{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NLMYGXZIKBJ7S533IQW7FKDOJ2","short_pith_number":"pith:NLMYGXZI","canonical_record":{"source":{"id":"1607.00979","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-04T18:07:34Z","cross_cats_sorted":[],"title_canon_sha256":"ccfb34a69d4c95b046556a2c9296c9faffd89a014c49a12d5b49449f2b92641c","abstract_canon_sha256":"13b0fecaca3745fa5aca55f4d9b2a8f4e8484c9abdcc14f3d352239e01c33ff1"},"schema_version":"1.0"},"canonical_sha256":"6ad9835f285053f9777b442df2a86e4e875bacaddb73bd8c2a5cb57035ff35cd","source":{"kind":"arxiv","id":"1607.00979","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00979","created_at":"2026-05-18T00:32:51Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00979v1","created_at":"2026-05-18T00:32:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00979","created_at":"2026-05-18T00:32:51Z"},{"alias_kind":"pith_short_12","alias_value":"NLMYGXZIKBJ7","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NLMYGXZIKBJ7S533","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NLMYGXZI","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NLMYGXZIKBJ7S533IQW7FKDOJ2","target":"record","payload":{"canonical_record":{"source":{"id":"1607.00979","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-04T18:07:34Z","cross_cats_sorted":[],"title_canon_sha256":"ccfb34a69d4c95b046556a2c9296c9faffd89a014c49a12d5b49449f2b92641c","abstract_canon_sha256":"13b0fecaca3745fa5aca55f4d9b2a8f4e8484c9abdcc14f3d352239e01c33ff1"},"schema_version":"1.0"},"canonical_sha256":"6ad9835f285053f9777b442df2a86e4e875bacaddb73bd8c2a5cb57035ff35cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:51.229561Z","signature_b64":"pWWDGbJgsA3rABJ0FuPYU6yGrNuQIi6np55GlRxsKAnPpNHfdTzjlQ7gAifQnH+i6nIr6EcDJgcFwg3gxQuvBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ad9835f285053f9777b442df2a86e4e875bacaddb73bd8c2a5cb57035ff35cd","last_reissued_at":"2026-05-18T00:32:51.229025Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:51.229025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.00979","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":"2026-05-18T00:32:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kpbAS513FEd8Ia/5vWPRYqdsYRfy7PCMoy/vEg6eLRSHl3BfLwBenwZnT8y8cHamUIx080txhjcFLcTcvl1BBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:25:32.650045Z"},"content_sha256":"f6c81dcad018b63c5f0a42abe095222e0b3134b160bb24636d38e3412c3ca988","schema_version":"1.0","event_id":"sha256:f6c81dcad018b63c5f0a42abe095222e0b3134b160bb24636d38e3412c3ca988"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NLMYGXZIKBJ7S533IQW7FKDOJ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximal operators of exotic and non-exotic Laguerre and other semigroups associated with classical orthogonal expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Adam Nowak, Peter Sj\\\"ogren, Tomasz Z. Szarek","submitted_at":"2016-07-04T18:07:34Z","abstract_excerpt":"Classical settings of discrete and continuous orthogonal expansions, like Laguerre, Bessel and Jacobi, are associated with second order differential operators playing the role of the Laplacian. These depend on certain parameters of type that are usually restricted to a half-line, or a product of half-lines if higher dimensions are considered. Following earlier research done by Hajmirzaahmad, we deal in this paper with Laplacians in the above-mentioned contexts with no restrictions on the type parameters and bring to attention naturally associated orthogonal systems that in fact involve the cla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00979","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":"2026-05-18T00:32:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WqASDAtlmaH1+j5ph8UFlU/UcYdqVQq4PL0w/dj4hSOSqgAZNC94NF7aE7lG6us6UNS9U5Oxd1onnrbSnzuJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:25:32.650501Z"},"content_sha256":"4b0263ed1460f9aa6dd036534101864de0175b5632243490144d94796dd2aa4f","schema_version":"1.0","event_id":"sha256:4b0263ed1460f9aa6dd036534101864de0175b5632243490144d94796dd2aa4f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NLMYGXZIKBJ7S533IQW7FKDOJ2/bundle.json","state_url":"https://pith.science