N5HITW4UOEVUA2Z6WSBEK3BBDG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N5HITW4UOEVUA2Z6WSBEK3BBDG/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":"2026-08-07T09:28:27Z","links":{"resolver":"https://pith.science/pith/N5HITW4UOEVUA2Z6WSBEK3BBDG","bundle":"https://pith.science/pith/N5HITW4UOEVUA2Z6WSBEK3BBDG/bundle.json","state":"https://pith.science/pith/N5HITW4UOEVUA2Z6WSBEK3BBDG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N5HITW4UOEVUA2Z6WSBEK3BBDG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:N5HITW4UOEVUA2Z6WSBEK3BBDG","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":"d2404720b39277c245281a60d00e00abe9870a85771ddf7143bec45464167d80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-01T03:58:37Z","title_canon_sha256":"567aea95fb52924b4e8a9f66c680f905b5829bbb06a6dc184941641603480734"},"schema_version":"1.0","source":{"id":"1607.00105","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00105","created_at":"2026-07-05T00:39:07Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00105v2","created_at":"2026-07-05T00:39:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00105","created_at":"2026-07-05T00:39:07Z"},{"alias_kind":"pith_short_12","alias_value":"N5HITW4UOEVU","created_at":"2026-07-05T00:39:07Z"},{"alias_kind":"pith_short_16","alias_value":"N5HITW4UOEVUA2Z6","created_at":"2026-07-05T00:39:07Z"},{"alias_kind":"pith_short_8","alias_value":"N5HITW4U","created_at":"2026-07-05T00:39:07Z"}],"graph_snapshots":[{"event_id":"sha256:727d8f62a473b8dd2466d992aaac13202e897d21dc887cb2ea4ef15c2babad82","target":"graph","created_at":"2026-07-05T00:39:07Z","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/1607.00105/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Over the last years, considerable attention has been paid to the role of the quaternion differential equations (QDEs) which extend the ordinary differential equations. The theory of QDEs was recently well established and it has wide applications in physics and life science. This paper establishes a systematic frame work for the theory of linear quaternion dynamic equations on time scales (QDETS), which can be applied to wave phenomena modeling, fluid dynamics and filter design. The algebraic structure of the solutions to the QDETS is actually a left- or right- module, not a linear vector space","authors_text":"Dong Cheng, Kit Ian Kou, Yong Hui Xia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-01T03:58:37Z","title":"A Unified Analysis of Linear Quaternion Dynamic Equations on Time Scales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00105","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:c5257dd4fe9a5bb31644fc0573d9a0984b4df7d4897708d573dd01746699f8c7","target":"record","created_at":"2026-07-05T00:39:07Z","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":"d2404720b39277c245281a60d00e00abe9870a85771ddf7143bec45464167d80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-01T03:58:37Z","title_canon_sha256":"567aea95fb52924b4e8a9f66c680f905b5829bbb06a6dc184941641603480734"},"schema_version":"1.0","source":{"id":"1607.00105","kind":"arxiv","version":2}},"canonical_sha256":"6f4e89db94712b406b3eb482456c2119a6f0a94b75449d5e2ce19495078b1580","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f4e89db94712b406b3eb482456c2119a6f0a94b75449d5e2ce19495078b1580","first_computed_at":"2026-07-05T00:39:07.161925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:39:07.161925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y36obL7sXdi6V1wmYSnXDrD0W2oxIKCMZu61Ag4XQc4NyhCwJltmIlmds5JrgocuNrj4gQCraI+j41hE6s7aAA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:39:07.162443Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.00105","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5257dd4fe9a5bb31644fc0573d9a0984b4df7d4897708d573dd01746699f8c7","sha256:727d8f62a473b8dd2466d992aaac13202e897d21dc887cb2ea4ef15c2babad82"],"state_sha256":"98d857aab365dcfff41d41174bdfb4692d6148d7e11fc8897f8f2976110af1e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Juum6aiR+XhRVOhyptDjMfX8jn7Br2PuTvrvYmFm8XpwMAGm5fMtRG0rYQGvRqn2Y+B0cnxoxkti/u6BNuiDBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T09:28:27.241635Z","bundle_sha256":"53a8bf783d3af11eaf190fd4df2b1ae96a476afac6fccdd3b5d2f98e660ae67a"}}