{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:25VUXUPH4B6SW7Z3UQKDU3G25X","short_pith_number":"pith:25VUXUPH","schema_version":"1.0","canonical_sha256":"d76b4bd1e7e07d2b7f3ba4143a6cdaedcc14ecd6e5585a001bee2cd944dd7579","source":{"kind":"arxiv","id":"1412.3759","version":2},"attestation_state":"computed","paper":{"title":"Tensor product of dualizing complexes over a field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Liran Shaul","submitted_at":"2014-12-11T18:51:21Z","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."},"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":"1412.3759","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-11T18:51:21Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"91570ae1dbf881599eb2978a481d456ae88d62dee3c6f73432fa1bd5c1b118f8","abstract_canon_sha256":"9c9771514fee5299b75811d0ab8c3f028df0f89cb946114a2175ac52ab4055e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:24.349391Z","signature_b64":"A3fiiH7ngCyb4LJRTs7aEeAvD62jvleHhd1It+mNcy9HyzjLPF8BOOIcpTsr5z0GlMD7TzWUUmAWzCCukhsBBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d76b4bd1e7e07d2b7f3ba4143a6cdaedcc14ecd6e5585a001bee2cd944dd7579","last_reissued_at":"2026-05-18T00:08:24.348855Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:24.348855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tensor product of dualizing complexes over a field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Liran Shaul","submitted_at":"2014-12-11T18:51:21Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3759","kind":"arxiv","version":2},"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":"1412.3759","created_at":"2026-05-18T00:08:24.348928+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.3759v2","created_at":"2026-05-18T00:08:24.348928+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3759","created_at":"2026-05-18T00:08:24.348928+00:00"},{"alias_kind":"pith_short_12","alias_value":"25VUXUPH4B6S","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"25VUXUPH4B6SW7Z3","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"25VUXUPH","created_at":"2026-05-18T12:28:09.283467+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/25VUXUPH4B6SW7Z3UQKDU3G25X","json":"https://pith.science/pith/25VUXUPH4B6SW7Z3UQKDU3G25X.json","graph_json":"https://pith.science/api/pith-number/25VUXUPH4B6SW7Z3UQKDU3G25X/graph.json","events_json":"https://pith.science/api/pith-number/25VUXUPH4B6SW7Z3UQKDU3G25X/events.json","paper":"https://pith.science/paper/25VUXUPH"},"agent_actions":{"view_html":"https://pith.science/pith/25VUXUPH4B6SW7Z3UQKDU3G25X","download_json":"https://pith.science/pith/25VUXUPH4B6SW7Z3UQKDU3G25X.json","view_paper":"https://pith.science/paper/25VUXUPH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.3759&json=true","fetch_graph":"https://pith.science/api/pith-number/25VUXUPH4B6SW7Z3UQKDU3G25X/graph.json","fetch_events":"https://pith.science/api/pith-number/25VUXUPH4B6SW7Z3UQKDU3G25X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/25VUXUPH4B6SW7Z3UQKDU3G25X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/25VUXUPH4B6SW7Z3UQKDU3G25X/action/storage_attestation","attest_author":"https://pith.science/pith/25VUXUPH4B6SW7Z3UQKDU3G25X/action/author_attestation","sign_citation":"https://pith.science/pith/25VUXUPH4B6SW7Z3UQKDU3G25X/action/citation_signature","submit_replication":"https://pith.science/pith/25VUXUPH4B6SW7Z3UQKDU3G25X/action/replication_record"}},"created_at":"2026-05-18T00:08:24.348928+00:00","updated_at":"2026-05-18T00:08:24.348928+00:00"}