{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PGRR7TXA2OVW77T7TEFZXJRS77","short_pith_number":"pith:PGRR7TXA","canonical_record":{"source":{"id":"1603.07542","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-24T12:11:58Z","cross_cats_sorted":[],"title_canon_sha256":"fcb3d955041a1634df3cdf357c2bcfadbea31cfccd7837661da6b95880ac485c","abstract_canon_sha256":"a8a4bef306f196e5c00046d4f7c5c25c0c20d891bfe79fb60f6212f92695b7d2"},"schema_version":"1.0"},"canonical_sha256":"79a31fcee0d3ab6ffe7f990b9ba632ffcb014fc88efed9021d99286f97f99512","source":{"kind":"arxiv","id":"1603.07542","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07542","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07542v1","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07542","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"pith_short_12","alias_value":"PGRR7TXA2OVW","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PGRR7TXA2OVW77T7","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PGRR7TXA","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PGRR7TXA2OVW77T7TEFZXJRS77","target":"record","payload":{"canonical_record":{"source":{"id":"1603.07542","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-24T12:11:58Z","cross_cats_sorted":[],"title_canon_sha256":"fcb3d955041a1634df3cdf357c2bcfadbea31cfccd7837661da6b95880ac485c","abstract_canon_sha256":"a8a4bef306f196e5c00046d4f7c5c25c0c20d891bfe79fb60f6212f92695b7d2"},"schema_version":"1.0"},"canonical_sha256":"79a31fcee0d3ab6ffe7f990b9ba632ffcb014fc88efed9021d99286f97f99512","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:20.591193Z","signature_b64":"E8rNJjX+sRPjrR0Avdi/AAXFfvBw8jVqSRovgkpYPViKAdJ9Jkh0UblDJ8bhHxYFOCrFu8fG9MoIVJvwaxDDDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79a31fcee0d3ab6ffe7f990b9ba632ffcb014fc88efed9021d99286f97f99512","last_reissued_at":"2026-05-18T01:18:20.590661Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:20.590661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.07542","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":"2026-05-18T01:18:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ax66JAnSTBn+kO1LQkJoQ/pjmD3RjEqKpiWD+ARW+O2tsMDCXqWYF1Y425Sw7S6YEAoGdmuyMJsRcWYMy1UAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T11:33:41.334611Z"},"content_sha256":"fb71bf5d099e32228d53218bef18214a5f9d2e0a63d6126b7d589d3ee66bc9b3","schema_version":"1.0","event_id":"sha256:fb71bf5d099e32228d53218bef18214a5f9d2e0a63d6126b7d589d3ee66bc9b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PGRR7TXA2OVW77T7TEFZXJRS77","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-adjoint boundary conditions for the prolate spheroid differential operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Victor Katsnelson","submitted_at":"2016-03-24T12:11:58Z","abstract_excerpt":"We consider the formal prolate spheroid differential operator on a finite symmetric interval and describe all its self-adjoint boundary conditions. Only one of these boundary conditions corresponds to a self-adjoint differential operator which commute with the Fourier operator truncated on the considered finite symmetric interval."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07542","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":"2026-05-18T01:18:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k4BFd8ErXFlU4UxcxwK5AJLWSi37dBaN1gIe/bOuxuUgKlo5/rFUI5UjhOxxSyFylwKvCjEVwCQEJnfra3PMCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T11:33:41.334958Z"},"content_sha256":"9aab2642c06a2edd7774cc9b0e7c5e0666544fab4648875ed9007765785dee51","schema_version":"1.0","event_id":"sha256:9aab2642c06a2edd7774cc9b0e7c5e0666544fab4648875ed9007765785dee51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PGRR7TXA2OVW77T7TEFZXJRS77/bundle.json","state_url":"https://pith.science/pith/PGRR7TXA2OVW77T7TEFZXJRS77/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PGRR7TXA2OVW77T7TEFZXJRS77/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":"2026-06-21T11:33:41Z","links":{"resolver":"https://pith.science/pith/PGRR7TXA2OVW77T7TEFZXJRS77","bundle":"https://pith.science/pith/PGRR7TXA2OVW77T7TEFZXJRS77/bundle.json","state":"https://pith.science/pith/PGRR7TXA2OVW77T7TEFZXJRS77/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PGRR7TXA2OVW77T7TEFZXJRS77/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PGRR7TXA2OVW77T7TEFZXJRS77","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":"a8a4bef306f196e5c00046d4f7c5c25c0c20d891bfe79fb60f6212f92695b7d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-24T12:11:58Z","title_canon_sha256":"fcb3d955041a1634df3cdf357c2bcfadbea31cfccd7837661da6b95880ac485c"},"schema_version":"1.0","source":{"id":"1603.07542","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07542","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07542v1","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07542","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"pith_short_12","alias_value":"PGRR7TXA2OVW","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PGRR7TXA2OVW77T7","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PGRR7TXA","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:9aab2642c06a2edd7774cc9b0e7c5e0666544fab4648875ed9007765785dee51","target":"graph","created_at":"2026-05-18T01:18:20Z","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 consider the formal prolate spheroid differential operator on a finite symmetric interval and describe all its self-adjoint boundary conditions. Only one of these boundary conditions corresponds to a self-adjoint differential operator which commute with the Fourier operator truncated on the considered finite symmetric interval.","authors_text":"Victor Katsnelson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-24T12:11:58Z","title":"Self-adjoint boundary conditions for the prolate spheroid differential operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07542","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:fb71bf5d099e32228d53218bef18214a5f9d2e0a63d6126b7d589d3ee66bc9b3","target":"record","created_at":"2026-05-18T01:18:20Z","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":"a8a4bef306f196e5c00046d4f7c5c25c0c20d891bfe79fb60f6212f92695b7d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-24T12:11:58Z","title_canon_sha256":"fcb3d955041a1634df3cdf357c2bcfadbea31cfccd7837661da6b95880ac485c"},"schema_version":"1.0","source":{"id":"1603.07542","kind":"arxiv","version":1}},"canonical_sha256":"79a31fcee0d3ab6ffe7f990b9ba632ffcb014fc88efed9021d99286f97f99512","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79a31fcee0d3ab6ffe7f990b9ba632ffcb014fc88efed9021d99286f97f99512","first_computed_at":"2026-05-18T01:18:20.590661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:20.590661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E8rNJjX+sRPjrR0Avdi/AAXFfvBw8jVqSRovgkpYPViKAdJ9Jkh0UblDJ8bhHxYFOCrFu8fG9MoIVJvwaxDDDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:20.591193Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07542","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb71bf5d099e32228d53218bef18214a5f9d2e0a63d6126b7d589d3ee66bc9b3","sha256:9aab2642c06a2edd7774cc9b0e7c5e0666544fab4648875ed9007765785dee51"],"state_sha256":"682a13aa82523923799842bba2493833148be431e46270728ee587aa1231370e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uxcgqw6K/F131wOwk9lghrhACQLjpN92kLkmaEsDdf1KFdOXpIwr9gY9h+wbCr+H1Epvff2Vgc5nle0jz5dxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T11:33:41.336982Z","bundle_sha256":"89a06826875e352cbeba3e84800a1036c1298e529780a42e7ec592a83e12313b"}}