/pith/NLMYGXZIKBJ7S533IQW7FKDOJ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NLMYGXZIKBJ7S533IQW7FKDOJ2/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":"2026-06-01T22:25:32Z","links":{"resolver":"https://pith.science/pith/NLMYGXZIKBJ7S533IQW7FKDOJ2","bundle":"https://pith.science/pith/NLMYGXZIKBJ7S533IQW7FKDOJ2/bundle.json","state":"https://pith.science/pith/NLMYGXZIKBJ7S533IQW7FKDOJ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NLMYGXZIKBJ7S533IQW7FKDOJ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NLMYGXZIKBJ7S533IQW7FKDOJ2","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":"13b0fecaca3745fa5aca55f4d9b2a8f4e8484c9abdcc14f3d352239e01c33ff1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-04T18:07:34Z","title_canon_sha256":"ccfb34a69d4c95b046556a2c9296c9faffd89a014c49a12d5b49449f2b92641c"},"schema_version":"1.0","source":{"id":"1607.00979","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00979","created_at":"2026-05-18T00:32:51Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00979v1","created_at":"2026-05-18T00:32:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00979","created_at":"2026-05-18T00:32:51Z"},{"alias_kind":"pith_short_12","alias_value":"NLMYGXZIKBJ7","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NLMYGXZIKBJ7S533","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NLMYGXZI","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:4b0263ed1460f9aa6dd036534101864de0175b5632243490144d94796dd2aa4f","target":"graph","created_at":"2026-05-18T00:32:51Z","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":"Classical settings of discrete and continuous orthogonal expansions, like Laguerre, Bessel and Jacobi, are associated with second order differential operators playing the role of the Laplacian. These depend on certain parameters of type that are usually restricted to a half-line, or a product of half-lines if higher dimensions are considered. Following earlier research done by Hajmirzaahmad, we deal in this paper with Laplacians in the above-mentioned contexts with no restrictions on the type parameters and bring to attention naturally associated orthogonal systems that in fact involve the cla","authors_text":"Adam Nowak, Peter Sj\\\"ogren, Tomasz Z. Szarek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-04T18:07:34Z","title":"Maximal operators of exotic and non-exotic Laguerre and other semigroups associated with classical orthogonal expansions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00979","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:f6c81dcad018b63c5f0a42abe095222e0b3134b160bb24636d38e3412c3ca988","target":"record","created_at":"2026-05-18T00:32:51Z","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":"13b0fecaca3745fa5aca55f4d9b2a8f4e8484c9abdcc14f3d352239e01c33ff1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-04T18:07:34Z","title_canon_sha256":"ccfb34a69d4c95b046556a2c9296c9faffd89a014c49a12d5b49449f2b92641c"},"schema_version":"1.0","source":{"id":"1607.00979","kind":"arxiv","version":1}},"canonical_sha256":"6ad9835f285053f9777b442df2a86e4e875bacaddb73bd8c2a5cb57035ff35cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ad9835f285053f9777b442df2a86e4e875bacaddb73bd8c2a5cb57035ff35cd","first_computed_at":"2026-05-18T00:32:51.229025Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:51.229025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pWWDGbJgsA3rABJ0FuPYU6yGrNuQIi6np55GlRxsKAnPpNHfdTzjlQ7gAifQnH+i6nIr6EcDJgcFwg3gxQuvBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:51.229561Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.00979","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6c81dcad018b63c5f0a42abe095222e0b3134b160bb24636d38e3412c3ca988","sha256:4b0263ed1460f9aa6dd036534101864de0175b5632243490144d94796dd2aa4f"],"state_sha256":"aa1502f92c6cea431ef144b385702cf145c6118cb839861e375546f4e82b73d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tAlv+YxJJ2Anu3m8pRvZuiUoFkkkdp0L+CoGIc3WNa/OTz4I/NHoQ6gH8dWqhoGk13UfM3l9RSJq7Edi4Dc0DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T22:25:32.652336Z","bundle_sha256":"b7266da05ced5ddabfb1c2a2bd2dc23ce840c3f3c9e33f3a2621398baacd82a1"}}