{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2LOSNXGMME3JDX4JO6KMZAR35U","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":"2ef2332cf7390365244e23f200aa0d087cbe5a3f0b48a4aed4d9b680aeb2c310","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2017-02-15T12:21:07Z","title_canon_sha256":"7bcd030740a40a647e9ecf6e4aa814d21be3752115fd90defa2e2e9bef508b49"},"schema_version":"1.0","source":{"id":"1702.04575","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04575","created_at":"2026-05-18T00:34:22Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04575v2","created_at":"2026-05-18T00:34:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04575","created_at":"2026-05-18T00:34:22Z"},{"alias_kind":"pith_short_12","alias_value":"2LOSNXGMME3J","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2LOSNXGMME3JDX4J","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2LOSNXGM","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:61f26ec99ac7a130c0e709d0aa97c3115f23b098133a9b5a53f3ef033ffd9050","target":"graph","created_at":"2026-05-18T00:34:22Z","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 provide a framework connecting several well known theories related to the linearity of graded modules over graded algebras. In the first part, we pay a particular attention to the tensor products of graded bimodules over graded algebras. Finally, we provide a tool to evaluate the possible degrees of a module appearing in a graded projective resolution once the generating degrees for the first term of some particular projective resolution are known.","authors_text":"Andrea Solotar, Eduardo Marcos, Yury Volkov","cross_cats":["math.RA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2017-02-15T12:21:07Z","title":"Generating degrees for graded projective resolutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04575","kind":"arxiv","version":2},"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:eb5eda8f86fdbd53219ed89508a7398775bce09930908ffb65aefca27beb8c02","target":"record","created_at":"2026-05-18T00:34:22Z","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":"2ef2332cf7390365244e23f200aa0d087cbe5a3f0b48a4aed4d9b680aeb2c310","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2017-02-15T12:21:07Z","title_canon_sha256":"7bcd030740a40a647e9ecf6e4aa814d21be3752115fd90defa2e2e9bef508b49"},"schema_version":"1.0","source":{"id":"1702.04575","kind":"arxiv","version":2}},"canonical_sha256":"d2dd26dccc613691df897794cc823bed1db3379464eb9be44e74ca37407084ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2dd26dccc613691df897794cc823bed1db3379464eb9be44e74ca37407084ba","first_computed_at":"2026-05-18T00:34:22.872132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:22.872132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yp7XTvH+kdFXWVbW0m2ABK04ZToeULAgPusnE6V7QxRQ8pN/hfagqV0JJq6vycq+aU+CoNmVIsYzeUjLrsxvCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:22.872611Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.04575","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb5eda8f86fdbd53219ed89508a7398775bce09930908ffb65aefca27beb8c02","sha256:61f26ec99ac7a130c0e709d0aa97c3115f23b098133a9b5a53f3ef033ffd9050"],"state_sha256":"66a6a49e51c76ebf0722d8ed5c34865e3ecaa6da481a5785312caf2e945bd4a8"}