{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EH6TU6A742CENR53BIGQTC5CVH","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":"00d52e525ea8f50d69eb20b405d744fd175b7dab20cefbf4ad8d29ec0a9acf2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-08-18T19:05:36Z","title_canon_sha256":"bfacb31377d6aafafbdad563f4523081d8d3d8a4b7cc70f9dff0346191a9ee5c"},"schema_version":"1.0","source":{"id":"1208.3777","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3777","created_at":"2026-05-17T23:41:37Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3777v3","created_at":"2026-05-17T23:41:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3777","created_at":"2026-05-17T23:41:37Z"},{"alias_kind":"pith_short_12","alias_value":"EH6TU6A742CE","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EH6TU6A742CENR53","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EH6TU6A7","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:10aeaa9aa9c850c260986e045e8819bd0ce73dfb42825784368b46b740a65c27","target":"graph","created_at":"2026-05-17T23:41:37Z","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, we deal with a fourth-order boundary value problem problem with eigenparameter dependent boundary conditions and transmission conditions at a interior point. A self-adjoint linear operator A is defined in a suitable Hilbert space H such that the eigenvalues of such a problem coincide with those of A. Following Mukhtarov and his students methods [2,4,6] we obtain asymptotic formulae for its eigenvalues and fundamental solutions. Our applications possess a number of interesting properties for studying in boundary value problems which we state in this paper.","authors_text":"Erdo\\u{g}an \\c{S}en, Mehmet Acikgoz, Serkan Araci","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-08-18T19:05:36Z","title":"Asymptotic expressions of eigenvalues and fundamental solutions of a discontinuous fourth-order boundary value problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3777","kind":"arxiv","version":3},"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:c1098ce8825c643452196e9a876ce3e93269f12a5add055e9efb66d3f7f180dd","target":"record","created_at":"2026-05-17T23:41:37Z","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":"00d52e525ea8f50d69eb20b405d744fd175b7dab20cefbf4ad8d29ec0a9acf2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-08-18T19:05:36Z","title_canon_sha256":"bfacb31377d6aafafbdad563f4523081d8d3d8a4b7cc70f9dff0346191a9ee5c"},"schema_version":"1.0","source":{"id":"1208.3777","kind":"arxiv","version":3}},"canonical_sha256":"21fd3a781fe68446c7bb0a0d098ba2a9d0da3efb59c1fdda3159f29ea4c6d7f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21fd3a781fe68446c7bb0a0d098ba2a9d0da3efb59c1fdda3159f29ea4c6d7f1","first_computed_at":"2026-05-17T23:41:37.771050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:37.771050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GURYh8LxxFtvIn7PEGN0bgf5XPI2vswSECh+mlrWkTUEGmHm8HwuxXC4rF2YDIpFGopsV1DuW+MFwkE/mDfHCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:37.772195Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.3777","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1098ce8825c643452196e9a876ce3e93269f12a5add055e9efb66d3f7f180dd","sha256:10aeaa9aa9c850c260986e045e8819bd0ce73dfb42825784368b46b740a65c27"],"state_sha256":"9ab27b168a9b2aa9d74e4884e77cc8ed64ecb9eecbca665e917fba1ac9ae2874"}