{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:TO2XPCZDOSLMMNQV42DNV66T5F","short_pith_number":"pith:TO2XPCZD","canonical_record":{"source":{"id":"2109.01512","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2021-09-03T13:36:04Z","cross_cats_sorted":["math.AT","math.CT"],"title_canon_sha256":"7620089b42ead31019a0470dfc211e705f3ebd97f0576c1ab440940230c3e3b1","abstract_canon_sha256":"46dee773fc778c1b6c1dfc37818817c0975e62260730087743c7d2ccfcda9f36"},"schema_version":"1.0"},"canonical_sha256":"9bb5778b237496c63615e686dafbd3e94ef1cb890f6cac2a2187e24a70b18433","source":{"kind":"arxiv","id":"2109.01512","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.01512","created_at":"2026-07-05T04:49:29Z"},{"alias_kind":"arxiv_version","alias_value":"2109.01512v3","created_at":"2026-07-05T04:49:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.01512","created_at":"2026-07-05T04:49:29Z"},{"alias_kind":"pith_short_12","alias_value":"TO2XPCZDOSLM","created_at":"2026-07-05T04:49:29Z"},{"alias_kind":"pith_short_16","alias_value":"TO2XPCZDOSLMMNQV","created_at":"2026-07-05T04:49:29Z"},{"alias_kind":"pith_short_8","alias_value":"TO2XPCZD","created_at":"2026-07-05T04:49:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:TO2XPCZDOSLMMNQV42DNV66T5F","target":"record","payload":{"canonical_record":{"source":{"id":"2109.01512","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2021-09-03T13:36:04Z","cross_cats_sorted":["math.AT","math.CT"],"title_canon_sha256":"7620089b42ead31019a0470dfc211e705f3ebd97f0576c1ab440940230c3e3b1","abstract_canon_sha256":"46dee773fc778c1b6c1dfc37818817c0975e62260730087743c7d2ccfcda9f36"},"schema_version":"1.0"},"canonical_sha256":"9bb5778b237496c63615e686dafbd3e94ef1cb890f6cac2a2187e24a70b18433","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:49:29.689779Z","signature_b64":"I2S0Sh5aWBDS41vg0+cEOkQthZgHxjsp06qr/GWjjEmn/jHv/eclM74LrSH90P/G0GRf4FHdpp/kOXOWeUfNBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bb5778b237496c63615e686dafbd3e94ef1cb890f6cac2a2187e24a70b18433","last_reissued_at":"2026-07-05T04:49:29.689377Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:49:29.689377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.01512","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:49:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fOmDYxj95xkhCqEmJ9H91r2TTsQi1dindyxoxvX7HWCWL8zfmv9JVkoZfj1E2kEzutnH+IxDo+j76KDNwdBfDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T06:09:18.852437Z"},"content_sha256":"6ce3d7e9ae77c4c63a2a849c198143ee5b9f59fc17dbe4000768e273493069b4","schema_version":"1.0","event_id":"sha256:6ce3d7e9ae77c4c63a2a849c198143ee5b9f59fc17dbe4000768e273493069b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:TO2XPCZDOSLMMNQV42DNV66T5F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The additivity of traces in stable $\\infty$-categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT"],"primary_cat":"math.KT","authors_text":"Maxime Ramzi","submitted_at":"2021-09-03T13:36:04Z","abstract_excerpt":"We prove a version of J.P. May's theorem on the additivity of traces, in symmetric monoidal stable $\\infty$-categories. Our proof proceeds via a categorification, namely we use the additivity of topological Hochschild homology as an invariant of stable $\\infty$-categories and construct a morphism of spectra $\\mathrm{THH}(\\mathbf C)\\to \\mathrm{End}(\\mathbf 1_\\mathbf C)$ for $\\mathbf C$ a stably symmetric monoidal rigid $\\infty$-category. We also explain how to get a more general statement involving traces of finite (homotopy) colimits."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.01512","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2109.01512/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:49:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qc7AKqJIkoDCsMs9O5qcNdV/Ie4a7YiU7Bs4XakBWxvQZ9+T8/PkO9ZbMw7Nu6I0FxmXy7GDld1KjafpjUoCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T06:09:18.852929Z"},"content_sha256":"2eee6aa1b52159c1c7f56fbc26d387c239bfee306c245088b019146f60e2e993","schema_version":"1.0","event_id":"sha256:2eee6aa1b52159c1c7f56fbc26d387c239bfee306c245088b019146f60e2e993"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TO2XPCZDOSLMMNQV42DNV66T5F/bundle.json","state_url":"https