{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FRAINMM3KUGWHDSBLPJ3I5RULD","short_pith_number":"pith:FRAINMM3","canonical_record":{"source":{"id":"1602.04507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-14T21:01:00Z","cross_cats_sorted":[],"title_canon_sha256":"e35b3d175f7dc9d3fabd6573b66ff68e3012aaf6bc1b49d6e1938f28d4f54135","abstract_canon_sha256":"eea38804c21ba1111273192c1b3a9c7dafc046328bea5abb4f68abf6eba45a03"},"schema_version":"1.0"},"canonical_sha256":"2c4086b19b550d638e415bd3b4763458c8906567e1c4d77fee0c650ef5b641ce","source":{"kind":"arxiv","id":"1602.04507","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04507","created_at":"2026-05-18T01:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04507v1","created_at":"2026-05-18T01:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04507","created_at":"2026-05-18T01:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"FRAINMM3KUGW","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FRAINMM3KUGWHDSB","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FRAINMM3","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FRAINMM3KUGWHDSBLPJ3I5RULD","target":"record","payload":{"canonical_record":{"source":{"id":"1602.04507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-14T21:01:00Z","cross_cats_sorted":[],"title_canon_sha256":"e35b3d175f7dc9d3fabd6573b66ff68e3012aaf6bc1b49d6e1938f28d4f54135","abstract_canon_sha256":"eea38804c21ba1111273192c1b3a9c7dafc046328bea5abb4f68abf6eba45a03"},"schema_version":"1.0"},"canonical_sha256":"2c4086b19b550d638e415bd3b4763458c8906567e1c4d77fee0c650ef5b641ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:49.765852Z","signature_b64":"CMC+IViVpi06SZ4d/0FoHYgD01ST3oDUq6zly35ihUx66qKFwtig+JhN+iQNnvgp24mYVyu2Z2Jk/TQ23zLGBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c4086b19b550d638e415bd3b4763458c8906567e1c4d77fee0c650ef5b641ce","last_reissued_at":"2026-05-18T01:20:49.765305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:49.765305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.04507","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":"2026-05-18T01:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KTok+JQGk1Y6NcXskLnHZ+hQ4vL5IrFxlzPqZvm3XXPEFp9igzbFaSQrTZSvYYpYtOxpwxKxM9M3jXGVKtrGBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T10:33:07.563451Z"},"content_sha256":"8b48394948692b776f4e5068005d535fb99fbeda8fa7984a524b09220039cdcd","schema_version":"1.0","event_id":"sha256:8b48394948692b776f4e5068005d535fb99fbeda8fa7984a524b09220039cdcd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FRAINMM3KUGWHDSBLPJ3I5RULD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universal central extensions of superdialgebras of matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Manuel Ladra, Xabier Garc\\'ia-Mart\\'inez","submitted_at":"2016-02-14T21:01:00Z","abstract_excerpt":"We complete the problem of finding the universal central extension in the category of Leibniz superalgebras of $\\mathfrak{sl}(m, n, D)$ when $m+n \\geq 3$ and $D$ is a superdialgebra, solving in particular the problem when $D$ is an associative algebra, superalgebra or dialgebra. To accomplish this task we use a different method than the standard studied in the literature. We introduce and use the non-abelian tensor square of Leibniz superalgebras and its relations with the universal central extension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04507","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":"2026-05-18T01:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rIgvWYSvpPMFbDjxhW3+sUZw78jMZHzsMkw4ZjDE22HHTyjurC9QqiryYJdCoWOLuTOJ8I1AAc8iAkFC6+8lAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T10:33:07.563851Z"},"content_sha256":"d37c87c89d97b2559992ef81416d2bc4f15e56a9932083d2e2206917a884a415","schema_version":"1.0","event_id":"sha256:d37c87c89d97b2559992ef81416d2bc4f15e56a9932083d2e2206917a884a415"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FRAINMM3KUGWHDSBLPJ3I5RULD/bundle.json","state_url":"https://pith.science