{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PVQO5LJU7SI3YK6JFAF5GTAZ3H","short_pith_number":"pith:PVQO5LJU","canonical_record":{"source":{"id":"1205.6353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-29T13:12:51Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"8252c3852f9b44140f90059647bfc944c8c9c61fba4cff25986426568ee665e4","abstract_canon_sha256":"3bba23983de0550564c58f40f6c128e5e501a36424f5ee1a2a934feee66528f2"},"schema_version":"1.0"},"canonical_sha256":"7d60eead34fc91bc2bc9280bd34c19d9f15551d4898db6833efdec3f1e800a70","source":{"kind":"arxiv","id":"1205.6353","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6353","created_at":"2026-05-18T01:57:16Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6353v1","created_at":"2026-05-18T01:57:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6353","created_at":"2026-05-18T01:57:16Z"},{"alias_kind":"pith_short_12","alias_value":"PVQO5LJU7SI3","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PVQO5LJU7SI3YK6J","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PVQO5LJU","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PVQO5LJU7SI3YK6JFAF5GTAZ3H","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-29T13:12:51Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"8252c3852f9b44140f90059647bfc944c8c9c61fba4cff25986426568ee665e4","abstract_canon_sha256":"3bba23983de0550564c58f40f6c128e5e501a36424f5ee1a2a934feee66528f2"},"schema_version":"1.0"},"canonical_sha256":"7d60eead34fc91bc2bc9280bd34c19d9f15551d4898db6833efdec3f1e800a70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:16.101585Z","signature_b64":"WJ/i9Fhq5m5zxgME6E58kUkaUgjYMDZumuW4RXwYsM4ZQT5Ge+WPAU70X4SIkyLqQpRZd6kZVf+s7jzwtohMBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d60eead34fc91bc2bc9280bd34c19d9f15551d4898db6833efdec3f1e800a70","last_reissued_at":"2026-05-18T01:57:16.100891Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:16.100891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6353","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":"2026-05-18T01:57:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jsy+yCuOJu/g8qYG8Vc1WMcz4i6kLRMz3Rs8uGob9XZpL71IeiXStKmArweUk/mB7zHL2A+BjWzH2WQ3Ua0nCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:44:50.663045Z"},"content_sha256":"caa1130f54acdd317fc8f14f5a1d73ed4ce135fbfb004ab555eb3b76ebeb5113","schema_version":"1.0","event_id":"sha256:caa1130f54acdd317fc8f14f5a1d73ed4ce135fbfb004ab555eb3b76ebeb5113"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PVQO5LJU7SI3YK6JFAF5GTAZ3H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coherent Orthogonal Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"E Celeghini, Mariano A del Olmo","submitted_at":"2012-05-29T13:12:51Z","abstract_excerpt":"We discuss as a fundamental characteristic of orthogonal polynomials like the existence of a Lie algebra behind them, can be added to their other relevant aspects. At the basis of the complete framework for orthogonal polynomials we put thus --in addition to differential equations, recurrence relations, Hilbert spaces and square integrable functions-- Lie algebra theory.\n  We start here from the square integrable functions on the open connected subset of the real line whose bases are related to orthogonal polynomials. All these one-dimensional continuous spaces allow, besides the standard unco"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6353","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":"2026-05-18T01:57:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yE4KowT5/o+t35grXtc/d/aI3JvKM4Jud0q2PeaORY6fCAhGFs4ihYOJrhOIA2gT3UDZdAjS8wffDGuSkUJAAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:44:50.663408Z"},"content_sha256":"095b4f72612d1634508b09a2467a9e822f6f4fb528312b893e912943702c22e0","schema_version":"1.0","event_id":"sha256:095b4f72612d1634508b09a2467a9e822f6f4fb528312b893e912943702c22e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PVQO5LJU7SI3YK6JFAF5GTAZ3H/bundle.json","state_url":"https://pith.science/pith/PVQO5LJU7SI3YK6JFAF5GTAZ3