{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:MEVA5BH6JDDLMAWK6NQAD6GYYC","short_pith_number":"pith:MEVA5BH6","schema_version":"1.0","canonical_sha256":"612a0e84fe48c6b602caf36001f8d8c0adc748d885d5370e69112e469e3b0fdb","source":{"kind":"arxiv","id":"1212.3277","version":3},"attestation_state":"computed","paper":{"title":"The additivity of traces in monoidal derivators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CT"],"primary_cat":"math.AT","authors_text":"Kate Ponto, Michael Shulman, Moritz Groth","submitted_at":"2012-12-13T19:23:36Z","abstract_excerpt":"Motivated by traces of matrices and Euler characteristics of topological spaces, we expect abstract traces in a symmetric monoidal category to be \"additive\". When the category is \"stable\" in some sense, additivity along cofiber sequences is a question about the interaction of stability and the monoidal structure.\n  May proved such an additivity theorem when the stable structure is a triangulation, based on new axioms for monoidal triangulated categories. In this paper we use stable derivators instead, which are a different model for \"stable homotopy theories\". We define and study monoidal stru"},"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":"1212.3277","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-12-13T19:23:36Z","cross_cats_sorted":["math.AG","math.CT"],"title_canon_sha256":"14efc19224176cb9c233a506ab3f74f9595895ccdbf44f8b889dc78e8886557b","abstract_canon_sha256":"f81724001e74a072500eab0fddbfeb109eb0f237227befae628b018ee993ee20"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:58.528859Z","signature_b64":"aT7qVunVp33s2F3CpJh0Lsdseiph9jorDa10vq1Skg8H/xcGGQjnMhQ13J6beyR4m5wBNFJ7oLUJiZhaR3KZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"612a0e84fe48c6b602caf36001f8d8c0adc748d885d5370e69112e469e3b0fdb","last_reissued_at":"2026-05-18T02:56:58.528421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:58.528421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The additivity of traces in monoidal derivators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CT"],"primary_cat":"math.AT","authors_text":"Kate Ponto, Michael Shulman, Moritz Groth","submitted_at":"2012-12-13T19:23:36Z","abstract_excerpt":"Motivated by traces of matrices and Euler characteristics of topological spaces, we expect abstract traces in a symmetric monoidal category to be \"additive\". When the category is \"stable\" in some sense, additivity along cofiber sequences is a question about the interaction of stability and the monoidal structure.\n  May proved such an additivity theorem when the stable structure is a triangulation, based on new axioms for monoidal triangulated categories. In this paper we use stable derivators instead, which are a different model for \"stable homotopy theories\". We define and study monoidal stru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3277","kind":"arxiv","version":3},"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":"1212.3277","created_at":"2026-05-18T02:56:58.528486+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.3277v3","created_at":"2026-05-18T02:56:58.528486+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3277","created_at":"2026-05-18T02:56:58.528486+00:00"},{"alias_kind":"pith_short_12","alias_value":"MEVA5BH6JDDL","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"MEVA5BH6JDDLMAWK","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"MEVA5BH6","created_at":"2026-05-18T12:27:14.488303+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/MEVA5BH6JDDLMAWK6NQAD6GYYC","json":"https://pith.science/pith/MEVA5BH6JDDLMAWK6NQAD6GYYC.json","graph_json":"https://pith.science/api/pith-number/MEVA5BH6JDDLMAWK6NQAD6GYYC/graph.json","events_json":"https://pith.science/api/pith-number/MEVA5BH6JDDLMAWK6NQAD6GYYC/events.json","paper":"https://pith.science/paper/MEVA5BH6"},"agent_actions":{"view_html":"https://pith.science/pith/MEVA5BH6JDDLMAWK6NQAD6GYYC","download_json":"https://pith.science/pith/MEVA5BH6JDDLMAWK6NQAD6GYYC.json","view_paper":"https://pith.science/paper/MEVA5BH6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.3277&json=true","fetch_graph":"https://pith.science/api/pith-number/MEVA5BH6JDDLMAWK6NQAD6GYYC/graph.json","fetch_events":"https://pith.science/api/pith-number/MEVA5BH6JDDLMAWK6NQAD6GYYC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MEVA5BH6JDDLMAWK6NQAD6GYYC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MEVA5BH6JDDLMAWK6NQAD6GYYC/action/storage_attestation","attest_author":"https://pith.science/pith/MEVA5BH6JDDLMAWK6NQAD6GYYC/action/author_attestation","sign_citation":"https://pith.science/pith/MEVA5BH6JDDLMAWK6NQAD6GYYC/action/citation_signature","submit_replication":"https://pith.science/pith/MEVA5BH6JDDLMAWK6NQAD6GYYC/action/replication_record"}},"created_at":"2026-05-18T02:56:58.528486+00:00","updated_at":"2026-05-18T02:56:58.528486+00:00"}