{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:DB4G3EIUNCVAONGA2ML2TYFEGG","short_pith_number":"pith:DB4G3EIU","canonical_record":{"source":{"id":"2012.07431","kind":"arxiv","version":7},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.FA","submitted_at":"2020-12-14T11:35:13Z","cross_cats_sorted":[],"title_canon_sha256":"b182b9c15327838a07b43a34ee3106951cae999be38d7817c14ec11ee9477082","abstract_canon_sha256":"8c70cdd20a898d298b2ca83203609a0dbe9c6500a9d47bbae334bc5da50389e9"},"schema_version":"1.0"},"canonical_sha256":"18786d911468aa0734c0d317a9e0a431bfb10d870e564dcbfac01a5a588e2d90","source":{"kind":"arxiv","id":"2012.07431","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.07431","created_at":"2026-05-20T01:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"2012.07431v7","created_at":"2026-05-20T01:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.07431","created_at":"2026-05-20T01:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"DB4G3EIUNCVA","created_at":"2026-05-20T01:04:47Z"},{"alias_kind":"pith_short_16","alias_value":"DB4G3EIUNCVAONGA","created_at":"2026-05-20T01:04:47Z"},{"alias_kind":"pith_short_8","alias_value":"DB4G3EIU","created_at":"2026-05-20T01:04:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:DB4G3EIUNCVAONGA2ML2TYFEGG","target":"record","payload":{"canonical_record":{"source":{"id":"2012.07431","kind":"arxiv","version":7},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.FA","submitted_at":"2020-12-14T11:35:13Z","cross_cats_sorted":[],"title_canon_sha256":"b182b9c15327838a07b43a34ee3106951cae999be38d7817c14ec11ee9477082","abstract_canon_sha256":"8c70cdd20a898d298b2ca83203609a0dbe9c6500a9d47bbae334bc5da50389e9"},"schema_version":"1.0"},"canonical_sha256":"18786d911468aa0734c0d317a9e0a431bfb10d870e564dcbfac01a5a588e2d90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:04:47.475245Z","signature_b64":"bydoP1QLhjcxVpr+/iokw4NedN40Fo4r05V3Pv31WYXRubDMDySrybVLbgrWiUAcWXakyH+qlQwYdQVTkuGuCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18786d911468aa0734c0d317a9e0a431bfb10d870e564dcbfac01a5a588e2d90","last_reissued_at":"2026-05-20T01:04:47.474726Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:04:47.474726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2012.07431","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T01:04:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YSiO6fb/KKXRAWgsmiTI6Ya/8XgvkSjxW3kPH6x6VOg1KmfdBirxxQWSr5Q0I+lZcAOnvSbZuu5C+tN+1b5mBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T17:37:27.019702Z"},"content_sha256":"9a7f3f462e0d89cb5ad5f48df0d9ef0b0bc46ccfac27cd2764ac4c87e86d123d","schema_version":"1.0","event_id":"sha256:9a7f3f462e0d89cb5ad5f48df0d9ef0b0bc46ccfac27cd2764ac4c87e86d123d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:DB4G3EIUNCVAONGA2ML2TYFEGG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Continual Lie algebras determined by chain complexes","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Zuevsky","submitted_at":"2020-12-14T11:35:13Z","abstract_excerpt":"Continual Lie algebras are infinite-dimensional generalizations of Lie algebras with discrete root system by considering continual root systems. In this paper we establish the general relation between chain complexes and continual Lie algebras. The natural orthogonality condition with respect to a product among elements of a chain complex $\\mathcal C$ spaces brings about to $\\mathcal C$ the structure of a graded algebra with differential relations. We prove the main result of this paper: a chain complex endowed with an appropriate Leibniz-property product of elements of its spaces and the Jaco"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.07431","kind":"arxiv","version":7},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.07431/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-20T01:04:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+V3K+mRI/Ay7MJE5UFDuBAHoQIyQ5t2jB44WaStktCHJWQ/ZpyHrSEsM5IP13p48ekm/qadsz74Dc6a++yMcCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T17:37:27.020455Z"},"content_sha256":"8468e2985da99e0e07e9179036bb2596db85013be4f393f74e48c55e1c94fba8","schema_version":"1.0","event_id":"sha256:8468e2985da99e0e07e9179036bb2596db85013be4f393f74e48c55e1c94fba8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DB4G3EIUNCVAONGA2ML2TYFEGG/bundle.json","state_url":"https://pith.science