H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PVQO5LJU7SI3YK6JFAF5GTAZ3H/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":"2026-05-30T14:44:50Z","links":{"resolver":"https://pith.science/pith/PVQO5LJU7SI3YK6JFAF5GTAZ3H","bundle":"https://pith.science/pith/PVQO5LJU7SI3YK6JFAF5GTAZ3H/bundle.json","state":"https://pith.science/pith/PVQO5LJU7SI3YK6JFAF5GTAZ3H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PVQO5LJU7SI3YK6JFAF5GTAZ3H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PVQO5LJU7SI3YK6JFAF5GTAZ3H","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":"3bba23983de0550564c58f40f6c128e5e501a36424f5ee1a2a934feee66528f2","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-29T13:12:51Z","title_canon_sha256":"8252c3852f9b44140f90059647bfc944c8c9c61fba4cff25986426568ee665e4"},"schema_version":"1.0","source":{"id":"1205.6353","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6353","created_at":"2026-05-18T01:57:16Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6353v1","created_at":"2026-05-18T01:57:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6353","created_at":"2026-05-18T01:57:16Z"},{"alias_kind":"pith_short_12","alias_value":"PVQO5LJU7SI3","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PVQO5LJU7SI3YK6J","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PVQO5LJU","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:095b4f72612d1634508b09a2467a9e822f6f4fb528312b893e912943702c22e0","target":"graph","created_at":"2026-05-18T01:57:16Z","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 discuss as a fundamental characteristic of orthogonal polynomials like the existence of a Lie algebra behind them, can be added to their other relevant aspects. At the basis of the complete framework for orthogonal polynomials we put thus --in addition to differential equations, recurrence relations, Hilbert spaces and square integrable functions-- Lie algebra theory.\n  We start here from the square integrable functions on the open connected subset of the real line whose bases are related to orthogonal polynomials. All these one-dimensional continuous spaces allow, besides the standard unco","authors_text":"E Celeghini, Mariano A del Olmo","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-29T13:12:51Z","title":"Coherent Orthogonal Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6353","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:caa1130f54acdd317fc8f14f5a1d73ed4ce135fbfb004ab555eb3b76ebeb5113","target":"record","created_at":"2026-05-18T01:57:16Z","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":"3bba23983de0550564c58f40f6c128e5e501a36424f5ee1a2a934feee66528f2","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-29T13:12:51Z","title_canon_sha256":"8252c3852f9b44140f90059647bfc944c8c9c61fba4cff25986426568ee665e4"},"schema_version":"1.0","source":{"id":"1205.6353","kind":"arxiv","version":1}},"canonical_sha256":"7d60eead34fc91bc2bc9280bd34c19d9f15551d4898db6833efdec3f1e800a70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d60eead34fc91bc2bc9280bd34c19d9f15551d4898db6833efdec3f1e800a70","first_computed_at":"2026-05-18T01:57:16.100891Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:16.100891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WJ/i9Fhq5m5zxgME6E58kUkaUgjYMDZumuW4RXwYsM4ZQT5Ge+WPAU70X4SIkyLqQpRZd6kZVf+s7jzwtohMBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:16.101585Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6353","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caa1130f54acdd317fc8f14f5a1d73ed4ce135fbfb004ab555eb3b76ebeb5113","sha256:095b4f72612d1634508b09a2467a9e822f6f4fb528312b893e912943702c22e0"],"state_sha256":"6fdf5181351dc1f38215b473587c196dfe5e25a4dcc3d03612a0ffa32e3ffc0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jp9G/aQlP+5WEURqkBVo3qOHCmekvF8TwpdxPlo4LuWXTYHZb3FJMWbG0bF9J0iAeTMPgUEgWzkvdu6GW+RrDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T14:44:50.665384Z","bundle_sha256":"b435a9dfe1d7d47b5e8a37aa2501608ce3dfc2658814657a794d56a61ea6a4b3"}}