{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7DYFXJ5TI3WHOSRU7OPAZ7QIM6","short_pith_number":"pith:7DYFXJ5T","canonical_record":{"source":{"id":"1607.03094","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-11T19:50:57Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"3ca9da45531354f18ab8a05ad8fa611ff42e094752992d46b777c18594573e8e","abstract_canon_sha256":"ff8b3681ac9bffb614e56bcd954f1c12c584a4e74ab45d1fbbf34fead581bdf3"},"schema_version":"1.0"},"canonical_sha256":"f8f05ba7b346ec774a34fb9e0cfe08679c4b503f581f6f9e7dd71949f7d80faf","source":{"kind":"arxiv","id":"1607.03094","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03094","created_at":"2026-05-18T00:44:57Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03094v3","created_at":"2026-05-18T00:44:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03094","created_at":"2026-05-18T00:44:57Z"},{"alias_kind":"pith_short_12","alias_value":"7DYFXJ5TI3WH","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7DYFXJ5TI3WHOSRU","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7DYFXJ5T","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7DYFXJ5TI3WHOSRU7OPAZ7QIM6","target":"record","payload":{"canonical_record":{"source":{"id":"1607.03094","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-11T19:50:57Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"3ca9da45531354f18ab8a05ad8fa611ff42e094752992d46b777c18594573e8e","abstract_canon_sha256":"ff8b3681ac9bffb614e56bcd954f1c12c584a4e74ab45d1fbbf34fead581bdf3"},"schema_version":"1.0"},"canonical_sha256":"f8f05ba7b346ec774a34fb9e0cfe08679c4b503f581f6f9e7dd71949f7d80faf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:57.912395Z","signature_b64":"AHNdMS/1HQS6WaTPjOq+WyttG3EPSIYx9ut+RORT0Wf9Ffm04syZFyM6V00YDAp6w3T09bIe19TPVPyhQIYHBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8f05ba7b346ec774a34fb9e0cfe08679c4b503f581f6f9e7dd71949f7d80faf","last_reissued_at":"2026-05-18T00:44:57.911800Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:57.911800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.03094","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":"2026-05-18T00:44:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oVppejdrauqq1jIC0D3sf+50TnhvV8BlJgAzX7rRRfJH/XKXF3YC/jjSXqiURtBKDf6pbQbWScGv7OWZgI73CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T13:40:03.168079Z"},"content_sha256":"f5c691e81e7ace14bdac2b17d64ec217e6dc365c78abb582b1bda1d69c32d958","schema_version":"1.0","event_id":"sha256:f5c691e81e7ace14bdac2b17d64ec217e6dc365c78abb582b1bda1d69c32d958"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7DYFXJ5TI3WHOSRU7OPAZ7QIM6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on secondary K-theory II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"math.AG","authors_text":"Goncalo Tabuada","submitted_at":"2016-07-11T19:50:57Z","abstract_excerpt":"This note is the sequel to [A note on secondary K-theory. Algebra and Number Theory 10 (2016), no. 4, 887-906]. Making use of the recent theory of noncommutative motives, we prove that the canonical map from the derived Brauer group to the secondary Grothendieck ring has the following injectivity properties: in the case of a regular integral quasi-compact quasi-separated scheme, it is injective; in the case of an integral normal Noetherian scheme with a single isolated singularity, it distinguishes any two derived Brauer classes whose difference is of infinite order. As an application, we show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03094","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XRBptjuzfLQjcW2RNRT4BcCPyVkqDziVG+zKIG9BXHYMvG3R6xDQllLYA5uSi2JSCqrfCuGOPqK4rqqTJhjfCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T13:40:03.168932Z"},"content_sha256":"2686cf508724d86d158c13620560565e820b11ca67b1e79b42a7a59d9e4e6c65","schema_version":"1.0","event_id":"sha256:2686cf508724d86d158c13620560565e820b11ca67b1e79b42a7a59d9e4e6c65"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7DYFXJ5TI3WHOSRU7OPAZ7QIM6/bundle.json","state_url":"https://pith.science/pith/7DYFXJ5TI3WHOSRU7OPAZ7QIM6