{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4GJL7X2FOJ42AZTXF6I5QJISPY","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":"7a0db596b912533f968a4eaa4afdc82f878cb1cdb134a07608bce4e91a651f7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-10-06T21:02:52Z","title_canon_sha256":"8102e382663b262165ad618921a891bdf35cdc5594ef3ef11ea0d849ca22576d"},"schema_version":"1.0","source":{"id":"1010.1278","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1278","created_at":"2026-05-18T04:39:48Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1278v1","created_at":"2026-05-18T04:39:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1278","created_at":"2026-05-18T04:39:48Z"},{"alias_kind":"pith_short_12","alias_value":"4GJL7X2FOJ42","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4GJL7X2FOJ42AZTX","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4GJL7X2F","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:8123cede778769b8761d2aadf7eb4750bd2b70bc38362b44e76d7f2b9543762d","target":"graph","created_at":"2026-05-18T04:39:48Z","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":"Let R be a commutative local noetherian ring, and let L and L' be R-modules. We investigate the properties of the functors Tor_i^R(L,-) and Ext^i_R(L,-). For instance, we show the following:\n  (a) if L is artinian and L' is noetherian, then Hom_R(L,L') has finite length;\n  (b) if L and L' are artinian, then the tensor product L \\otimes_R L' has finite length;\n  (c) if L and L' are artinian, then Tor_i^R(L,L') is artinian, and Ext^i_R(L,L') is noetherian over the completion \\hat R; and\n  (d) if L is artinian and L' is Matlis reflexive, then Ext^i_R(L,L'), Ext^i_R(L',L), and Tor_i^R(L,L') are Ma","authors_text":"Bethany Kubik, Micah J. Leamer, Sean Sather-Wagstaff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-10-06T21:02:52Z","title":"Homology of artinian and Matlis reflexive modules, I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1278","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:baa2bec69414e24efd528ff7d72cd8215354ee20a35d8fe9d090d733d02bb2a1","target":"record","created_at":"2026-05-18T04:39:48Z","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":"7a0db596b912533f968a4eaa4afdc82f878cb1cdb134a07608bce4e91a651f7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-10-06T21:02:52Z","title_canon_sha256":"8102e382663b262165ad618921a891bdf35cdc5594ef3ef11ea0d849ca22576d"},"schema_version":"1.0","source":{"id":"1010.1278","kind":"arxiv","version":1}},"canonical_sha256":"e192bfdf457279a066772f91d825127e2212d7edebbc9fac1c64303b989f03e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e192bfdf457279a066772f91d825127e2212d7edebbc9fac1c64303b989f03e9","first_computed_at":"2026-05-18T04:39:48.993666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:48.993666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yyNMDCSnyPjqec0GID6N03CGFJvLRLj1ZvniocgfOhfNHHdZkTLswBonp229dOq8KcQLidQcbqHiAOfEKWKQCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:48.994280Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.1278","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:baa2bec69414e24efd528ff7d72cd8215354ee20a35d8fe9d090d733d02bb2a1","sha256:8123cede778769b8761d2aadf7eb4750bd2b70bc38362b44e76d7f2b9543762d"],"state_sha256":"cf4f677e9198202cec2d0ce17642a21e135b4543a77991929703aa25bad17f7d"}