{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BWDNUNZY56R4GMQFIJIF5INCFD","short_pith_number":"pith:BWDNUNZY","canonical_record":{"source":{"id":"1309.0637","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-09-03T10:45:33Z","cross_cats_sorted":["math.AG","math.AT","math.NT"],"title_canon_sha256":"39c76c480328cc35dae957cf048070b3758aa911f6e325fc728b7ddab55064de","abstract_canon_sha256":"e57de533e22cea200cd4e8ed44f5c20c6042a5a7da2f7461b423c7d489c63f2a"},"schema_version":"1.0"},"canonical_sha256":"0d86da3738efa3c3320542505ea1a228ec3230ac263a183272d08d527eb0b1d3","source":{"kind":"arxiv","id":"1309.0637","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0637","created_at":"2026-05-17T23:57:19Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0637v6","created_at":"2026-05-17T23:57:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0637","created_at":"2026-05-17T23:57:19Z"},{"alias_kind":"pith_short_12","alias_value":"BWDNUNZY56R4","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BWDNUNZY56R4GMQF","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BWDNUNZY","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BWDNUNZY56R4GMQFIJIF5INCFD","target":"record","payload":{"canonical_record":{"source":{"id":"1309.0637","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-09-03T10:45:33Z","cross_cats_sorted":["math.AG","math.AT","math.NT"],"title_canon_sha256":"39c76c480328cc35dae957cf048070b3758aa911f6e325fc728b7ddab55064de","abstract_canon_sha256":"e57de533e22cea200cd4e8ed44f5c20c6042a5a7da2f7461b423c7d489c63f2a"},"schema_version":"1.0"},"canonical_sha256":"0d86da3738efa3c3320542505ea1a228ec3230ac263a183272d08d527eb0b1d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:19.875521Z","signature_b64":"mXszHTSGJ861vXyHk9B9RUfa5kRAu1Vby6M59O4Lo5oj+EUCvO2Xh7pJ4br+5vQlnhGOX5arZJqTg6sOUelyDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d86da3738efa3c3320542505ea1a228ec3230ac263a183272d08d527eb0b1d3","last_reissued_at":"2026-05-17T23:57:19.874870Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:19.874870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.0637","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ktk2Ktq09zczx2Cc1tOhD2s8paA09gAIBxV2PhVe02JAiIZNvAqSA474OuBp83yZWpA5BBH/1lteL3VAxS7TBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:14:26.191410Z"},"content_sha256":"571a519fae614268609768efdf59d744385ef7d3955a9d42d1dc3b8f63f345af","schema_version":"1.0","event_id":"sha256:571a519fae614268609768efdf59d744385ef7d3955a9d42d1dc3b8f63f345af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BWDNUNZY56R4GMQFIJIF5INCFD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tannaka duality for enhanced triangulated categories II: $t$-structures and homotopy types","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT","math.NT"],"primary_cat":"math.KT","authors_text":"J.P.Pridham","submitted_at":"2013-09-03T10:45:33Z","abstract_excerpt":"We consider the effect of $t$-structures on the Tannaka duality theory for dg categories developed in our previous paper. We associate non-negative dg coalgebras $C$ to dg functors on the hearts of $t$-structures, and relate dg $C$-comodules to the original dg category. We give several applications for pro-algebraic homotopy types associated to various cohomology theories, and for motivic Galois groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0637","kind":"arxiv","version":6},"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":"2026-05-17T23:57:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A0xcMJwhWp5YU8oHAQ/pmfeneAWLCP2up6WD6SuwKvwZnPnDtWOZ+vdI5reF2kU3y39oOtD9ebhT5PpeVINnCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:14:26.191752Z"},"content_sha256":"dcf17bb44d40f41bff176d0ad172157a47e66a9f3018cfead449977fcfbd65ea","schema_version":"1.0","event_id":"sha256:dcf17bb44d40f41bff176d0ad172157a47e66a9f3018cfead449977fcfbd65ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BWDNUNZY56R4GMQFIJIF5INCFD/bundle.json","state_url":"https://pith.science/pith/BWDNUNZY56R4GMQFIJIF5INCFD