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7DYFXJ5TI3WHOSRU7OPAZ7QIM6/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":"2026-08-19T13:40:03Z","links":{"resolver":"https://pith.science/pith/7DYFXJ5TI3WHOSRU7OPAZ7QIM6","bundle":"https://pith.science/pith/7DYFXJ5TI3WHOSRU7OPAZ7QIM6/bundle.json","state":"https://pith.science/pith/7DYFXJ5TI3WHOSRU7OPAZ7QIM6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7DYFXJ5TI3WHOSRU7OPAZ7QIM6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7DYFXJ5TI3WHOSRU7OPAZ7QIM6","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":"ff8b3681ac9bffb614e56bcd954f1c12c584a4e74ab45d1fbbf34fead581bdf3","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-11T19:50:57Z","title_canon_sha256":"3ca9da45531354f18ab8a05ad8fa611ff42e094752992d46b777c18594573e8e"},"schema_version":"1.0","source":{"id":"1607.03094","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03094","created_at":"2026-05-18T00:44:57Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03094v3","created_at":"2026-05-18T00:44:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03094","created_at":"2026-05-18T00:44:57Z"},{"alias_kind":"pith_short_12","alias_value":"7DYFXJ5TI3WH","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7DYFXJ5TI3WHOSRU","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7DYFXJ5T","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:2686cf508724d86d158c13620560565e820b11ca67b1e79b42a7a59d9e4e6c65","target":"graph","created_at":"2026-05-18T00:44:57Z","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"},"paper":{"abstract_excerpt":"This note is the sequel to [A note on secondary K-theory. Algebra and Number Theory 10 (2016), no. 4, 887-906]. Making use of the recent theory of noncommutative motives, we prove that the canonical map from the derived Brauer group to the secondary Grothendieck ring has the following injectivity properties: in the case of a regular integral quasi-compact quasi-separated scheme, it is injective; in the case of an integral normal Noetherian scheme with a single isolated singularity, it distinguishes any two derived Brauer classes whose difference is of infinite order. As an application, we show","authors_text":"Goncalo Tabuada","cross_cats":["math.AT","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-11T19:50:57Z","title":"A note on secondary K-theory II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03094","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:f5c691e81e7ace14bdac2b17d64ec217e6dc365c78abb582b1bda1d69c32d958","target":"record","created_at":"2026-05-18T00:44:57Z","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":"ff8b3681ac9bffb614e56bcd954f1c12c584a4e74ab45d1fbbf34fead581bdf3","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-11T19:50:57Z","title_canon_sha256":"3ca9da45531354f18ab8a05ad8fa611ff42e094752992d46b777c18594573e8e"},"schema_version":"1.0","source":{"id":"1607.03094","kind":"arxiv","version":3}},"canonical_sha256":"f8f05ba7b346ec774a34fb9e0cfe08679c4b503f581f6f9e7dd71949f7d80faf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8f05ba7b346ec774a34fb9e0cfe08679c4b503f581f6f9e7dd71949f7d80faf","first_computed_at":"2026-05-18T00:44:57.911800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:57.911800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AHNdMS/1HQS6WaTPjOq+WyttG3EPSIYx9ut+RORT0Wf9Ffm04syZFyM6V00YDAp6w3T09bIe19TPVPyhQIYHBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:57.912395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.03094","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5c691e81e7ace14bdac2b17d64ec217e6dc365c78abb582b1bda1d69c32d958","sha256:2686cf508724d86d158c13620560565e820b11ca67b1e79b42a7a59d9e4e6c65"],"state_sha256":"d550ba2c331fe56bdd5098869b997cfa71fe43e63c453cac9a98297daf34af5c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FlPNwq8kwkx1ZZxZfPHlx4e0EsX9a0k3w+u2fMSD4ic/G5rrKbOLK1EFxUl/E70/cP+hMPVqcpL1PSWamwDTDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T13:40:03.176711Z","bundle_sha256":"074d5e4de34c7955d3418c189a3414dba6c1ffbf030906476ceaa37d678d2499"}}