{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:DHIIGHGDM76IBRANN2PHJOEBM2","short_pith_number":"pith:DHIIGHGD","canonical_record":{"source":{"id":"1901.01655","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-07T03:29:12Z","cross_cats_sorted":[],"title_canon_sha256":"b905bae4d9ddee32a1b7a5506d7209ea4f4dade00b349423ee7b5841a81ad86d","abstract_canon_sha256":"7036fc5dae52531656421245c3692de6210691ac201929edee7e66021b0cccdc"},"schema_version":"1.0"},"canonical_sha256":"19d0831cc367fc80c40d6e9e74b88166b320227fcf73433465e5afbc1e9f9da3","source":{"kind":"arxiv","id":"1901.01655","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.01655","created_at":"2026-05-17T23:56:51Z"},{"alias_kind":"arxiv_version","alias_value":"1901.01655v1","created_at":"2026-05-17T23:56:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01655","created_at":"2026-05-17T23:56:51Z"},{"alias_kind":"pith_short_12","alias_value":"DHIIGHGDM76I","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"DHIIGHGDM76IBRAN","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"DHIIGHGD","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:DHIIGHGDM76IBRANN2PHJOEBM2","target":"record","payload":{"canonical_record":{"source":{"id":"1901.01655","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-07T03:29:12Z","cross_cats_sorted":[],"title_canon_sha256":"b905bae4d9ddee32a1b7a5506d7209ea4f4dade00b349423ee7b5841a81ad86d","abstract_canon_sha256":"7036fc5dae52531656421245c3692de6210691ac201929edee7e66021b0cccdc"},"schema_version":"1.0"},"canonical_sha256":"19d0831cc367fc80c40d6e9e74b88166b320227fcf73433465e5afbc1e9f9da3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:51.532776Z","signature_b64":"rpGBs9+QdBv4iYNr/TeuwRPBuv+3uWkF8sp9/VLBEhZPy7Y3mVzGca3YmunOzFkb1KcTthIb2yAAPZrn0W1bDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19d0831cc367fc80c40d6e9e74b88166b320227fcf73433465e5afbc1e9f9da3","last_reissued_at":"2026-05-17T23:56:51.532368Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:51.532368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.01655","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":"2026-05-17T23:56:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HCmnCdeFJTGpre3QnKbtGyq6+aqJ/ypSbg89dVGYmWAG7iE4Tivu2xnrcQFWwH5HG73SUIab3bc1XA43MuRaDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T18:47:25.362723Z"},"content_sha256":"bad386f29a0e0d74019bba4a7ca796e4dc873c49a5166625b99bf2271f4e21f2","schema_version":"1.0","event_id":"sha256:bad386f29a0e0d74019bba4a7ca796e4dc873c49a5166625b99bf2271f4e21f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:DHIIGHGDM76IBRANN2PHJOEBM2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Orthogonal decompositions of classical Lie algebras over finite commutative rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Songpon Sriwongsa","submitted_at":"2019-01-07T03:29:12Z","abstract_excerpt":"Let $R$ be a finite commutative ring with identity. In this paper, we give a necessary condition for the existence of an orthogonal decomposition of the special linear Lie algebra over $R$. Additionally, we study orthogonal decompositions of the symplectic Lie algebra and the special orthogonal Lie algebra over $R$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01655","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":"2026-05-17T23:56:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8S4C1vYqASXdPrri/+HA12efJsW0dX9S4cyyOuvcRPSDA+264jDAMMiZ9+4Qdkimr7pRMEmLR7XMg9oSKDR0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T18:47:25.363089Z"},"content_sha256":"8b324ce3994ccec16af61d5c0a4b10c0b376345cd15e7a23f66672017f13b3e0","schema_version":"1.0","event_id":"sha256:8b324ce3994ccec16af61d5c0a4b10c0b376345cd15e7a23f66672017f13b3e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DHIIGHGDM76IBRANN2PHJOEBM2/bundle.json","state_url":"https://pith.