{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:EH6TU6A742CENR53BIGQTC5CVH","short_pith_number":"pith:EH6TU6A7","canonical_record":{"source":{"id":"1208.3777","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-08-18T19:05:36Z","cross_cats_sorted":[],"title_canon_sha256":"bfacb31377d6aafafbdad563f4523081d8d3d8a4b7cc70f9dff0346191a9ee5c","abstract_canon_sha256":"00d52e525ea8f50d69eb20b405d744fd175b7dab20cefbf4ad8d29ec0a9acf2e"},"schema_version":"1.0"},"canonical_sha256":"21fd3a781fe68446c7bb0a0d098ba2a9d0da3efb59c1fdda3159f29ea4c6d7f1","source":{"kind":"arxiv","id":"1208.3777","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:EH6TU6A742CENR53BIGQTC5CVH","target":"record","payload":{"canonical_record":{"source":{"id":"1208.3777","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-08-18T19:05:36Z","cross_cats_sorted":[],"title_canon_sha256":"bfacb31377d6aafafbdad563f4523081d8d3d8a4b7cc70f9dff0346191a9ee5c","abstract_canon_sha256":"00d52e525ea8f50d69eb20b405d744fd175b7dab20cefbf4ad8d29ec0a9acf2e"},"schema_version":"1.0"},"canonical_sha256":"21fd3a781fe68446c7bb0a0d098ba2a9d0da3efb59c1fdda3159f29ea4c6d7f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:37.772195Z","signature_b64":"GURYh8LxxFtvIn7PEGN0bgf5XPI2vswSECh+mlrWkTUEGmHm8HwuxXC4rF2YDIpFGopsV1DuW+MFwkE/mDfHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21fd3a781fe68446c7bb0a0d098ba2a9d0da3efb59c1fdda3159f29ea4c6d7f1","last_reissued_at":"2026-05-17T23:41:37.771050Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:37.771050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.3777","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:41:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hBf038/GVmsLozHHtVKAxHwuWDHLtzM7cB1MvxdqZRsAMLgQspdozhu7a4vEbOno0THJzEfLKZkmZycykXDrDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:49:37.961920Z"},"content_sha256":"c1098ce8825c643452196e9a876ce3e93269f12a5add055e9efb66d3f7f180dd","schema_version":"1.0","event_id":"sha256:c1098ce8825c643452196e9a876ce3e93269f12a5add055e9efb66d3f7f180dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:EH6TU6A742CENR53BIGQTC5CVH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic expressions of eigenvalues and fundamental solutions of a discontinuous fourth-order boundary value problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Erdo\\u{g}an \\c{S}en, Mehmet Acikgoz, Serkan Araci","submitted_at":"2012-08-18T19:05:36Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3777","kind":"arxiv","version":3},"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":"2026-05-17T23:41:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TzAL7zDeaqNJw8//l/MeaBOOo+LUd6ZvQf6i2iE4gHXAikEyiWCvzfRHnv4vjW2OqvEtBysnxTE5d5405pTOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:49:37.962467Z"},"content_sha256":"10aeaa9aa9c850c260986e045e8819bd0ce73dfb42825784368b46b740a65c27","schema_version":"1.0","event_id":"sha256:10aeaa9aa9c850c260986e045e8819bd0ce73dfb42825784368b46b740a65c27"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EH6TU6A742CENR53BIGQTC5CVH/bundle.json","state_url":"https://pith.science/pith/EH6TU6A742CENR53BIGQTC5CVH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EH6TU6A742CENR53BIGQTC5CVH/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":"2026-06-02T19:49:37Z","links":{"resolver":"https://pith.science/pith/EH6TU6A742CENR53BIGQTC5CVH","bundle":"https://pith.science/pith/EH6TU6A742CENR53BIGQTC5CVH/bundle.json","state":"https://pith.science/pith/EH6TU6A742CENR53BIGQTC5CVH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EH6TU6A742CENR53BIGQTC5CVH/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RXh9pPDO1spy0g7WsUW/y3gEB+ieXf7Y87AFQQBPjzgF4kHfLRT7hBbcMsf27/dnq5NQaoG/SPfuC0O4vW5tBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:49:37.965051Z","bundle_sha256":"fa12d180d90857ed7626c94639c3f4a4194754e5a151f6947b2d00bf796a1cb1"}}