/pith/DB4G3EIUNCVAONGA2ML2TYFEGG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DB4G3EIUNCVAONGA2ML2TYFEGG/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":"2026-06-11T17:37:27Z","links":{"resolver":"https://pith.science/pith/DB4G3EIUNCVAONGA2ML2TYFEGG","bundle":"https://pith.science/pith/DB4G3EIUNCVAONGA2ML2TYFEGG/bundle.json","state":"https://pith.science/pith/DB4G3EIUNCVAONGA2ML2TYFEGG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DB4G3EIUNCVAONGA2ML2TYFEGG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:DB4G3EIUNCVAONGA2ML2TYFEGG","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":"8c70cdd20a898d298b2ca83203609a0dbe9c6500a9d47bbae334bc5da50389e9","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.FA","submitted_at":"2020-12-14T11:35:13Z","title_canon_sha256":"b182b9c15327838a07b43a34ee3106951cae999be38d7817c14ec11ee9477082"},"schema_version":"1.0","source":{"id":"2012.07431","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.07431","created_at":"2026-05-20T01:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"2012.07431v7","created_at":"2026-05-20T01:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.07431","created_at":"2026-05-20T01:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"DB4G3EIUNCVA","created_at":"2026-05-20T01:04:47Z"},{"alias_kind":"pith_short_16","alias_value":"DB4G3EIUNCVAONGA","created_at":"2026-05-20T01:04:47Z"},{"alias_kind":"pith_short_8","alias_value":"DB4G3EIU","created_at":"2026-05-20T01:04:47Z"}],"graph_snapshots":[{"event_id":"sha256:8468e2985da99e0e07e9179036bb2596db85013be4f393f74e48c55e1c94fba8","target":"graph","created_at":"2026-05-20T01:04:47Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2012.07431/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Continual Lie algebras are infinite-dimensional generalizations of Lie algebras with discrete root system by considering continual root systems. In this paper we establish the general relation between chain complexes and continual Lie algebras. The natural orthogonality condition with respect to a product among elements of a chain complex $\\mathcal C$ spaces brings about to $\\mathcal C$ the structure of a graded algebra with differential relations. We prove the main result of this paper: a chain complex endowed with an appropriate Leibniz-property product of elements of its spaces and the Jaco","authors_text":"A. Zuevsky","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.FA","submitted_at":"2020-12-14T11:35:13Z","title":"Continual Lie algebras determined by chain complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.07431","kind":"arxiv","version":7},"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":"sha256:9a7f3f462e0d89cb5ad5f48df0d9ef0b0bc46ccfac27cd2764ac4c87e86d123d","target":"record","created_at":"2026-05-20T01:04:47Z","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":"8c70cdd20a898d298b2ca83203609a0dbe9c6500a9d47bbae334bc5da50389e9","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.FA","submitted_at":"2020-12-14T11:35:13Z","title_canon_sha256":"b182b9c15327838a07b43a34ee3106951cae999be38d7817c14ec11ee9477082"},"schema_version":"1.0","source":{"id":"2012.07431","kind":"arxiv","version":7}},"canonical_sha256":"18786d911468aa0734c0d317a9e0a431bfb10d870e564dcbfac01a5a588e2d90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18786d911468aa0734c0d317a9e0a431bfb10d870e564dcbfac01a5a588e2d90","first_computed_at":"2026-05-20T01:04:47.474726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T01:04:47.474726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bydoP1QLhjcxVpr+/iokw4NedN40Fo4r05V3Pv31WYXRubDMDySrybVLbgrWiUAcWXakyH+qlQwYdQVTkuGuCA==","signature_status":"signed_v1","signed_at":"2026-05-20T01:04:47.475245Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.07431","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a7f3f462e0d89cb5ad5f48df0d9ef0b0bc46ccfac27cd2764ac4c87e86d123d","sha256:8468e2985da99e0e07e9179036bb2596db85013be4f393f74e48c55e1c94fba8"],"state_sha256":"34df4167a7813e6927a8241fe571b7cbea707b44ae7fcf46499e5b86e778c2e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QlwBYca1aOXyfm+oPKybFjieNtoBrg1pREiboFEhV+ToHmSgLuEjiQheG1cgsLUIfezvRIMGbcJG6uxRnsUlDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T17:37:27.024711Z","bundle_sha256":"162a8248fe6dcfbbc480cba22092dc34a5e7a89699f327a026c4b1c319765b80"}}