{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZHC3F56YJ3OSGBVEIM4LK4HH3M","short_pith_number":"pith:ZHC3F56Y","canonical_record":{"source":{"id":"1207.0472","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-07-02T18:58:28Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"d0c8b747c02d82dc1a43695cfa003d48999ebf2749b1349b5178921573faf491","abstract_canon_sha256":"37f4e921742360af7caf8ef408f64208982dee9266500c6b4429b413aabb679b"},"schema_version":"1.0"},"canonical_sha256":"c9c5b2f7d84edd2306a44338b570e7db38011fd40c8e92480494feb8d45b3d94","source":{"kind":"arxiv","id":"1207.0472","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0472","created_at":"2026-05-18T03:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0472v1","created_at":"2026-05-18T03:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0472","created_at":"2026-05-18T03:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"ZHC3F56YJ3OS","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZHC3F56YJ3OSGBVE","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZHC3F56Y","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZHC3F56YJ3OSGBVEIM4LK4HH3M","target":"record","payload":{"canonical_record":{"source":{"id":"1207.0472","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-07-02T18:58:28Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"d0c8b747c02d82dc1a43695cfa003d48999ebf2749b1349b5178921573faf491","abstract_canon_sha256":"37f4e921742360af7caf8ef408f64208982dee9266500c6b4429b413aabb679b"},"schema_version":"1.0"},"canonical_sha256":"c9c5b2f7d84edd2306a44338b570e7db38011fd40c8e92480494feb8d45b3d94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:59.242242Z","signature_b64":"AAjL2tEPpWjXxd/VqLgqSNX1AVfzd0YgOccHfhRzS8xtKNR0CTLqh1FhsORCNT4fVGYcfcjOlMgjshIupnr9Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9c5b2f7d84edd2306a44338b570e7db38011fd40c8e92480494feb8d45b3d94","last_reissued_at":"2026-05-18T03:51:59.241262Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:59.241262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.0472","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":"2026-05-18T03:51:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"93/7A1QZ6jFRyIWAXAay6OSJwJ0hXGxFG9FoEFrLxeCNAw836Rtd1C/GBSv02hjL37KbErvAcZu1EDQc8+JMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T20:29:14.891523Z"},"content_sha256":"a96148c97981f0b82ea6a350eaa768f95753fdd8ee4c66b6720535481821f9b0","schema_version":"1.0","event_id":"sha256:a96148c97981f0b82ea6a350eaa768f95753fdd8ee4c66b6720535481821f9b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZHC3F56YJ3OSGBVEIM4LK4HH3M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Relative Theory for Leibniz n-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.KT","authors_text":"Guy R. Biyogmam","submitted_at":"2012-07-02T18:58:28Z","abstract_excerpt":"In this paper we show that for a $n$-Filippov algebra $\\g,$ the tensor power $\\g^{\\otimes n-1}$ is endowed with a structure of anti-symmetric co-representation over the Leibniz algebra $\\g^{\\wedge n-1}$. This co-representation is used to define two relative theories for Leibniz $n$-algebras with $n>2$ and obtain exact sequences relating them. As a result, we construct a spectral sequence for the Leibniz homology of Filippov algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0472","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":"2026-05-18T03:51:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y0I364HwJFH53C46ElbixZbpY6D7Hahw3XMUiYRuGNG2Y2KDlBlx2iY274BgnwHWi9j4YIVP5W1DBHtSrSglDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T20:29:14.891874Z"},"content_sha256":"6b4af3c138e15c04d5f89038706fb758e2d8e8907bc4df98e151726859ed5cfa","schema_version":"1.0","event_id":"sha256:6b4af3c138e15c04d5f89038706fb758e2d8e8907bc4df98e151726859ed5cfa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZHC3F56YJ3OSGBVEIM4LK4HH3M/bundle.json","state_url":"https://pith.science/pith/ZHC3F56YJ3OSGBVEIM4LK4HH3M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZHC3F56YJ3OSGBVEIM4LK4HH3M/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":"2026-06-30T20:29:14Z","links":{"resolver":"https://pith.science/pith/ZHC3F56YJ3OSGBVEIM4LK4HH3M","bundle":"https://pith.science/pith/ZHC3F56YJ3OSGBVEIM4LK4HH3M/bundle.json","state":"https://pith.science/pith/ZHC3F56YJ3OSGBVEIM4LK4HH3M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZHC3F56YJ3OSGBVEIM4LK4HH3M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZHC3F56YJ3OSGBVEIM4LK4HH3M","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":"37f4e921742360af7caf8ef408f64208982dee9266500c6b4429b413aabb679b","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-07-02T18:58:28Z","title_canon_sha256":"d0c8b747c02d82dc1a43695cfa003d48999ebf2749b1349b5178921573faf491"},"schema_version":"1.0","source":{"id":"1207.0472","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0472","created_at":"2026-05-18T03:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0472v1","created_at":"2026-05-18T03:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0472","created_at":"2026-05-18T03:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"ZHC3F56YJ3OS","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZHC3F56YJ3OSGBVE","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZHC3F56Y","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:6b4af3c138e15c04d5f89038706fb758e2d8e8907bc4df98e151726859ed5cfa","target":"graph","created_at":"2026-05-18T03:51:59Z","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":"In this paper we show that for a $n$-Filippov algebra $\\g,$ the tensor power $\\g^{\\otimes n-1}$ is endowed with a structure of anti-symmetric co-representation over the Leibniz algebra $\\g^{\\wedge n-1}$. This co-representation is used to define two relative theories for Leibniz $n$-algebras with $n>2$ and obtain exact sequences relating them. As a result, we construct a spectral sequence for the Leibniz homology of Filippov algebras.","authors_text":"Guy R. Biyogmam","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-07-02T18:58:28Z","title":"A Relative Theory for Leibniz n-Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0472","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:a96148c97981f0b82ea6a350eaa768f95753fdd8ee4c66b6720535481821f9b0","target":"record","created_at":"2026-05-18T03:51:59Z","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":"37f4e921742360af7caf8ef408f64208982dee9266500c6b4429b413aabb679b","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-07-02T18:58:28Z","title_canon_sha256":"d0c8b747c02d82dc1a43695cfa003d48999ebf2749b1349b5178921573faf491"},"schema_version":"1.0","source":{"id":"1207.0472","kind":"arxiv","version":1}},"canonical_sha256":"c9c5b2f7d84edd2306a44338b570e7db38011fd40c8e92480494feb8d45b3d94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9c5b2f7d84edd2306a44338b570e7db38011fd40c8e92480494feb8d45b3d94","first_computed_at":"2026-05-18T03:51:59.241262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:59.241262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AAjL2tEPpWjXxd/VqLgqSNX1AVfzd0YgOccHfhRzS8xtKNR0CTLqh1FhsORCNT4fVGYcfcjOlMgjshIupnr9Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:59.242242Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.0472","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a96148c97981f0b82ea6a350eaa768f95753fdd8ee4c66b6720535481821f9b0","sha256:6b4af3c138e15c04d5f89038706fb758e2d8e8907bc4df98e151726859ed5cfa"],"state_sha256":"6dfdfd10051804c7269bb0d9631e471291ae5d31dff14bfb70787bd93611621f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x3j1Bet7E/c5uR5HvI0e59jSvGFhrhAOmI0p7McaBzvgrPTuh48p5v4h5qdWXTz0Mh4WOI7Zsc/l3b218EODDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T20:29:14.894045Z","bundle_sha256":"42f1fe0c726048438717fda3ff2510b12cbc7a3e15d2c6edd906f9fd39db904a"}}