{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:63Q3WCGEPM26PEIK5DQMPQ4VQM","short_pith_number":"pith:63Q3WCGE","canonical_record":{"source":{"id":"1011.4929","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-22T20:34:41Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"936c75ef8e70817ed56ae312e190a80219b021c62c026efa9eea2378ededa082","abstract_canon_sha256":"3391cbf1b9bc1d1382ae0c54c0f71fedf9f679ed6f740f0fe74141fbf2bf9806"},"schema_version":"1.0"},"canonical_sha256":"f6e1bb08c47b35e7910ae8e0c7c395830e0d44dda70a74f432007c80fe1fcbcb","source":{"kind":"arxiv","id":"1011.4929","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4929","created_at":"2026-05-18T03:20:57Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4929v5","created_at":"2026-05-18T03:20:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4929","created_at":"2026-05-18T03:20:57Z"},{"alias_kind":"pith_short_12","alias_value":"63Q3WCGEPM26","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"63Q3WCGEPM26PEIK","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"63Q3WCGE","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:63Q3WCGEPM26PEIK5DQMPQ4VQM","target":"record","payload":{"canonical_record":{"source":{"id":"1011.4929","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-22T20:34:41Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"936c75ef8e70817ed56ae312e190a80219b021c62c026efa9eea2378ededa082","abstract_canon_sha256":"3391cbf1b9bc1d1382ae0c54c0f71fedf9f679ed6f740f0fe74141fbf2bf9806"},"schema_version":"1.0"},"canonical_sha256":"f6e1bb08c47b35e7910ae8e0c7c395830e0d44dda70a74f432007c80fe1fcbcb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:57.317013Z","signature_b64":"O8wZHRkoMvjbGiPWuoA37NgXIoLpPJhaifH9EHCW5XZpKRX2sGCgpqbIcxEZMU6olIvM8oOeLRw2XVm3o6pzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6e1bb08c47b35e7910ae8e0c7c395830e0d44dda70a74f432007c80fe1fcbcb","last_reissued_at":"2026-05-18T03:20:57.316294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:57.316294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.4929","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:20:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ZzH+AAT50OgfcvyTMkShwmxEslIChxEJf+7NPjwlcbvnS6FVHqzLvAHYjlthyWMTb/pRQ/Cn7BM5FOp0CjMAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:10:43.478348Z"},"content_sha256":"cb4fef7859107f01a244c33110372c24035b0a9503e2e466343f5b2adb14737a","schema_version":"1.0","event_id":"sha256:cb4fef7859107f01a244c33110372c24035b0a9503e2e466343f5b2adb14737a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:63Q3WCGEPM26PEIK5DQMPQ4VQM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards a q-analogue of the Kibble--Slepian formula in 3 dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CA","authors_text":"Pawe{\\l} J. Szab{\\l}owski","submitted_at":"2010-11-22T20:34:41Z","abstract_excerpt":"We study a generalization of the Kibble-Slepian (KS) expansion formula in 3 dimensions. The generalization is obtained by replacing the Hermite polynomials by the q-Hermite ones. If such a replacement would lead to non-negativity for all allowed values of parameters and for all values of variables ranging over certain Cartesian product of compact intervals then we would deal with a generalization of the 3 dimensional Normal distribution. We show that this is not the case. We indicate some values of the parameters and some compact set in R^{3} of positive measure, such that the values of the ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4929","kind":"arxiv","version":5},"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":"2026-05-18T03:20:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hzTVHiTbIikDNpBungcsFiPO09W/fCVMGAuKCvJm2jxD3UOC3EPSnaRNNkQIH9wbw8Yg1fQkyrmDkg6GoFuADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:10:43.478691Z"},"content_sha256":"e27741e1cd0eaa8aa641be57cb87194e8b4bbe5269bb5086e64916cc2e83587c","schema_version":"1.0","event_id":"sha256:e27741e1cd0eaa8aa641be57cb87194e8b4bbe5269bb5086e64916cc2e83587c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/63Q3WCGEPM26PEIK5DQMPQ4VQM/bundle.json","state_url":"https://pith