{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:25VUXUPH4B6SW7Z3UQKDU3G25X","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":"9c9771514fee5299b75811d0ab8c3f028df0f89cb946114a2175ac52ab4055e2","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-11T18:51:21Z","title_canon_sha256":"91570ae1dbf881599eb2978a481d456ae88d62dee3c6f73432fa1bd5c1b118f8"},"schema_version":"1.0","source":{"id":"1412.3759","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3759","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3759v2","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3759","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"25VUXUPH4B6S","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"25VUXUPH4B6SW7Z3","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"25VUXUPH","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:8a92efa8795e8b00145b0f39bbc1efcbfe33c48eb7ce8e449de60eb63465411c","target":"graph","created_at":"2026-05-18T00:08:24Z","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 $k$ be a field, and let $X,Y$ be two locally noetherian $k$-schemes (respectively $k$-formal schemes) with dualizing complexes $R_X$ and $R_Y$ respectively. We show that $R_X \\boxtimes_{k} R_Y$ (respectively its derived completion) is a dualizing complex over $X\\times_{k} Y$ if and only if $X\\times_{k} Y$ is locally noetherian of finite Krull dimension.","authors_text":"Liran Shaul","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-11T18:51:21Z","title":"Tensor product of dualizing complexes over a field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3759","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":"sha256:1e0d58df3084823bab65c7095c13b18ec11d58a42424d2b704282463bdf364cc","target":"record","created_at":"2026-05-18T00:08:24Z","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":"9c9771514fee5299b75811d0ab8c3f028df0f89cb946114a2175ac52ab4055e2","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-11T18:51:21Z","title_canon_sha256":"91570ae1dbf881599eb2978a481d456ae88d62dee3c6f73432fa1bd5c1b118f8"},"schema_version":"1.0","source":{"id":"1412.3759","kind":"arxiv","version":2}},"canonical_sha256":"d76b4bd1e7e07d2b7f3ba4143a6cdaedcc14ecd6e5585a001bee2cd944dd7579","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d76b4bd1e7e07d2b7f3ba4143a6cdaedcc14ecd6e5585a001bee2cd944dd7579","first_computed_at":"2026-05-18T00:08:24.348855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:24.348855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A3fiiH7ngCyb4LJRTs7aEeAvD62jvleHhd1It+mNcy9HyzjLPF8BOOIcpTsr5z0GlMD7TzWUUmAWzCCukhsBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:24.349391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3759","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e0d58df3084823bab65c7095c13b18ec11d58a42424d2b704282463bdf364cc","sha256:8a92efa8795e8b00145b0f39bbc1efcbfe33c48eb7ce8e449de60eb63465411c"],"state_sha256":"95114c6614ef042a62356ecebfa5c5e2bf897ae7bac3016d6b711352ba593aa6"}