{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:EOOI2JZ7YURIUVFZJ3FXRQTFPH","short_pith_number":"pith:EOOI2JZ7","schema_version":"1.0","canonical_sha256":"239c8d273fc5228a54b94ecb78c26579cc3392f11635438aa33e5d3ac49719d8","source":{"kind":"arxiv","id":"1711.10664","version":1},"attestation_state":"computed","paper":{"title":"$s$-homogeneous algebras via $s$-homogeneous triples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.KT","authors_text":"Eduardo do Nascimento Marcos, Yury Volkov","submitted_at":"2017-11-29T03:33:55Z","abstract_excerpt":"To study $s$-homogeneous algebras, we introduce the category of quivers with $s$-homogeneous corelations and the category of $s$-homogeneous triples. We show that both of these categories are equivalent to the category of $s$-homogeneous algebras. We prove some properties of the elements of $s$-homogeneous triples and give some consequences for $s$-Koszul algebras. Then we discuss the relations between the $s$-Koszulity and the Hilbert series of $s$-homogeneous triples. We give some application of the obtained results to $s$-homogeneous algebras with simple zero component. We describe all $s$-"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1711.10664","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2017-11-29T03:33:55Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"240a6de542dbad0b03f6cd1be884390d7a669c208417da22c0d35b17f1f10919","abstract_canon_sha256":"a54f1223c8f1ec433cffb0dd1f9acfb4728cb81f9567bdfb3d64c50890c21bb4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:17.335131Z","signature_b64":"PttuT5sFK2DdbvEayPW8XzdCOaJz9cLQ7hWuND8GPENUlnwS/oe+Yz5qwfvkSo4quLOyN5898DcgD1Y+PLyICw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"239c8d273fc5228a54b94ecb78c26579cc3392f11635438aa33e5d3ac49719d8","last_reissued_at":"2026-05-18T00:29:17.334337Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:17.334337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$s$-homogeneous algebras via $s$-homogeneous triples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.KT","authors_text":"Eduardo do Nascimento Marcos, Yury Volkov","submitted_at":"2017-11-29T03:33:55Z","abstract_excerpt":"To study $s$-homogeneous algebras, we introduce the category of quivers with $s$-homogeneous corelations and the category of $s$-homogeneous triples. We show that both of these categories are equivalent to the category of $s$-homogeneous algebras. We prove some properties of the elements of $s$-homogeneous triples and give some consequences for $s$-Koszul algebras. Then we discuss the relations between the $s$-Koszulity and the Hilbert series of $s$-homogeneous triples. We give some application of the obtained results to $s$-homogeneous algebras with simple zero component. We describe all $s$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10664","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1711.10664","created_at":"2026-05-18T00:29:17.334481+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.10664v1","created_at":"2026-05-18T00:29:17.334481+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10664","created_at":"2026-05-18T00:29:17.334481+00:00"},{"alias_kind":"pith_short_12","alias_value":"EOOI2JZ7YURI","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"EOOI2JZ7YURIUVFZ","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"EOOI2JZ7","created_at":"2026-05-18T12:31:12.930513+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EOOI2JZ7YURIUVFZJ3FXRQTFPH","json":"https://pith.science/pith/EOOI2JZ7YURIUVFZJ3FXRQTFPH.json","graph_json":"https://pith.science/api/pith-number/EOOI2JZ7YURIUVFZJ3FXRQTFPH/graph.json","events_json":"https://pith.science/api/pith-number/EOOI2JZ7YURIUVFZJ3FXRQTFPH/events.json","paper":"https://pith.science/paper/EOOI2JZ7"},"agent_actions":{"view_html":"https://pith.science/pith/EOOI2JZ7YURIUVFZJ3FXRQTFPH","download_json":"https://pith.science/pith/EOOI2JZ7YURIUVFZJ3FXRQTFPH.json","view_paper":"https://pith.science/paper/EOOI2JZ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.10664&json=true","fetch_graph":"https://pith.science/api/pith-number/EOOI2JZ7YURIUVFZJ3FXRQTFPH/graph.json","fetch_events":"https://pith.science/api/pith-number/EOOI2JZ7YURIUVFZJ3FXRQTFPH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EOOI2JZ7YURIUVFZJ3FXRQTFPH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EOOI2JZ7YURIUVFZJ3FXRQTFPH/action/storage_attestation","attest_author":"https://pith.science/pith/EOOI2JZ7YURIUVFZJ3FXRQTFPH/action/author_attestation","sign_citation":"https://pith.science/pith/EOOI2JZ7YURIUVFZJ3FXRQTFPH/action/citation_signature","submit_replication":"https://pith.science/pith/EOOI2JZ7YURIUVFZJ3FXRQTFPH/action/replication_record"}},"created_at":"2026-05-18T00:29:17.334481+00:00","updated_at":"2026-05-18T00:29:17.334481+00:00"}