{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:D4HEWBBKL5FIGTLILOQRAUXC2B","short_pith_number":"pith:D4HEWBBK","canonical_record":{"source":{"id":"1805.03150","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-08T16:39:22Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"365149d8c9bc13fcaf314099c295dcd41eaa0236198a1d0fb261036d50ac6e75","abstract_canon_sha256":"8a8f6ef5d5223c2069c20780cbc2117544c4574920527129ee7c9822f14553a4"},"schema_version":"1.0"},"canonical_sha256":"1f0e4b042a5f4a834d685ba11052e2d07df23af720822c393974d1e6b0315929","source":{"kind":"arxiv","id":"1805.03150","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.03150","created_at":"2026-05-18T00:16:34Z"},{"alias_kind":"arxiv_version","alias_value":"1805.03150v1","created_at":"2026-05-18T00:16:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.03150","created_at":"2026-05-18T00:16:34Z"},{"alias_kind":"pith_short_12","alias_value":"D4HEWBBKL5FI","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"D4HEWBBKL5FIGTLI","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"D4HEWBBK","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:D4HEWBBKL5FIGTLILOQRAUXC2B","target":"record","payload":{"canonical_record":{"source":{"id":"1805.03150","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-08T16:39:22Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"365149d8c9bc13fcaf314099c295dcd41eaa0236198a1d0fb261036d50ac6e75","abstract_canon_sha256":"8a8f6ef5d5223c2069c20780cbc2117544c4574920527129ee7c9822f14553a4"},"schema_version":"1.0"},"canonical_sha256":"1f0e4b042a5f4a834d685ba11052e2d07df23af720822c393974d1e6b0315929","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:34.469854Z","signature_b64":"/fYIZwkzlJXf/5fSXp13VOdlA+FktZVUT7SLeTuXAq7AU+UztIEWop9FhE4J9KfR4K4LRZjMsJE+enmLhLMTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f0e4b042a5f4a834d685ba11052e2d07df23af720822c393974d1e6b0315929","last_reissued_at":"2026-05-18T00:16:34.469253Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:34.469253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.03150","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":"2026-05-18T00:16:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3xd02fOPBkAI7lcSgITpyAP3wANiLbMrAyqObxk/oKakwanBmp/glHns3tgtZJGIog1yg8eiAZYWCLB+GA0gAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T11:02:20.739939Z"},"content_sha256":"5b2ebc9000300d39341e84712c4d0e573407717d7fc4f166e35dd0a5df41dea0","schema_version":"1.0","event_id":"sha256:5b2ebc9000300d39341e84712c4d0e573407717d7fc4f166e35dd0a5df41dea0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:D4HEWBBKL5FIGTLILOQRAUXC2B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A different perspective on H-like Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.DG","authors_text":"Cathy Kriloff, Tracy Payne","submitted_at":"2018-05-08T16:39:22Z","abstract_excerpt":"We characterize H-like Lie algebras in terms of subspaces of cones over conjugacy classes in $\\mathfrak{so}(\\mathbb{R}^q)$, translating the classification problem for H-like Lie algebras to an equivalent problem in linear algebra. We study properties of H-like Lie algebras, present new methods for constructing them, including tensor products and central sums, and classify H-like Lie algebras whose associated $J_Z$-maps have rank two for all nonzero $Z$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03150","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":"2026-05-18T00:16:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CJNgw3mVPWFbMGp3Uw8B3hv2cfKT1jqjGS0yCAfR+k/+Ea8q8NtVPX5g5ivgvyoC43/FAMIx7KSrm/IiFL2ACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T11:02:20.740279Z"},"content_sha256":"3ae3e3a54a8cd1c68eaaa5cd34c3c91b449e2090c59ff96da68064132d034df2","schema_version":"1.0","event_id":"sha256:3ae3e3a54a8cd1c68eaaa5cd34c3c91b449e2090c59ff96da68064132d034df2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D4HEWBBKL5FIGTLILOQRAUXC2B/bundle.json","state_url":"https