{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:KOZYF2IUNZSFIHY4VLEO4PXEBX","short_pith_number":"pith:KOZYF2IU","schema_version":"1.0","canonical_sha256":"53b382e9146e64541f1caac8ee3ee40dd369e1511f0b7ded57b84f04db4aae14","source":{"kind":"arxiv","id":"1407.5025","version":3},"attestation_state":"computed","paper":{"title":"A cohomological interpretation of derivations on graded algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mathias Schulze, Xia Liao","submitted_at":"2014-07-18T15:05:15Z","abstract_excerpt":"We trace derivations through Demazure's correspondence between a finitely generated positively graded normal $k$-algebras $A$ and normal projective $k$-varieties $X$ equipped with an ample $\\mathbb{Q}$-Cartier $\\mathbb{Q}$-divisor $D$. We obtain a generalized Euler sequence involving a sheaf on $X$ whose space of global sections consists of all homogeneous $k$-linear derivations of $A$ and a sheaf of logarithmic derivations on $X$."},"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":"1407.5025","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-18T15:05:15Z","cross_cats_sorted":[],"title_canon_sha256":"f38406b7f2e801fa738788e68a9e51fe59d7a0dd24fa0386b505ac411868718b","abstract_canon_sha256":"7613726c1bf33b66c858e9905f596613298daa2ad11fc90a757d03a80bbc4ee4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:50.248380Z","signature_b64":"/1kkCcUecH5B3W+0/mEZC7pWzaI7hHSWqs+SahjY2gq/s2sllFHTVNWN19HrebidhQTB8s2JTvzL5S1GqY8jCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53b382e9146e64541f1caac8ee3ee40dd369e1511f0b7ded57b84f04db4aae14","last_reissued_at":"2026-05-18T00:02:50.247799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:50.247799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A cohomological interpretation of derivations on graded algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mathias Schulze, Xia Liao","submitted_at":"2014-07-18T15:05:15Z","abstract_excerpt":"We trace derivations through Demazure's correspondence between a finitely generated positively graded normal $k$-algebras $A$ and normal projective $k$-varieties $X$ equipped with an ample $\\mathbb{Q}$-Cartier $\\mathbb{Q}$-divisor $D$. We obtain a generalized Euler sequence involving a sheaf on $X$ whose space of global sections consists of all homogeneous $k$-linear derivations of $A$ and a sheaf of logarithmic derivations on $X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5025","kind":"arxiv","version":3},"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":"1407.5025","created_at":"2026-05-18T00:02:50.247888+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.5025v3","created_at":"2026-05-18T00:02:50.247888+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5025","created_at":"2026-05-18T00:02:50.247888+00:00"},{"alias_kind":"pith_short_12","alias_value":"KOZYF2IUNZSF","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"KOZYF2IUNZSFIHY4","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"KOZYF2IU","created_at":"2026-05-18T12:28:35.611951+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/KOZYF2IUNZSFIHY4VLEO4PXEBX","json":"https://pith.science/pith/KOZYF2IUNZSFIHY4VLEO4PXEBX.json","graph_json":"https://pith.science/api/pith-number/KOZYF2IUNZSFIHY4VLEO4PXEBX/graph.json","events_json":"https://pith.science/api/pith-number/KOZYF2IUNZSFIHY4VLEO4PXEBX/events.json","paper":"https://pith.science/paper/KOZYF2IU"},"agent_actions":{"view_html":"https://pith.science/pith/KOZYF2IUNZSFIHY4VLEO4PXEBX","download_json":"https://pith.science/pith/KOZYF2IUNZSFIHY4VLEO4PXEBX.json","view_paper":"https://pith.science/paper/KOZYF2IU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.5025&json=true","fetch_graph":"https://pith.science/api/pith-number/KOZYF2IUNZSFIHY4VLEO4PXEBX/graph.json","fetch_events":"https://pith.science/api/pith-number/KOZYF2IUNZSFIHY4VLEO4PXEBX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KOZYF2IUNZSFIHY4VLEO4PXEBX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KOZYF2IUNZSFIHY4VLEO4PXEBX/action/storage_attestation","attest_author":"https://pith.science/pith/KOZYF2IUNZSFIHY4VLEO4PXEBX/action/author_attestation","sign_citation":"https://pith.science/pith/KOZYF2IUNZSFIHY4VLEO4PXEBX/action/citation_signature","submit_replication":"https://pith.science/pith/KOZYF2IUNZSFIHY4VLEO4PXEBX/action/replication_record"}},"created_at":"2026-05-18T00:02:50.247888+00:00","updated_at":"2026-05-18T00:02:50.247888+00:00"}