{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3DIZDSKA4UIVEMJF2O2X34ZO5H","short_pith_number":"pith:3DIZDSKA","canonical_record":{"source":{"id":"1709.03193","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-10T22:53:19Z","cross_cats_sorted":[],"title_canon_sha256":"d7274adcfc290cdfc628275bdc9957837bd22d7f3e3b7b7a1e40e6ae323b485f","abstract_canon_sha256":"1f4da5949562751178e9cd80d532b65c07f9a18df39e1a499dee1a349a78f960"},"schema_version":"1.0"},"canonical_sha256":"d8d191c940e511523125d3b57df32ee9fc28c28454a6c5dae1737a9a92012c2d","source":{"kind":"arxiv","id":"1709.03193","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03193","created_at":"2026-05-18T00:30:30Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03193v2","created_at":"2026-05-18T00:30:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03193","created_at":"2026-05-18T00:30:30Z"},{"alias_kind":"pith_short_12","alias_value":"3DIZDSKA4UIV","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3DIZDSKA4UIVEMJF","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3DIZDSKA","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3DIZDSKA4UIVEMJF2O2X34ZO5H","target":"record","payload":{"canonical_record":{"source":{"id":"1709.03193","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-10T22:53:19Z","cross_cats_sorted":[],"title_canon_sha256":"d7274adcfc290cdfc628275bdc9957837bd22d7f3e3b7b7a1e40e6ae323b485f","abstract_canon_sha256":"1f4da5949562751178e9cd80d532b65c07f9a18df39e1a499dee1a349a78f960"},"schema_version":"1.0"},"canonical_sha256":"d8d191c940e511523125d3b57df32ee9fc28c28454a6c5dae1737a9a92012c2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:30.098645Z","signature_b64":"6poGGceW4kF97ihKKkbo4HZMpc7CQlk0yZjdiKSdTaNX1okDm++00snq5wgKauFhtxbgFcifq92xNbHmH6PtDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8d191c940e511523125d3b57df32ee9fc28c28454a6c5dae1737a9a92012c2d","last_reissued_at":"2026-05-18T00:30:30.097915Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:30.097915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.03193","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":"2026-05-18T00:30:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MgZxzCn4GvjN3+63200rz00vDExWP2kvzDXo0XjFBDAPew7RvSZjCPtaKNkHOlrMkEdFQxkH8MpONpYT1tlVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T17:00:57.771787Z"},"content_sha256":"ccd124f9e6b0deae684a6d181ebe7efe0d74e832dbd25bed988676a9064f4558","schema_version":"1.0","event_id":"sha256:ccd124f9e6b0deae684a6d181ebe7efe0d74e832dbd25bed988676a9064f4558"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3DIZDSKA4UIVEMJF2O2X34ZO5H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperbolicity and solvability for linear systems on time scales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sergey Kryzhevich","submitted_at":"2017-09-10T22:53:19Z","abstract_excerpt":"We believe that the difference between time scale systems and ordinary differential equations is not as big as people use to think. We consider linear operators that correspond to linear dynamic systems on time scales. We study solvability of these operators in ${\\mathbb L}^\\infty$. For ordinary differential equations such solvability is equivalent to hyperbolicity of the considered linear system. Using this approach and transformations of the time variable, we spread the concept of hyperbolicity to time scale dynamics. We provide some analogs of well-known facts of Hyperbolic Systems Theory, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03193","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":""},"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":"2026-05-18T00:30:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dAn3xxogpWH3jlkhgBPduOSEEZNpHbCfiaA5CE5c+anM8L9Fk4MoQMAMkgWZlD6QqEWsJNUEcyLh2KzckTkmBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T17:00:57.772126Z"},"content_sha256":"f49642b3e9c91d1129c2ce51dfc14671bd3f36bfb29c7e3ba9b97c7f70d20c48","schema_version":"1.0","event_id":"sha256:f49642b3e9c91d1129c2ce51dfc14671bd3f36bfb29c7e3ba9b97c7f70d20c48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3DIZDSKA4UIVEMJF2O2X34ZO5H/bundle.json","state_url":"https://pith.science/pith/3DIZDSKA4UIVEMJF2O2X34ZO5H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3DIZDSKA4UIVEMJF2O2X34ZO5H/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":"2026-07-03T17:00:57Z","links":{"resolver":"https://pith.science/pith/3DIZDSKA4UIVEMJF2O2X34ZO5H","bundle":"https://pith.science/pith/3DIZDSKA4UIVEMJF2O2X34ZO5H/bundle.json","state":"https://pith.science/pith/3DIZDSKA4UIVEMJF2O2X34ZO5H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3DIZDSKA4UIVEMJF2O2X34ZO5H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3DIZDSKA4UIVEMJF2O2X34ZO5H","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":"1f4da5949562751178e9cd80d532b65c07f9a18df39e1a499dee1a349a78f960","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-10T22:53:19Z","title_canon_sha256":"d7274adcfc290cdfc628275bdc9957837bd22d7f3e3b7b7a1e40e6ae323b485f"},"schema_version":"1.0","source":{"id":"1709.03193","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03193","created_at":"2026-05-18T00:30:30Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03193v2","created_at":"2026-05-18T00:30:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03193","created_at":"2026-05-18T00:30:30Z"},{"alias_kind":"pith_short_12","alias_value":"3DIZDSKA4UIV","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3DIZDSKA4UIVEMJF","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3DIZDSKA","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:f49642b3e9c91d1129c2ce51dfc14671bd3f36bfb29c7e3ba9b97c7f70d20c48","target":"graph","created_at":"2026-05-18T00:30:30Z","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 believe that the difference between time scale systems and ordinary differential equations is not as big as people use to think. We consider linear operators that correspond to linear dynamic systems on time scales. We study solvability of these operators in ${\\mathbb L}^\\infty$. For ordinary differential equations such solvability is equivalent to hyperbolicity of the considered linear system. Using this approach and transformations of the time variable, we spread the concept of hyperbolicity to time scale dynamics. We provide some analogs of well-known facts of Hyperbolic Systems Theory, ","authors_text":"Sergey Kryzhevich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-10T22:53:19Z","title":"Hyperbolicity and solvability for linear systems on time scales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03193","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:ccd124f9e6b0deae684a6d181ebe7efe0d74e832dbd25bed988676a9064f4558","target":"record","created_at":"2026-05-18T00:30:30Z","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":"1f4da5949562751178e9cd80d532b65c07f9a18df39e1a499dee1a349a78f960","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-10T22:53:19Z","title_canon_sha256":"d7274adcfc290cdfc628275bdc9957837bd22d7f3e3b7b7a1e40e6ae323b485f"},"schema_version":"1.0","source":{"id":"1709.03193","kind":"arxiv","version":2}},"canonical_sha256":"d8d191c940e511523125d3b57df32ee9fc28c28454a6c5dae1737a9a92012c2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8d191c940e511523125d3b57df32ee9fc28c28454a6c5dae1737a9a92012c2d","first_computed_at":"2026-05-18T00:30:30.097915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:30.097915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6poGGceW4kF97ihKKkbo4HZMpc7CQlk0yZjdiKSdTaNX1okDm++00snq5wgKauFhtxbgFcifq92xNbHmH6PtDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:30.098645Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.03193","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccd124f9e6b0deae684a6d181ebe7efe0d74e832dbd25bed988676a9064f4558","sha256:f49642b3e9c91d1129c2ce51dfc14671bd3f36bfb29c7e3ba9b97c7f70d20c48"],"state_sha256":"da45d4a161038395c023ce49520ff8d0f464bd46782bfc7717cce066e8826957"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MS2ro840esWOmxaKmnX5EJuI69UGs+f4xW+lpJxJjaImeeTohjzNAwNihV8XU/EZCcB+Jkw+V52NTVPIpoArAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T17:00:57.774016Z","bundle_sha256":"c216ee28c1291288f6e019c5b40fe5cc07fcb845f5cc01a1bad71a1c4f40362f"}}