.science/pith/63Q3WCGEPM26PEIK5DQMPQ4VQM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/63Q3WCGEPM26PEIK5DQMPQ4VQM/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":"2026-06-25T17:10:43Z","links":{"resolver":"https://pith.science/pith/63Q3WCGEPM26PEIK5DQMPQ4VQM","bundle":"https://pith.science/pith/63Q3WCGEPM26PEIK5DQMPQ4VQM/bundle.json","state":"https://pith.science/pith/63Q3WCGEPM26PEIK5DQMPQ4VQM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/63Q3WCGEPM26PEIK5DQMPQ4VQM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:63Q3WCGEPM26PEIK5DQMPQ4VQM","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":"3391cbf1b9bc1d1382ae0c54c0f71fedf9f679ed6f740f0fe74141fbf2bf9806","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-22T20:34:41Z","title_canon_sha256":"936c75ef8e70817ed56ae312e190a80219b021c62c026efa9eea2378ededa082"},"schema_version":"1.0","source":{"id":"1011.4929","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4929","created_at":"2026-05-18T03:20:57Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4929v5","created_at":"2026-05-18T03:20:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4929","created_at":"2026-05-18T03:20:57Z"},{"alias_kind":"pith_short_12","alias_value":"63Q3WCGEPM26","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"63Q3WCGEPM26PEIK","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"63Q3WCGE","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:e27741e1cd0eaa8aa641be57cb87194e8b4bbe5269bb5086e64916cc2e83587c","target":"graph","created_at":"2026-05-18T03:20:57Z","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 a generalization of the Kibble-Slepian (KS) expansion formula in 3 dimensions. The generalization is obtained by replacing the Hermite polynomials by the q-Hermite ones. If such a replacement would lead to non-negativity for all allowed values of parameters and for all values of variables ranging over certain Cartesian product of compact intervals then we would deal with a generalization of the 3 dimensional Normal distribution. We show that this is not the case. We indicate some values of the parameters and some compact set in R^{3} of positive measure, such that the values of the ex","authors_text":"Pawe{\\l} J. Szab{\\l}owski","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-22T20:34:41Z","title":"Towards a q-analogue of the Kibble--Slepian formula in 3 dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4929","kind":"arxiv","version":5},"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:cb4fef7859107f01a244c33110372c24035b0a9503e2e466343f5b2adb14737a","target":"record","created_at":"2026-05-18T03:20:57Z","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":"3391cbf1b9bc1d1382ae0c54c0f71fedf9f679ed6f740f0fe74141fbf2bf9806","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-22T20:34:41Z","title_canon_sha256":"936c75ef8e70817ed56ae312e190a80219b021c62c026efa9eea2378ededa082"},"schema_version":"1.0","source":{"id":"1011.4929","kind":"arxiv","version":5}},"canonical_sha256":"f6e1bb08c47b35e7910ae8e0c7c395830e0d44dda70a74f432007c80fe1fcbcb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6e1bb08c47b35e7910ae8e0c7c395830e0d44dda70a74f432007c80fe1fcbcb","first_computed_at":"2026-05-18T03:20:57.316294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:57.316294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O8wZHRkoMvjbGiPWuoA37NgXIoLpPJhaifH9EHCW5XZpKRX2sGCgpqbIcxEZMU6olIvM8oOeLRw2XVm3o6pzCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:57.317013Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.4929","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb4fef7859107f01a244c33110372c24035b0a9503e2e466343f5b2adb14737a","sha256:e27741e1cd0eaa8aa641be57cb87194e8b4bbe5269bb5086e64916cc2e83587c"],"state_sha256":"69df12448d58445bfef7dffe984fe4b95d063058c0fa1e3f825a41c69d5c85da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UO9sSq57m32BXN7RmYjpzU0HoMKtyvwEWGmkJAHwVVkFgXwQq5QH0R0x5/+sVjlLQW5l6oMEdxy+4MgjZoSRCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T17:10:43.480479Z","bundle_sha256":"0e7b7c9f7b4b2f438fc6cfd93536a591e2e0eb639590496f6a1a26755ef5f4ad"}}