{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DS6BODWLS6J4L7YDSIHHK63ROZ","short_pith_number":"pith:DS6BODWL","canonical_record":{"source":{"id":"1601.08178","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-29T16:20:34Z","cross_cats_sorted":[],"title_canon_sha256":"a9ab56b613b5beffe4bc084fb587b02e49b8484ffa2eaa15587498d88d9e249b","abstract_canon_sha256":"e111d1a1ccd06e35326f369a8a28eb20689baabecdf59c025da77de5de4a5e69"},"schema_version":"1.0"},"canonical_sha256":"1cbc170ecb9793c5ff03920e757b71765cb8bfdd16e5c1e6ff1836334aa57a6f","source":{"kind":"arxiv","id":"1601.08178","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.08178","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"arxiv_version","alias_value":"1601.08178v1","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.08178","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"pith_short_12","alias_value":"DS6BODWLS6J4","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DS6BODWLS6J4L7YD","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DS6BODWL","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DS6BODWLS6J4L7YDSIHHK63ROZ","target":"record","payload":{"canonical_record":{"source":{"id":"1601.08178","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-29T16:20:34Z","cross_cats_sorted":[],"title_canon_sha256":"a9ab56b613b5beffe4bc084fb587b02e49b8484ffa2eaa15587498d88d9e249b","abstract_canon_sha256":"e111d1a1ccd06e35326f369a8a28eb20689baabecdf59c025da77de5de4a5e69"},"schema_version":"1.0"},"canonical_sha256":"1cbc170ecb9793c5ff03920e757b71765cb8bfdd16e5c1e6ff1836334aa57a6f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:40.151302Z","signature_b64":"YiXEfi+ohj1YOpDE45yIP5rdFIJvlR+hyGw0fHUoRzLMtcDCyU+HApfW+KFu9Rvfni1yj35FlHLER/UfsiOpCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cbc170ecb9793c5ff03920e757b71765cb8bfdd16e5c1e6ff1836334aa57a6f","last_reissued_at":"2026-05-18T01:21:40.150831Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:40.150831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.08178","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":"2026-05-18T01:21:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I72q3HxClsiNynE9BoreAGeVkkaPclLIdYWhaTSndW/riLM1Ot10ZpyPlvCXKIlQvrQKaT+yCx8KNFEZG5knCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:17:40.112125Z"},"content_sha256":"647ca73b4d3a56bd1825778fa12d4d45cec1e5d796c7c81a7f98a604a5c1aa5d","schema_version":"1.0","event_id":"sha256:647ca73b4d3a56bd1825778fa12d4d45cec1e5d796c7c81a7f98a604a5c1aa5d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DS6BODWLS6J4L7YDSIHHK63ROZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The orthogonality of Al-Salam-Carlitz polynomials for complex parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"H. S. Cohl, R. S. Costas-Santos, W. Xu","submitted_at":"2016-01-29T16:20:34Z","abstract_excerpt":"In this contribution, we study the orthogonality conditions satisfied by Al-Salam-Carlitz polynomials $U^{(a)}_n(x;q)$ when the parameters $a$ and $q$ are not necessarily real nor `classical', i.e., the linear functional $\\bf u$ with respect to such polynomial sequence is quasi-definite and not positive definite. We establish orthogonality on a simple contour in the complex plane which depends on the parameters. In all cases we show that the orthogonality conditions characterize the Al-Salam-Carlitz polynomials $U_n^{(a)}(x;q)$ of degree $n$ up to a constant factor. We also obtain a generaliza"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.08178","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":"2026-05-18T01:21:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5WyW13dHycbG0mEW5moqzU0Jn7Zlv/CvhQVB+n1NFpV1hvXRuQUssjU3AmysXQ/0tlVmWShLw1T7ZNWZ4pNlDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:17:40.112515Z"},"content_sha256":"049945da0588655fefa080bac65738f57309e724297d4ce85a86d862476b045f","schema_version":"1.0","event_id":"sha256:049945da0588655fefa080bac65738f57309e724297d4ce85a86d862476b045f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DS6BODWLS6J4L7YDSIHHK63ROZ/bundle.json","state_url":"https://pith.science