://pith.science/pith/TO2XPCZDOSLMMNQV42DNV66T5F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TO2XPCZDOSLMMNQV42DNV66T5F/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T06:09:18Z","links":{"resolver":"https://pith.science/pith/TO2XPCZDOSLMMNQV42DNV66T5F","bundle":"https://pith.science/pith/TO2XPCZDOSLMMNQV42DNV66T5F/bundle.json","state":"https://pith.science/pith/TO2XPCZDOSLMMNQV42DNV66T5F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TO2XPCZDOSLMMNQV42DNV66T5F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:TO2XPCZDOSLMMNQV42DNV66T5F","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":"46dee773fc778c1b6c1dfc37818817c0975e62260730087743c7d2ccfcda9f36","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2021-09-03T13:36:04Z","title_canon_sha256":"7620089b42ead31019a0470dfc211e705f3ebd97f0576c1ab440940230c3e3b1"},"schema_version":"1.0","source":{"id":"2109.01512","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.01512","created_at":"2026-07-05T04:49:29Z"},{"alias_kind":"arxiv_version","alias_value":"2109.01512v3","created_at":"2026-07-05T04:49:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.01512","created_at":"2026-07-05T04:49:29Z"},{"alias_kind":"pith_short_12","alias_value":"TO2XPCZDOSLM","created_at":"2026-07-05T04:49:29Z"},{"alias_kind":"pith_short_16","alias_value":"TO2XPCZDOSLMMNQV","created_at":"2026-07-05T04:49:29Z"},{"alias_kind":"pith_short_8","alias_value":"TO2XPCZD","created_at":"2026-07-05T04:49:29Z"}],"graph_snapshots":[{"event_id":"sha256:2eee6aa1b52159c1c7f56fbc26d387c239bfee306c245088b019146f60e2e993","target":"graph","created_at":"2026-07-05T04:49:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.01512/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a version of J.P. May's theorem on the additivity of traces, in symmetric monoidal stable $\\infty$-categories. Our proof proceeds via a categorification, namely we use the additivity of topological Hochschild homology as an invariant of stable $\\infty$-categories and construct a morphism of spectra $\\mathrm{THH}(\\mathbf C)\\to \\mathrm{End}(\\mathbf 1_\\mathbf C)$ for $\\mathbf C$ a stably symmetric monoidal rigid $\\infty$-category. We also explain how to get a more general statement involving traces of finite (homotopy) colimits.","authors_text":"Maxime Ramzi","cross_cats":["math.AT","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2021-09-03T13:36:04Z","title":"The additivity of traces in stable $\\infty$-categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.01512","kind":"arxiv","version":3},"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":"sha256:6ce3d7e9ae77c4c63a2a849c198143ee5b9f59fc17dbe4000768e273493069b4","target":"record","created_at":"2026-07-05T04:49:29Z","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":"46dee773fc778c1b6c1dfc37818817c0975e62260730087743c7d2ccfcda9f36","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2021-09-03T13:36:04Z","title_canon_sha256":"7620089b42ead31019a0470dfc211e705f3ebd97f0576c1ab440940230c3e3b1"},"schema_version":"1.0","source":{"id":"2109.01512","kind":"arxiv","version":3}},"canonical_sha256":"9bb5778b237496c63615e686dafbd3e94ef1cb890f6cac2a2187e24a70b18433","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bb5778b237496c63615e686dafbd3e94ef1cb890f6cac2a2187e24a70b18433","first_computed_at":"2026-07-05T04:49:29.689377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:49:29.689377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I2S0Sh5aWBDS41vg0+cEOkQthZgHxjsp06qr/GWjjEmn/jHv/eclM74LrSH90P/G0GRf4FHdpp/kOXOWeUfNBA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:49:29.689779Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.01512","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ce3d7e9ae77c4c63a2a849c198143ee5b9f59fc17dbe4000768e273493069b4","sha256:2eee6aa1b52159c1c7f56fbc26d387c239bfee306c245088b019146f60e2e993"],"state_sha256":"637b40cfa99b82d2d78e6dbec9c140ec1ac0e7564e15ced02ece4ae1bf89a268"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AsLqvAnH+xGV+4aM/r2LKuZwJ899tx2Wn+nae5izlfVf5fV8Pvk6w/wiBdUkKYjIdYfVub523uCCtFCxiQIKCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T06:09:18.856778Z","bundle_sha256":"289eebddddcd493218d458c1b0b035e83f59b32a4d16579f8efbcb68e654d3ea"}}