{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2000:SOZHQPTLHVOZT4KUKQTTGPJQNR","short_pith_number":"pith:SOZHQPTL","schema_version":"1.0","canonical_sha256":"93b2783e6b3d5d99f1545427333d306c794850a37b1948f624b3690661bf6bfa","source":{"kind":"arxiv","id":"math/0012125","version":2},"attestation_state":"computed","paper":{"title":"Tensor products of C(X)-algebras over C(X)","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Etienne Blanchard","submitted_at":"2000-12-15T12:54:56Z","abstract_excerpt":"Given a Hausdorff compact space X, we study the C^*-(semi)-norms on the algebraic tensor product $A\\otimes_{alg,C(X)} B$ of two C(X)-algebras A and B over C(X). In particular, if one of the two C(X)-algebras defines a continuous field of C^*-algebras over X, there exist minimal and maximal C^*-norms on $A\\otimes_{alg,C(X)} B$ but there does not exist any C^*-norm on $A\\otimes_{alg,C(X)} B$ in general."},"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":"math/0012125","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2000-12-15T12:54:56Z","cross_cats_sorted":[],"title_canon_sha256":"e34b9aaaae2aa47e6400099de5625cc78313288e17aea90ba3e50e12518c599c","abstract_canon_sha256":"413c272562651570efc94fe11ee5dd9b42c0c029837a707e67e5b6efb4bc8683"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:38.022509Z","signature_b64":"DfSMtWfiPS2BsrGVclL7mbcgc7NShbVX2wkeqSdlVVuWy/UtGO18GQCq5xv1IRflKSSU3vQoUskYs3xlfjJ1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93b2783e6b3d5d99f1545427333d306c794850a37b1948f624b3690661bf6bfa","last_reissued_at":"2026-05-18T01:05:38.021784Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:38.021784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tensor products of C(X)-algebras over C(X)","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Etienne Blanchard","submitted_at":"2000-12-15T12:54:56Z","abstract_excerpt":"Given a Hausdorff compact space X, we study the C^*-(semi)-norms on the algebraic tensor product $A\\otimes_{alg,C(X)} B$ of two C(X)-algebras A and B over C(X). In particular, if one of the two C(X)-algebras defines a continuous field of C^*-algebras over X, there exist minimal and maximal C^*-norms on $A\\otimes_{alg,C(X)} B$ but there does not exist any C^*-norm on $A\\otimes_{alg,C(X)} B$ in general."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0012125","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":"math/0012125","created_at":"2026-05-18T01:05:38.021904+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0012125v2","created_at":"2026-05-18T01:05:38.021904+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0012125","created_at":"2026-05-18T01:05:38.021904+00:00"},{"alias_kind":"pith_short_12","alias_value":"SOZHQPTLHVOZ","created_at":"2026-05-18T12:25:50.254431+00:00"},{"alias_kind":"pith_short_16","alias_value":"SOZHQPTLHVOZT4KU","created_at":"2026-05-18T12:25:50.254431+00:00"},{"alias_kind":"pith_short_8","alias_value":"SOZHQPTL","created_at":"2026-05-18T12:25:50.254431+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/SOZHQPTLHVOZT4KUKQTTGPJQNR","json":"https://pith.science/pith/SOZHQPTLHVOZT4KUKQTTGPJQNR.json","graph_json":"https://pith.science/api/pith-number/SOZHQPTLHVOZT4KUKQTTGPJQNR/graph.json","events_json":"https://pith.science/api/pith-number/SOZHQPTLHVOZT4KUKQTTGPJQNR/events.json","paper":"https://pith.science/paper/SOZHQPTL"},"agent_actions":{"view_html":"https://pith.science/pith/SOZHQPTLHVOZT4KUKQTTGPJQNR","download_json":"https://pith.science/pith/SOZHQPTLHVOZT4KUKQTTGPJQNR.json","view_paper":"https://pith.science/paper/SOZHQPTL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0012125&json=true","fetch_graph":"https://pith.science/api/pith-number/SOZHQPTLHVOZT4KUKQTTGPJQNR/graph.json","fetch_events":"https://pith.science/api/pith-number/SOZHQPTLHVOZT4KUKQTTGPJQNR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SOZHQPTLHVOZT4KUKQTTGPJQNR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SOZHQPTLHVOZT4KUKQTTGPJQNR/action/storage_attestation","attest_author":"https://pith.science/pith/SOZHQPTLHVOZT4KUKQTTGPJQNR/action/author_attestation","sign_citation":"https://pith.science/pith/SOZHQPTLHVOZT4KUKQTTGPJQNR/action/citation_signature","submit_replication":"https://pith.science/pith/SOZHQPTLHVOZT4KUKQTTGPJQNR/action/replication_record"}},"created_at":"2026-05-18T01:05:38.021904+00:00","updated_at":"2026-05-18T01:05:38.021904+00:00"}