{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZQBKJHKAS7PHGITZFZ3G3GS3SE","short_pith_number":"pith:ZQBKJHKA","schema_version":"1.0","canonical_sha256":"cc02a49d4097de7322792e766d9a5b911bd611ca689ffea0fee4f51d4c955403","source":{"kind":"arxiv","id":"1512.09101","version":2},"attestation_state":"computed","paper":{"title":"Picard groups, weight structures, and (noncommutative) mixed motives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT","math.KT","math.RT"],"primary_cat":"math.AG","authors_text":"Goncalo Tabuada, Mikhail Bondarko","submitted_at":"2015-12-30T20:22:30Z","abstract_excerpt":"We develop a general theory which enables the computation of the Picard group of a symmetric monoidal triangulated category, equipped with a weight structure, in terms of the Picard group of the associated heart. As an application, we compute the Picard group of several categories of motivic nature - mixed Artin motives, mixed Artin-Tate motives, motivic spectra, noncommutative mixed Artin motives, noncommutative mixed motives of central simple algebras, noncommutative mixed motives of separable algebras - as well as the Picard group of the derived categories of symmetric ring spectra."},"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":"1512.09101","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-30T20:22:30Z","cross_cats_sorted":["math.AT","math.CT","math.KT","math.RT"],"title_canon_sha256":"27f3bda4fc6e21080cecf0369e5d62205e66bcc263cd0f4479e0e45d040fe255","abstract_canon_sha256":"1141c3ce5f1160d5478b48b700f0973eec8dbd8709f91ec7716d84b55e6d7e1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:28.470891Z","signature_b64":"Gc5abK6UMCpfybGAxL+/Q/DjZj33/pA65FQxm7tXe5/f23dtBbQMyWmYMpatOMrZJ9ecKmR6mNouuGe6oHRbAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc02a49d4097de7322792e766d9a5b911bd611ca689ffea0fee4f51d4c955403","last_reissued_at":"2026-05-18T01:23:28.469965Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:28.469965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Picard groups, weight structures, and (noncommutative) mixed motives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT","math.KT","math.RT"],"primary_cat":"math.AG","authors_text":"Goncalo Tabuada, Mikhail Bondarko","submitted_at":"2015-12-30T20:22:30Z","abstract_excerpt":"We develop a general theory which enables the computation of the Picard group of a symmetric monoidal triangulated category, equipped with a weight structure, in terms of the Picard group of the associated heart. As an application, we compute the Picard group of several categories of motivic nature - mixed Artin motives, mixed Artin-Tate motives, motivic spectra, noncommutative mixed Artin motives, noncommutative mixed motives of central simple algebras, noncommutative mixed motives of separable algebras - as well as the Picard group of the derived categories of symmetric ring spectra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09101","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":"1512.09101","created_at":"2026-05-18T01:23:28.470115+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.09101v2","created_at":"2026-05-18T01:23:28.470115+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.09101","created_at":"2026-05-18T01:23:28.470115+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZQBKJHKAS7PH","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZQBKJHKAS7PHGITZ","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZQBKJHKA","created_at":"2026-05-18T12:29:52.810259+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/ZQBKJHKAS7PHGITZFZ3G3GS3SE","json":"https://pith.science/pith/ZQBKJHKAS7PHGITZFZ3G3GS3SE.json","graph_json":"https://pith.science/api/pith-number/ZQBKJHKAS7PHGITZFZ3G3GS3SE/graph.json","events_json":"https://pith.science/api/pith-number/ZQBKJHKAS7PHGITZFZ3G3GS3SE/events.json","paper":"https://pith.science/paper/ZQBKJHKA"},"agent_actions":{"view_html":"https://pith.science/pith/ZQBKJHKAS7PHGITZFZ3G3GS3SE","download_json":"https://pith.science/pith/ZQBKJHKAS7PHGITZFZ3G3GS3SE.json","view_paper":"https://pith.science/paper/ZQBKJHKA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.09101&json=true","fetch_graph":"https://pith.science/api/pith-number/ZQBKJHKAS7PHGITZFZ3G3GS3SE/graph.json","fetch_events":"https://pith.science/api/pith-number/ZQBKJHKAS7PHGITZFZ3G3GS3SE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZQBKJHKAS7PHGITZFZ3G3GS3SE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZQBKJHKAS7PHGITZFZ3G3GS3SE/action/storage_attestation","attest_author":"https://pith.science/pith/ZQBKJHKAS7PHGITZFZ3G3GS3SE/action/author_attestation","sign_citation":"https://pith.science/pith/ZQBKJHKAS7PHGITZFZ3G3GS3SE/action/citation_signature","submit_replication":"https://pith.science/pith/ZQBKJHKAS7PHGITZFZ3G3GS3SE/action/replication_record"}},"created_at":"2026-05-18T01:23:28.470115+00:00","updated_at":"2026-05-18T01:23:28.470115+00:00"}