{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:R4FLV7FZ7OQS7R6Y3FYXKM365G","short_pith_number":"pith:R4FLV7FZ","canonical_record":{"source":{"id":"1801.04977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-13T22:25:29Z","cross_cats_sorted":[],"title_canon_sha256":"35609f7c2a71d5edf8853455b7f60ad2a9649c93260c82853ee42ce7b26b6fa2","abstract_canon_sha256":"406868a60fbd099c18fbbb531676ae13bcebd09511c1f0de3f514c629a7eaa0e"},"schema_version":"1.0"},"canonical_sha256":"8f0abafcb9fba12fc7d8d97175337ee99929989b79e1e97200e192d9087ae18e","source":{"kind":"arxiv","id":"1801.04977","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04977","created_at":"2026-05-18T00:25:50Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04977v1","created_at":"2026-05-18T00:25:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04977","created_at":"2026-05-18T00:25:50Z"},{"alias_kind":"pith_short_12","alias_value":"R4FLV7FZ7OQS","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R4FLV7FZ7OQS7R6Y","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R4FLV7FZ","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:R4FLV7FZ7OQS7R6Y3FYXKM365G","target":"record","payload":{"canonical_record":{"source":{"id":"1801.04977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-13T22:25:29Z","cross_cats_sorted":[],"title_canon_sha256":"35609f7c2a71d5edf8853455b7f60ad2a9649c93260c82853ee42ce7b26b6fa2","abstract_canon_sha256":"406868a60fbd099c18fbbb531676ae13bcebd09511c1f0de3f514c629a7eaa0e"},"schema_version":"1.0"},"canonical_sha256":"8f0abafcb9fba12fc7d8d97175337ee99929989b79e1e97200e192d9087ae18e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:50.429004Z","signature_b64":"abSUeZGP0BhmUDu7qVRtJvlDQLhX+vYxWDD6XJ1x3I1/HVZ5RlLq4Hhm7bxVaYilm4PqqiBoSH0Lcz1s2lQUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f0abafcb9fba12fc7d8d97175337ee99929989b79e1e97200e192d9087ae18e","last_reissued_at":"2026-05-18T00:25:50.428449Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:50.428449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.04977","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:25:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QmetjLGj3vcRTiMeAQYsmfPqck45NVOBK0rgNT89bVg4y0bItlLsSt6jRt6HjVay8Gsiq5usp7aTbxQ97xsqDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:30:03.913912Z"},"content_sha256":"51b748304e9d571f57bf1f3421e9c80f27e80d498a84e2d478926b40e2aeab95","schema_version":"1.0","event_id":"sha256:51b748304e9d571f57bf1f3421e9c80f27e80d498a84e2d478926b40e2aeab95"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:R4FLV7FZ7OQS7R6Y3FYXKM365G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectra of Tridiagonal Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"D. K. Hammond, J. J. P. Veerman, Pablo E. Baldivieso","submitted_at":"2017-12-13T22:25:29Z","abstract_excerpt":"We characterize the eigenvalues and eigenvectors of a class of complex valued tridiagonal $n$ by $n$ matrices subject to arbitrary boundary conditions, i.e. with arbitrary elements on the first and last rows of the matrix. %By boundary conditions, we mean the first and last row of the matrix. For large $n$, we show there are up to $4$ eigenvalues, the so-called \\emph{special eigenvalues}, whose behavior depends sensitively on the boundary conditions. The other eigenvalues, the so-called \\emph{regular eigenvalues} vary very little as function of the boundary conditions. For large $n$, we determ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04977","kind":"arxiv","version":1},"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":"2026-05-18T00:25:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3s/erA88Hsgqkmm7bUEh4sUYISe5lKR1uYMaV8Q4LzM32wXqZgkMHGtixJGuSBdIxZt+dBMdAB88zBUJ+aa5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:30:03.914258Z"},"content_sha256":"cff72bf01ec112a07f84b7e7df9e1aa1863f48ca4368bb9120e4c320f810a7f4","schema_version":"1.0","event_id":"sha256:cff72bf01ec112a07f84b7e7df9e1aa1863f48ca4368bb9120e4c320f810a7f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R4FLV7FZ7OQS7R6Y3FYXKM365G/bundle.json","state_url":"https://pith.science