science/pith/DHIIGHGDM76IBRANN2PHJOEBM2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DHIIGHGDM76IBRANN2PHJOEBM2/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":"2026-05-24T18:47:25Z","links":{"resolver":"https://pith.science/pith/DHIIGHGDM76IBRANN2PHJOEBM2","bundle":"https://pith.science/pith/DHIIGHGDM76IBRANN2PHJOEBM2/bundle.json","state":"https://pith.science/pith/DHIIGHGDM76IBRANN2PHJOEBM2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DHIIGHGDM76IBRANN2PHJOEBM2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DHIIGHGDM76IBRANN2PHJOEBM2","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":"7036fc5dae52531656421245c3692de6210691ac201929edee7e66021b0cccdc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-07T03:29:12Z","title_canon_sha256":"b905bae4d9ddee32a1b7a5506d7209ea4f4dade00b349423ee7b5841a81ad86d"},"schema_version":"1.0","source":{"id":"1901.01655","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.01655","created_at":"2026-05-17T23:56:51Z"},{"alias_kind":"arxiv_version","alias_value":"1901.01655v1","created_at":"2026-05-17T23:56:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01655","created_at":"2026-05-17T23:56:51Z"},{"alias_kind":"pith_short_12","alias_value":"DHIIGHGDM76I","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"DHIIGHGDM76IBRAN","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"DHIIGHGD","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:8b324ce3994ccec16af61d5c0a4b10c0b376345cd15e7a23f66672017f13b3e0","target":"graph","created_at":"2026-05-17T23:56:51Z","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":"Let $R$ be a finite commutative ring with identity. In this paper, we give a necessary condition for the existence of an orthogonal decomposition of the special linear Lie algebra over $R$. Additionally, we study orthogonal decompositions of the symplectic Lie algebra and the special orthogonal Lie algebra over $R$.","authors_text":"Songpon Sriwongsa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-07T03:29:12Z","title":"Orthogonal decompositions of classical Lie algebras over finite commutative rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01655","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:bad386f29a0e0d74019bba4a7ca796e4dc873c49a5166625b99bf2271f4e21f2","target":"record","created_at":"2026-05-17T23:56:51Z","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":"7036fc5dae52531656421245c3692de6210691ac201929edee7e66021b0cccdc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-07T03:29:12Z","title_canon_sha256":"b905bae4d9ddee32a1b7a5506d7209ea4f4dade00b349423ee7b5841a81ad86d"},"schema_version":"1.0","source":{"id":"1901.01655","kind":"arxiv","version":1}},"canonical_sha256":"19d0831cc367fc80c40d6e9e74b88166b320227fcf73433465e5afbc1e9f9da3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19d0831cc367fc80c40d6e9e74b88166b320227fcf73433465e5afbc1e9f9da3","first_computed_at":"2026-05-17T23:56:51.532368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:51.532368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rpGBs9+QdBv4iYNr/TeuwRPBuv+3uWkF8sp9/VLBEhZPy7Y3mVzGca3YmunOzFkb1KcTthIb2yAAPZrn0W1bDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:51.532776Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.01655","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bad386f29a0e0d74019bba4a7ca796e4dc873c49a5166625b99bf2271f4e21f2","sha256:8b324ce3994ccec16af61d5c0a4b10c0b376345cd15e7a23f66672017f13b3e0"],"state_sha256":"1c7161daa675d807fd0acdbd4f93d2359bc67bc9f71a88fa47ede7c2b740394b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OwxXm9ox/CN2wrUoCMYLo2ePZhs0tgFzhPowzv6Yvpuov3Yef5A4pPFfy5NY0t1w34SefbLDi3RCJ2lc78fhAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T18:47:25.366085Z","bundle_sha256":"8ff7aa4ec6807554abf42f174cc1463488c29cf5d27715dc2fd0bcdf6869931f"}}