/pith/DS6BODWLS6J4L7YDSIHHK63ROZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DS6BODWLS6J4L7YDSIHHK63ROZ/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":"2026-06-22T23:17:40Z","links":{"resolver":"https://pith.science/pith/DS6BODWLS6J4L7YDSIHHK63ROZ","bundle":"https://pith.science/pith/DS6BODWLS6J4L7YDSIHHK63ROZ/bundle.json","state":"https://pith.science/pith/DS6BODWLS6J4L7YDSIHHK63ROZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DS6BODWLS6J4L7YDSIHHK63ROZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DS6BODWLS6J4L7YDSIHHK63ROZ","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":"e111d1a1ccd06e35326f369a8a28eb20689baabecdf59c025da77de5de4a5e69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-29T16:20:34Z","title_canon_sha256":"a9ab56b613b5beffe4bc084fb587b02e49b8484ffa2eaa15587498d88d9e249b"},"schema_version":"1.0","source":{"id":"1601.08178","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.08178","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"arxiv_version","alias_value":"1601.08178v1","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.08178","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"pith_short_12","alias_value":"DS6BODWLS6J4","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DS6BODWLS6J4L7YD","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DS6BODWL","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:049945da0588655fefa080bac65738f57309e724297d4ce85a86d862476b045f","target":"graph","created_at":"2026-05-18T01:21:40Z","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 this contribution, we study the orthogonality conditions satisfied by Al-Salam-Carlitz polynomials $U^{(a)}_n(x;q)$ when the parameters $a$ and $q$ are not necessarily real nor `classical', i.e., the linear functional $\\bf u$ with respect to such polynomial sequence is quasi-definite and not positive definite. We establish orthogonality on a simple contour in the complex plane which depends on the parameters. In all cases we show that the orthogonality conditions characterize the Al-Salam-Carlitz polynomials $U_n^{(a)}(x;q)$ of degree $n$ up to a constant factor. We also obtain a generaliza","authors_text":"H. S. Cohl, R. S. Costas-Santos, W. Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-29T16:20:34Z","title":"The orthogonality of Al-Salam-Carlitz polynomials for complex parameters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.08178","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":"sha256:647ca73b4d3a56bd1825778fa12d4d45cec1e5d796c7c81a7f98a604a5c1aa5d","target":"record","created_at":"2026-05-18T01:21:40Z","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":"e111d1a1ccd06e35326f369a8a28eb20689baabecdf59c025da77de5de4a5e69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-29T16:20:34Z","title_canon_sha256":"a9ab56b613b5beffe4bc084fb587b02e49b8484ffa2eaa15587498d88d9e249b"},"schema_version":"1.0","source":{"id":"1601.08178","kind":"arxiv","version":1}},"canonical_sha256":"1cbc170ecb9793c5ff03920e757b71765cb8bfdd16e5c1e6ff1836334aa57a6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cbc170ecb9793c5ff03920e757b71765cb8bfdd16e5c1e6ff1836334aa57a6f","first_computed_at":"2026-05-18T01:21:40.150831Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:40.150831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YiXEfi+ohj1YOpDE45yIP5rdFIJvlR+hyGw0fHUoRzLMtcDCyU+HApfW+KFu9Rvfni1yj35FlHLER/UfsiOpCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:40.151302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.08178","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:647ca73b4d3a56bd1825778fa12d4d45cec1e5d796c7c81a7f98a604a5c1aa5d","sha256:049945da0588655fefa080bac65738f57309e724297d4ce85a86d862476b045f"],"state_sha256":"d09f23b17c3a851521d71e18498f83c5cbb25fa377ea15f347db0b99e9d44024"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VR7uKAmimzp6xdAG/P3BZRPKQup0PTPRuRS2GNIrMFyHfPSXmo7rPFrLiEwguj3zVH/sQJi5+DDjoFQLwrCBCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:17:40.114908Z","bundle_sha256":"f8600b1524e7b1950d7de0fc70d7ba4135ecf450a00157a69a7fe084d4b41f84"}}