/pith/R4FLV7FZ7OQS7R6Y3FYXKM365G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R4FLV7FZ7OQS7R6Y3FYXKM365G/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":"2026-06-25T12:30:03Z","links":{"resolver":"https://pith.science/pith/R4FLV7FZ7OQS7R6Y3FYXKM365G","bundle":"https://pith.science/pith/R4FLV7FZ7OQS7R6Y3FYXKM365G/bundle.json","state":"https://pith.science/pith/R4FLV7FZ7OQS7R6Y3FYXKM365G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R4FLV7FZ7OQS7R6Y3FYXKM365G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:R4FLV7FZ7OQS7R6Y3FYXKM365G","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":"406868a60fbd099c18fbbb531676ae13bcebd09511c1f0de3f514c629a7eaa0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-13T22:25:29Z","title_canon_sha256":"35609f7c2a71d5edf8853455b7f60ad2a9649c93260c82853ee42ce7b26b6fa2"},"schema_version":"1.0","source":{"id":"1801.04977","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04977","created_at":"2026-05-18T00:25:50Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04977v1","created_at":"2026-05-18T00:25:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04977","created_at":"2026-05-18T00:25:50Z"},{"alias_kind":"pith_short_12","alias_value":"R4FLV7FZ7OQS","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R4FLV7FZ7OQS7R6Y","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R4FLV7FZ","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:cff72bf01ec112a07f84b7e7df9e1aa1863f48ca4368bb9120e4c320f810a7f4","target":"graph","created_at":"2026-05-18T00:25:50Z","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":"We characterize the eigenvalues and eigenvectors of a class of complex valued tridiagonal $n$ by $n$ matrices subject to arbitrary boundary conditions, i.e. with arbitrary elements on the first and last rows of the matrix. %By boundary conditions, we mean the first and last row of the matrix. For large $n$, we show there are up to $4$ eigenvalues, the so-called \\emph{special eigenvalues}, whose behavior depends sensitively on the boundary conditions. The other eigenvalues, the so-called \\emph{regular eigenvalues} vary very little as function of the boundary conditions. For large $n$, we determ","authors_text":"D. K. Hammond, J. J. P. Veerman, Pablo E. Baldivieso","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-13T22:25:29Z","title":"Spectra of Tridiagonal Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04977","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":"sha256:51b748304e9d571f57bf1f3421e9c80f27e80d498a84e2d478926b40e2aeab95","target":"record","created_at":"2026-05-18T00:25:50Z","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":"406868a60fbd099c18fbbb531676ae13bcebd09511c1f0de3f514c629a7eaa0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-13T22:25:29Z","title_canon_sha256":"35609f7c2a71d5edf8853455b7f60ad2a9649c93260c82853ee42ce7b26b6fa2"},"schema_version":"1.0","source":{"id":"1801.04977","kind":"arxiv","version":1}},"canonical_sha256":"8f0abafcb9fba12fc7d8d97175337ee99929989b79e1e97200e192d9087ae18e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f0abafcb9fba12fc7d8d97175337ee99929989b79e1e97200e192d9087ae18e","first_computed_at":"2026-05-18T00:25:50.428449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:50.428449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"abSUeZGP0BhmUDu7qVRtJvlDQLhX+vYxWDD6XJ1x3I1/HVZ5RlLq4Hhm7bxVaYilm4PqqiBoSH0Lcz1s2lQUCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:50.429004Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.04977","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51b748304e9d571f57bf1f3421e9c80f27e80d498a84e2d478926b40e2aeab95","sha256:cff72bf01ec112a07f84b7e7df9e1aa1863f48ca4368bb9120e4c320f810a7f4"],"state_sha256":"4958a82b5df26979769cfde0a3e5f61922903bf213a29213f64f1fb9788bc347"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OBSeBAFkC4ClJh6uMh8h0BdCtgE5lZDVP2F6nR6JFdQTiHryuDrdaeXstulyilhdy05vdFVDVY5p3iWzLlhDDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T12:30:03.916270Z","bundle_sha256":"66aaad12d404abad7825df3dad4b41a1b4f1b38cdf2e352e04183bf933b9e7d5"}}