://pith.science/pith/D4HEWBBKL5FIGTLILOQRAUXC2B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D4HEWBBKL5FIGTLILOQRAUXC2B/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":"2026-06-30T11:02:20Z","links":{"resolver":"https://pith.science/pith/D4HEWBBKL5FIGTLILOQRAUXC2B","bundle":"https://pith.science/pith/D4HEWBBKL5FIGTLILOQRAUXC2B/bundle.json","state":"https://pith.science/pith/D4HEWBBKL5FIGTLILOQRAUXC2B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D4HEWBBKL5FIGTLILOQRAUXC2B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:D4HEWBBKL5FIGTLILOQRAUXC2B","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":"8a8f6ef5d5223c2069c20780cbc2117544c4574920527129ee7c9822f14553a4","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-08T16:39:22Z","title_canon_sha256":"365149d8c9bc13fcaf314099c295dcd41eaa0236198a1d0fb261036d50ac6e75"},"schema_version":"1.0","source":{"id":"1805.03150","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.03150","created_at":"2026-05-18T00:16:34Z"},{"alias_kind":"arxiv_version","alias_value":"1805.03150v1","created_at":"2026-05-18T00:16:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.03150","created_at":"2026-05-18T00:16:34Z"},{"alias_kind":"pith_short_12","alias_value":"D4HEWBBKL5FI","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"D4HEWBBKL5FIGTLI","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"D4HEWBBK","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:3ae3e3a54a8cd1c68eaaa5cd34c3c91b449e2090c59ff96da68064132d034df2","target":"graph","created_at":"2026-05-18T00:16:34Z","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 characterize H-like Lie algebras in terms of subspaces of cones over conjugacy classes in $\\mathfrak{so}(\\mathbb{R}^q)$, translating the classification problem for H-like Lie algebras to an equivalent problem in linear algebra. We study properties of H-like Lie algebras, present new methods for constructing them, including tensor products and central sums, and classify H-like Lie algebras whose associated $J_Z$-maps have rank two for all nonzero $Z$.","authors_text":"Cathy Kriloff, Tracy Payne","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-08T16:39:22Z","title":"A different perspective on H-like Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03150","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":"sha256:5b2ebc9000300d39341e84712c4d0e573407717d7fc4f166e35dd0a5df41dea0","target":"record","created_at":"2026-05-18T00:16:34Z","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":"8a8f6ef5d5223c2069c20780cbc2117544c4574920527129ee7c9822f14553a4","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-08T16:39:22Z","title_canon_sha256":"365149d8c9bc13fcaf314099c295dcd41eaa0236198a1d0fb261036d50ac6e75"},"schema_version":"1.0","source":{"id":"1805.03150","kind":"arxiv","version":1}},"canonical_sha256":"1f0e4b042a5f4a834d685ba11052e2d07df23af720822c393974d1e6b0315929","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f0e4b042a5f4a834d685ba11052e2d07df23af720822c393974d1e6b0315929","first_computed_at":"2026-05-18T00:16:34.469253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:34.469253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/fYIZwkzlJXf/5fSXp13VOdlA+FktZVUT7SLeTuXAq7AU+UztIEWop9FhE4J9KfR4K4LRZjMsJE+enmLhLMTDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:34.469854Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.03150","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b2ebc9000300d39341e84712c4d0e573407717d7fc4f166e35dd0a5df41dea0","sha256:3ae3e3a54a8cd1c68eaaa5cd34c3c91b449e2090c59ff96da68064132d034df2"],"state_sha256":"79359edf3fbb58e901b88db8884782ba928a5f6114fbf673b3124ad6709f1066"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pPTwRPqIR2wqQPzuOBDpNxLnRy9/TwzRmaw2yvfJJ5DwiLGIyEFn5ZqyDAfyVTT5Dpyuh2PFXRRf65aRIvvgAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T11:02:20.742189Z","bundle_sha256":"2ad1c807e1972a2794cb3bb9950da2b0a7335cf735bbe223369a93fcf6c966d0"}}