{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:X6U4TOASRMF4LUZXRKLIYOJEVP","short_pith_number":"pith:X6U4TOAS","canonical_record":{"source":{"id":"1605.03276","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-11T04:39:28Z","cross_cats_sorted":[],"title_canon_sha256":"314247ff87fccb34d62f0f9ea6bd250c9aa70f3543b2b62e20c7e110f4cd877d","abstract_canon_sha256":"a3102649093bd30e8e27a052f34b4a7b5689a2781d3c4b311e944d15a8555e54"},"schema_version":"1.0"},"canonical_sha256":"bfa9c9b8128b0bc5d3378a968c3924abd446e65fea009f5ec8bc8956fb9b9ce7","source":{"kind":"arxiv","id":"1605.03276","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03276","created_at":"2026-05-18T01:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03276v1","created_at":"2026-05-18T01:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03276","created_at":"2026-05-18T01:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"X6U4TOASRMF4","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X6U4TOASRMF4LUZX","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X6U4TOAS","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:X6U4TOASRMF4LUZXRKLIYOJEVP","target":"record","payload":{"canonical_record":{"source":{"id":"1605.03276","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-11T04:39:28Z","cross_cats_sorted":[],"title_canon_sha256":"314247ff87fccb34d62f0f9ea6bd250c9aa70f3543b2b62e20c7e110f4cd877d","abstract_canon_sha256":"a3102649093bd30e8e27a052f34b4a7b5689a2781d3c4b311e944d15a8555e54"},"schema_version":"1.0"},"canonical_sha256":"bfa9c9b8128b0bc5d3378a968c3924abd446e65fea009f5ec8bc8956fb9b9ce7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:05.819778Z","signature_b64":"oLiNDEoJ7O/DcGl2TYGT2z5EaRkxECkdFl51+Rzo3Mci8/M0wYXncDs0sOgrKyI882bJJsVuR/Y9/lzR2uf8Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfa9c9b8128b0bc5d3378a968c3924abd446e65fea009f5ec8bc8956fb9b9ce7","last_reissued_at":"2026-05-18T01:15:05.819230Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:05.819230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.03276","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":"2026-05-18T01:15:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OI8PGPXFQiIWT2qzFK6EbJOEN8w76glIIstAyapEm4TtaoKqW4SfL6jJao0bl6bh0tx6rj/DpBMwRcCRXyG6CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T01:12:20.291400Z"},"content_sha256":"fb3ec358237d0bb71473505bb4ddd8e74ce630c95c9eb66f21a229d2ed2f67a7","schema_version":"1.0","event_id":"sha256:fb3ec358237d0bb71473505bb4ddd8e74ce630c95c9eb66f21a229d2ed2f67a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:X6U4TOASRMF4LUZXRKLIYOJEVP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inhomogeneous Jacobi matrices on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ryszard Szwarc","submitted_at":"2016-05-11T04:39:28Z","abstract_excerpt":"We study Jacobi matrices on trees with one end at inifinity. We show that the defect indices cannot be greater than 1 and give criteria for essential selfadjointness. We construct certain polynomials associated with matrices, which mimic orthogonal polynomials in the classical case. Nonnegativity of Jacobi matrices is studied as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03276","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":"2026-05-18T01:15:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F0aRejaxeZ2y5XZqIvStL83lYsUoXKCdnV5ZyqgYnHesWtYHRjWxzRs59lkhdiTuduzOppxGYvAXSypDiyAdAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T01:12:20.291751Z"},"content_sha256":"e54c7e3001cc454b65c22f6865da54008914f5ba69efb08ee9a076daad239e41","schema_version":"1.0","event_id":"sha256:e54c7e3001cc454b65c22f6865da54008914f5ba69efb08ee9a076daad239e41"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X6U4TOASRMF4LUZXRKLIYOJEVP/bundle.json","state_url":"https://pith.science/pith/X6U4TOASRMF4LUZXRKLIYOJEVP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X6U4TOASRMF4LUZXRKLIYOJEVP/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":"2026-06-04T01:12:20Z","links":{"resolver":"https://pith.science/pith/X6U4TOASRMF4LUZXRKLIYOJEVP","bundle":"https://pith.science/pith/X6U4TOASRMF4LUZXRKLIYOJEVP/bundle.json","state":"https://pith.science/pith/X6U4TOASRMF4LUZXRKLIYOJEVP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X6U4TOASRMF4LUZXRKLIYOJEVP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:X6U4TOASRMF4LUZXRKLIYOJEVP","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":"a3102649093bd30e8e27a052f34b4a7b5689a2781d3c4b311e944d15a8555e54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-11T04:39:28Z","title_canon_sha256":"314247ff87fccb34d62f0f9ea6bd250c9aa70f3543b2b62e20c7e110f4cd877d"},"schema_version":"1.0","source":{"id":"1605.03276","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03276","created_at":"2026-05-18T01:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03276v1","created_at":"2026-05-18T01:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03276","created_at":"2026-05-18T01:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"X6U4TOASRMF4","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X6U4TOASRMF4LUZX","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X6U4TOAS","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:e54c7e3001cc454b65c22f6865da54008914f5ba69efb08ee9a076daad239e41","target":"graph","created_at":"2026-05-18T01:15:05Z","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 study Jacobi matrices on trees with one end at inifinity. We show that the defect indices cannot be greater than 1 and give criteria for essential selfadjointness. We construct certain polynomials associated with matrices, which mimic orthogonal polynomials in the classical case. Nonnegativity of Jacobi matrices is studied as well.","authors_text":"Ryszard Szwarc","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-11T04:39:28Z","title":"Inhomogeneous Jacobi matrices on trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03276","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:fb3ec358237d0bb71473505bb4ddd8e74ce630c95c9eb66f21a229d2ed2f67a7","target":"record","created_at":"2026-05-18T01:15:05Z","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":"a3102649093bd30e8e27a052f34b4a7b5689a2781d3c4b311e944d15a8555e54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-11T04:39:28Z","title_canon_sha256":"314247ff87fccb34d62f0f9ea6bd250c9aa70f3543b2b62e20c7e110f4cd877d"},"schema_version":"1.0","source":{"id":"1605.03276","kind":"arxiv","version":1}},"canonical_sha256":"bfa9c9b8128b0bc5d3378a968c3924abd446e65fea009f5ec8bc8956fb9b9ce7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfa9c9b8128b0bc5d3378a968c3924abd446e65fea009f5ec8bc8956fb9b9ce7","first_computed_at":"2026-05-18T01:15:05.819230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:05.819230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oLiNDEoJ7O/DcGl2TYGT2z5EaRkxECkdFl51+Rzo3Mci8/M0wYXncDs0sOgrKyI882bJJsVuR/Y9/lzR2uf8Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:05.819778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.03276","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb3ec358237d0bb71473505bb4ddd8e74ce630c95c9eb66f21a229d2ed2f67a7","sha256:e54c7e3001cc454b65c22f6865da54008914f5ba69efb08ee9a076daad239e41"],"state_sha256":"1f784be9b2163be0f3d4566027f09a0bd2bc392943ef9dcf6331c798ee27f5d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I/bBJbDQSCulTEQVLL2zpOvPU7bJHjg+0bbuknNunVXe7Wq1H9zPW/UcdZxZA8c1d40B8bba4eqN2X3VKkBWBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T01:12:20.293695Z","bundle_sha256":"aae7f87b931e73d29fc82b561b6c58aa4ebc4b22f8d263c2f4a367b1f622faee"}}