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BWDNUNZY56R4GMQFIJIF5INCFD/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":"2026-06-24T07:14:26Z","links":{"resolver":"https://pith.science/pith/BWDNUNZY56R4GMQFIJIF5INCFD","bundle":"https://pith.science/pith/BWDNUNZY56R4GMQFIJIF5INCFD/bundle.json","state":"https://pith.science/pith/BWDNUNZY56R4GMQFIJIF5INCFD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BWDNUNZY56R4GMQFIJIF5INCFD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BWDNUNZY56R4GMQFIJIF5INCFD","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":"e57de533e22cea200cd4e8ed44f5c20c6042a5a7da2f7461b423c7d489c63f2a","cross_cats_sorted":["math.AG","math.AT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-09-03T10:45:33Z","title_canon_sha256":"39c76c480328cc35dae957cf048070b3758aa911f6e325fc728b7ddab55064de"},"schema_version":"1.0","source":{"id":"1309.0637","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0637","created_at":"2026-05-17T23:57:19Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0637v6","created_at":"2026-05-17T23:57:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0637","created_at":"2026-05-17T23:57:19Z"},{"alias_kind":"pith_short_12","alias_value":"BWDNUNZY56R4","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BWDNUNZY56R4GMQF","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BWDNUNZY","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:dcf17bb44d40f41bff176d0ad172157a47e66a9f3018cfead449977fcfbd65ea","target":"graph","created_at":"2026-05-17T23:57:19Z","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":"We consider the effect of $t$-structures on the Tannaka duality theory for dg categories developed in our previous paper. We associate non-negative dg coalgebras $C$ to dg functors on the hearts of $t$-structures, and relate dg $C$-comodules to the original dg category. We give several applications for pro-algebraic homotopy types associated to various cohomology theories, and for motivic Galois groups.","authors_text":"J.P.Pridham","cross_cats":["math.AG","math.AT","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-09-03T10:45:33Z","title":"Tannaka duality for enhanced triangulated categories II: $t$-structures and homotopy types"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0637","kind":"arxiv","version":6},"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":"sha256:571a519fae614268609768efdf59d744385ef7d3955a9d42d1dc3b8f63f345af","target":"record","created_at":"2026-05-17T23:57:19Z","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":"e57de533e22cea200cd4e8ed44f5c20c6042a5a7da2f7461b423c7d489c63f2a","cross_cats_sorted":["math.AG","math.AT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-09-03T10:45:33Z","title_canon_sha256":"39c76c480328cc35dae957cf048070b3758aa911f6e325fc728b7ddab55064de"},"schema_version":"1.0","source":{"id":"1309.0637","kind":"arxiv","version":6}},"canonical_sha256":"0d86da3738efa3c3320542505ea1a228ec3230ac263a183272d08d527eb0b1d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d86da3738efa3c3320542505ea1a228ec3230ac263a183272d08d527eb0b1d3","first_computed_at":"2026-05-17T23:57:19.874870Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:19.874870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mXszHTSGJ861vXyHk9B9RUfa5kRAu1Vby6M59O4Lo5oj+EUCvO2Xh7pJ4br+5vQlnhGOX5arZJqTg6sOUelyDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:19.875521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.0637","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:571a519fae614268609768efdf59d744385ef7d3955a9d42d1dc3b8f63f345af","sha256:dcf17bb44d40f41bff176d0ad172157a47e66a9f3018cfead449977fcfbd65ea"],"state_sha256":"dd7c22c19370d844a661115a7306cf61bff66c386a96e6fd62bcd79470929ef9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S+9UpMggv4BuxDEuCVwmDPC8gCCRsDBcthTkZLhvJrvKRDEcnnmBzI1MAgSLANnx+sTuCoInHBBkplJVfktXDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T07:14:26.193675Z","bundle_sha256":"39430bf289bc4c924f0edb0ab927af4d06ab92d5c855835d267df32099b819de"}}