/pith/FRAINMM3KUGWHDSBLPJ3I5RULD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FRAINMM3KUGWHDSBLPJ3I5RULD/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":"2026-05-26T10:33:07Z","links":{"resolver":"https://pith.science/pith/FRAINMM3KUGWHDSBLPJ3I5RULD","bundle":"https://pith.science/pith/FRAINMM3KUGWHDSBLPJ3I5RULD/bundle.json","state":"https://pith.science/pith/FRAINMM3KUGWHDSBLPJ3I5RULD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FRAINMM3KUGWHDSBLPJ3I5RULD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FRAINMM3KUGWHDSBLPJ3I5RULD","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":"eea38804c21ba1111273192c1b3a9c7dafc046328bea5abb4f68abf6eba45a03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-14T21:01:00Z","title_canon_sha256":"e35b3d175f7dc9d3fabd6573b66ff68e3012aaf6bc1b49d6e1938f28d4f54135"},"schema_version":"1.0","source":{"id":"1602.04507","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04507","created_at":"2026-05-18T01:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04507v1","created_at":"2026-05-18T01:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04507","created_at":"2026-05-18T01:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"FRAINMM3KUGW","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FRAINMM3KUGWHDSB","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FRAINMM3","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:d37c87c89d97b2559992ef81416d2bc4f15e56a9932083d2e2206917a884a415","target":"graph","created_at":"2026-05-18T01:20:49Z","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 complete the problem of finding the universal central extension in the category of Leibniz superalgebras of $\\mathfrak{sl}(m, n, D)$ when $m+n \\geq 3$ and $D$ is a superdialgebra, solving in particular the problem when $D$ is an associative algebra, superalgebra or dialgebra. To accomplish this task we use a different method than the standard studied in the literature. We introduce and use the non-abelian tensor square of Leibniz superalgebras and its relations with the universal central extension.","authors_text":"Manuel Ladra, Xabier Garc\\'ia-Mart\\'inez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-14T21:01:00Z","title":"Universal central extensions of superdialgebras of matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04507","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":"sha256:8b48394948692b776f4e5068005d535fb99fbeda8fa7984a524b09220039cdcd","target":"record","created_at":"2026-05-18T01:20:49Z","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":"eea38804c21ba1111273192c1b3a9c7dafc046328bea5abb4f68abf6eba45a03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-14T21:01:00Z","title_canon_sha256":"e35b3d175f7dc9d3fabd6573b66ff68e3012aaf6bc1b49d6e1938f28d4f54135"},"schema_version":"1.0","source":{"id":"1602.04507","kind":"arxiv","version":1}},"canonical_sha256":"2c4086b19b550d638e415bd3b4763458c8906567e1c4d77fee0c650ef5b641ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c4086b19b550d638e415bd3b4763458c8906567e1c4d77fee0c650ef5b641ce","first_computed_at":"2026-05-18T01:20:49.765305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:49.765305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CMC+IViVpi06SZ4d/0FoHYgD01ST3oDUq6zly35ihUx66qKFwtig+JhN+iQNnvgp24mYVyu2Z2Jk/TQ23zLGBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:49.765852Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04507","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b48394948692b776f4e5068005d535fb99fbeda8fa7984a524b09220039cdcd","sha256:d37c87c89d97b2559992ef81416d2bc4f15e56a9932083d2e2206917a884a415"],"state_sha256":"b9dc06589e97c8525b67efcbfe6d8112ea87ea396b899584f7d3b815812ea1ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W4dPuRJqaCMKfZ2qZJ44Kb06T8Ib7ODtLWgwePzKm4znLl58zYmElGX3SwLHLz48ooyqOsLKaDsFEYiK7PNVBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T10:33:07.566514Z","bundle_sha256":"210a66bc794d7d9629a172c4695b3e146a0aba6380eb03142e4b3da808772ab2"}}