{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:PAZVLBK4Q5ZXZPMLGIVKUP26MJ","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":"a9861d26610438cfbb31e2953be2724612f120306a0e7a73f088557d2b6d24fe","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"1995-03-08T00:00:00Z","title_canon_sha256":"9f7bda4afe8c8b3bc18d3decefd6c92033d3b65651f6ef5f992c59ea980fac93"},"schema_version":"1.0","source":{"id":"math/9503223","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9503223","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/9503223v1","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9503223","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"pith_short_12","alias_value":"PAZVLBK4Q5ZX","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"PAZVLBK4Q5ZXZPML","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"PAZVLBK4","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:377d219a4b9e54f0e73b6993fe3c05c848988aa27d866812cbecebc1df68489a","target":"graph","created_at":"2026-05-18T01:05:50Z","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":"Nonoscillatory second order differential equations always admit ``special'', principal solutions. For a certain type of oscillatory equation principal pairs of solutions were introduced by \\'A. Elbert, F. Neuman and J. Vosmansk\\'y, {\\em Diff. Int. Equations} {\\bf 5} (1992), 945--960. In this paper, the notion of principal pair is extended to a wider class of oscillatory equations. Also an interesting property of some of the principal pairs is presented that makes the notion of these ``special'' pairs more understandable.","authors_text":"Franti\\v{s}ek Neuman, Martin E. Muldoon","cross_cats":[],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"1995-03-08T00:00:00Z","title":"Principal pairs for oscillatory second order linear differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9503223","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":"sha256:74ec6c893857518de5d8f6acbc06bd27aaf22412eda959024e86c88387a1a760","target":"record","created_at":"2026-05-18T01:05:50Z","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":"a9861d26610438cfbb31e2953be2724612f120306a0e7a73f088557d2b6d24fe","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"1995-03-08T00:00:00Z","title_canon_sha256":"9f7bda4afe8c8b3bc18d3decefd6c92033d3b65651f6ef5f992c59ea980fac93"},"schema_version":"1.0","source":{"id":"math/9503223","kind":"arxiv","version":1}},"canonical_sha256":"783355855c87737cbd8b322aaa3f5e6277322acbbdcc40e06d1f4b0dac94c0af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"783355855c87737cbd8b322aaa3f5e6277322acbbdcc40e06d1f4b0dac94c0af","first_computed_at":"2026-05-18T01:05:50.343016Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:50.343016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+V18D+s0uwG82PNFy1b0y4TQ9JcJTsVb33nH5yARu2VS8CjWrFlcSfAdBLGoXGGtfJ3muOoVbFlgxDpOOiauBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:50.343659Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9503223","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74ec6c893857518de5d8f6acbc06bd27aaf22412eda959024e86c88387a1a760","sha256:377d219a4b9e54f0e73b6993fe3c05c848988aa27d866812cbecebc1df68489a"],"state_sha256":"69fcfd45879e14c192b0a16421e5d82b5b0ddb7891687885d8b56b2dcfd2afce"}