{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5APOC6ZOS77V6BWEGOS4F6FLKN","short_pith_number":"pith:5APOC6ZO","canonical_record":{"source":{"id":"1812.09577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-12-22T18:15:42Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"e5b543d4013bb3a9cbb423ff26e960f95fd70fae18484fb248306f4019927047","abstract_canon_sha256":"55f3297a1fd9ffdb17bde319cbdef344816742a9ef56090c466d83604c5d94ac"},"schema_version":"1.0"},"canonical_sha256":"e81ee17b2e97ff5f06c433a5c2f8ab536aa2aacc41e25c72f5e711d2e1fdc02f","source":{"kind":"arxiv","id":"1812.09577","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09577","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09577v1","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09577","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"pith_short_12","alias_value":"5APOC6ZOS77V","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5APOC6ZOS77V6BWE","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5APOC6ZO","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5APOC6ZOS77V6BWEGOS4F6FLKN","target":"record","payload":{"canonical_record":{"source":{"id":"1812.09577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-12-22T18:15:42Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"e5b543d4013bb3a9cbb423ff26e960f95fd70fae18484fb248306f4019927047","abstract_canon_sha256":"55f3297a1fd9ffdb17bde319cbdef344816742a9ef56090c466d83604c5d94ac"},"schema_version":"1.0"},"canonical_sha256":"e81ee17b2e97ff5f06c433a5c2f8ab536aa2aacc41e25c72f5e711d2e1fdc02f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:27.506464Z","signature_b64":"Y0C2A42DtqiE6VvupSReqtZqQt/q2YorE1YsPbDVY0RqmI00pFp7lLAXY8cwEEug5LxRoUfei2iqoVjt6uAuBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e81ee17b2e97ff5f06c433a5c2f8ab536aa2aacc41e25c72f5e711d2e1fdc02f","last_reissued_at":"2026-05-17T23:57:27.505867Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:27.505867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.09577","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":"2026-05-17T23:57:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cp+H8Cf3R00fZ2NX+P7IatpgtYHUKn7tJFhk+VJgxwOROVlFhjc/zrfrlvYlbRe53sLuz6TfRDfUmCK5kStaAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T09:47:31.744796Z"},"content_sha256":"93259f01f6db58d31f40972e9049d443270d95d31593c4c56ecbd5c216bcd067","schema_version":"1.0","event_id":"sha256:93259f01f6db58d31f40972e9049d443270d95d31593c4c56ecbd5c216bcd067"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5APOC6ZOS77V6BWEGOS4F6FLKN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Supersymmetric elements in divided powers algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Frantisek Marko","submitted_at":"2018-12-22T18:15:42Z","abstract_excerpt":"Description of adjoint invariants of general Linear Lie superalgebras $\\mathfrak{gl}(m|n)$ by Kantor and Trishin is given in terms of supersymmetric polynomials. Later, generators of invariants of the adjoint action of the general linear supergroup $GL(m|n)$ and generators of supersymmetric polynomials were determined over fields of positive characteristic. In this paper, we introduce the concept of supersymmetric elements in the divided powers algebra $Div[x_1, \\ldots, x_m,y_1, \\ldots, y_n]$, and give a characterization of supersymmetric elements via a system of linear equations. Then we dete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09577","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":"2026-05-17T23:57:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UztjBsowoulj+PACkwjH8HfYYTckHo8Np6AvxZDeUP1C5m8qucqvXeq3ZwKhtzJAQoLUq51Ft8ALQZ0/7jr8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T09:47:31.745140Z"},"content_sha256":"0a5738e42c369579074308ee95e1365474c56c56276d9a1cafc16b1a0c4238a2","schema_version":"1.0","event_id":"sha256:0a5738e42c369579074308ee95e1365474c56c56276d9a1cafc16b1a0c4238a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5APOC6ZOS77V6BWEGOS4F6FLKN/bundle.json","state_url":"https://pith.science/pith/5APOC6ZOS77V6BWEGOS4F6FLKN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5APOC6ZOS77V6BWEGOS4F6FLKN/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":"2026-06-30T09:47:31Z","links":{"resolver":"https://pith.science/pith/5APOC6ZOS77V6BWEGOS4F6FLKN","bundle":"https://pith.science/pith/5APOC6ZOS77V6BWEGOS4F6FLKN/bundle.json","state":"https://pith.science/pith/5APOC6ZOS77V6BWEGOS4F6FLKN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5APOC6ZOS77V6BWEGOS4F6FLKN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5APOC6ZOS77V6BWEGOS4F6FLKN","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":"55f3297a1fd9ffdb17bde319cbdef344816742a9ef56090c466d83604c5d94ac","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-12-22T18:15:42Z","title_canon_sha256":"e5b543d4013bb3a9cbb423ff26e960f95fd70fae18484fb248306f4019927047"},"schema_version":"1.0","source":{"id":"1812.09577","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09577","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09577v1","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09577","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"pith_short_12","alias_value":"5APOC6ZOS77V","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5APOC6ZOS77V6BWE","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5APOC6ZO","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:0a5738e42c369579074308ee95e1365474c56c56276d9a1cafc16b1a0c4238a2","target":"graph","created_at":"2026-05-17T23:57:27Z","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":"Description of adjoint invariants of general Linear Lie superalgebras $\\mathfrak{gl}(m|n)$ by Kantor and Trishin is given in terms of supersymmetric polynomials. Later, generators of invariants of the adjoint action of the general linear supergroup $GL(m|n)$ and generators of supersymmetric polynomials were determined over fields of positive characteristic. In this paper, we introduce the concept of supersymmetric elements in the divided powers algebra $Div[x_1, \\ldots, x_m,y_1, \\ldots, y_n]$, and give a characterization of supersymmetric elements via a system of linear equations. Then we dete","authors_text":"Frantisek Marko","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-12-22T18:15:42Z","title":"Supersymmetric elements in divided powers algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09577","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":"sha256:93259f01f6db58d31f40972e9049d443270d95d31593c4c56ecbd5c216bcd067","target":"record","created_at":"2026-05-17T23:57:27Z","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":"55f3297a1fd9ffdb17bde319cbdef344816742a9ef56090c466d83604c5d94ac","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-12-22T18:15:42Z","title_canon_sha256":"e5b543d4013bb3a9cbb423ff26e960f95fd70fae18484fb248306f4019927047"},"schema_version":"1.0","source":{"id":"1812.09577","kind":"arxiv","version":1}},"canonical_sha256":"e81ee17b2e97ff5f06c433a5c2f8ab536aa2aacc41e25c72f5e711d2e1fdc02f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e81ee17b2e97ff5f06c433a5c2f8ab536aa2aacc41e25c72f5e711d2e1fdc02f","first_computed_at":"2026-05-17T23:57:27.505867Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:27.505867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y0C2A42DtqiE6VvupSReqtZqQt/q2YorE1YsPbDVY0RqmI00pFp7lLAXY8cwEEug5LxRoUfei2iqoVjt6uAuBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:27.506464Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.09577","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93259f01f6db58d31f40972e9049d443270d95d31593c4c56ecbd5c216bcd067","sha256:0a5738e42c369579074308ee95e1365474c56c56276d9a1cafc16b1a0c4238a2"],"state_sha256":"c22573ee463ff6f6609b3277f8f5a7ac74e720851460a3095c85ef541c475b02"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"teSDySLfC61/HuSjSgVD/7pRp1S7c7frkPRUGKCOrGiY2tM1EfiFmFbOXloCsoonUL9KIypLYaE591tvCn+VAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T09:47:31.747093Z","bundle_sha256":"05cffd47623bc5e4cd7717031bd4aa04d7dfe11c848322039f3a58028426638a"}}