{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:XGBLAJEUCL37QGKD2TS2Y6PF3T","short_pith_number":"pith:XGBLAJEU","canonical_record":{"source":{"id":"2504.07473","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2025-04-10T05:55:43Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"d350a689e4243e5056cf26503ed339fc0e2d526a5bd972d24dde7b54d943f974","abstract_canon_sha256":"aa33141cc0a2e879afde0f708616503c7f61523e364f7bc2750de42931aae00a"},"schema_version":"1.0"},"canonical_sha256":"b982b0249412f7f81943d4e5ac79e5dce5263f7a9c9ab27e6b4faa8cec4c13e5","source":{"kind":"arxiv","id":"2504.07473","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.07473","created_at":"2026-07-05T10:47:09Z"},{"alias_kind":"arxiv_version","alias_value":"2504.07473v1","created_at":"2026-07-05T10:47:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.07473","created_at":"2026-07-05T10:47:09Z"},{"alias_kind":"pith_short_12","alias_value":"XGBLAJEUCL37","created_at":"2026-07-05T10:47:09Z"},{"alias_kind":"pith_short_16","alias_value":"XGBLAJEUCL37QGKD","created_at":"2026-07-05T10:47:09Z"},{"alias_kind":"pith_short_8","alias_value":"XGBLAJEU","created_at":"2026-07-05T10:47:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:XGBLAJEUCL37QGKD2TS2Y6PF3T","target":"record","payload":{"canonical_record":{"source":{"id":"2504.07473","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2025-04-10T05:55:43Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"d350a689e4243e5056cf26503ed339fc0e2d526a5bd972d24dde7b54d943f974","abstract_canon_sha256":"aa33141cc0a2e879afde0f708616503c7f61523e364f7bc2750de42931aae00a"},"schema_version":"1.0"},"canonical_sha256":"b982b0249412f7f81943d4e5ac79e5dce5263f7a9c9ab27e6b4faa8cec4c13e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:47:09.604184Z","signature_b64":"Hjfb/vOAVFvVJDN9fbeDWQj2xbPdDNej8Gwq3kjNkAtQg+Wl99lNQY/8yYrm9pCHrnV/S9pViqZKWqMrt+ErBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b982b0249412f7f81943d4e5ac79e5dce5263f7a9c9ab27e6b4faa8cec4c13e5","last_reissued_at":"2026-07-05T10:47:09.603703Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:47:09.603703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.07473","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:47:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5UCl2pxLTCG6Ym3Iu2yfb4mVVv/W9wuU/Edpc2Dp+RVi7a0Mi3u+9J0S0uFb8AZhBMxKV12iOG9Fxo9cYo50Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T23:26:47.932891Z"},"content_sha256":"eb676efe79e81858828a99d3cbeff2aeb695fe1007c7995deb2cbd3bb8276222","schema_version":"1.0","event_id":"sha256:eb676efe79e81858828a99d3cbeff2aeb695fe1007c7995deb2cbd3bb8276222"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:XGBLAJEUCL37QGKD2TS2Y6PF3T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Standard $t$-structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Jean-Baptiste Teyssier, Mauro Porta, Peter J. Haine","submitted_at":"2025-04-10T05:55:43Z","abstract_excerpt":"We provide a general construction of induced $t$-structures, that generalizes standard $t$-structures for $\\infty$-categories of sheaves. More precisely, given a presentable $\\infty$-category $\\mathcal{X}$ and a presentable stable $\\infty$-category $\\mathcal{E}$ equipped with an accessible $t$-structure $\\tau = (\\mathcal{E}_{\\geq 0}, \\mathcal{E}_{\\leq 0})$, we show that $\\mathcal{X} \\otimes \\mathcal{E}$ is equipped with a canonical $t$-structure whose coconnective part is given in $\\mathcal{X} \\otimes \\mathcal{E}_{\\leq 0}$. When $\\mathcal{X}$ is an $\\infty$-topos, we give a more explicit descr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.07473","kind":"arxiv","version":1},"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/2504.07473/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":"2026-07-05T10:47:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VZJE21OcLjS2i3iwKQdbcvYIPtVJpe1BHDRAUDslw+Mb0G4L/cza/PVID+yDZUpJB5XaNxwKz1yYfwPJrKagAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T23:26:47.933386Z"},"content_sha256":"12b337074777b5ae652acfbeec88edad21dda70bd46522ba0a1e0dbd0bf14105","schema_version":"1.0","event_id":"sha256:12b337074777b5ae652acfbeec88edad21dda70bd46522ba0a1e0dbd0bf14105"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XGBLAJEUCL37QGKD2TS2Y6PF3T/bundle.json","state_url":"https://pith.science/pith/XGBLAJEUCL37QGKD2TS2Y6PF3T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XGBLAJEUCL37QGKD2TS2Y6PF3T/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":"2026-08-10T23:26:47Z","links":{"resolver":"https://pith.science/pith/XGBLAJEUCL37QGKD2TS2Y6PF3T","bundle":"https://pith.science/pith/XGBLAJEUCL37QGKD2TS2Y6PF3T/bundle.json","state":"https://pith.science/pith/XGBLAJEUCL37QGKD2TS2Y6PF3T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XGBLAJEUCL37QGKD2TS2Y6PF3T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XGBLAJEUCL37QGKD2TS2Y6PF3T","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":"aa33141cc0a2e879afde0f708616503c7f61523e364f7bc2750de42931aae00a","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2025-04-10T05:55:43Z","title_canon_sha256":"d350a689e4243e5056cf26503ed339fc0e2d526a5bd972d24dde7b54d943f974"},"schema_version":"1.0","source":{"id":"2504.07473","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.07473","created_at":"2026-07-05T10:47:09Z"},{"alias_kind":"arxiv_version","alias_value":"2504.07473v1","created_at":"2026-07-05T10:47:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.07473","created_at":"2026-07-05T10:47:09Z"},{"alias_kind":"pith_short_12","alias_value":"XGBLAJEUCL37","created_at":"2026-07-05T10:47:09Z"},{"alias_kind":"pith_short_16","alias_value":"XGBLAJEUCL37QGKD","created_at":"2026-07-05T10:47:09Z"},{"alias_kind":"pith_short_8","alias_value":"XGBLAJEU","created_at":"2026-07-05T10:47:09Z"}],"graph_snapshots":[{"event_id":"sha256:12b337074777b5ae652acfbeec88edad21dda70bd46522ba0a1e0dbd0bf14105","target":"graph","created_at":"2026-07-05T10:47:09Z","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/2504.07473/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide a general construction of induced $t$-structures, that generalizes standard $t$-structures for $\\infty$-categories of sheaves. More precisely, given a presentable $\\infty$-category $\\mathcal{X}$ and a presentable stable $\\infty$-category $\\mathcal{E}$ equipped with an accessible $t$-structure $\\tau = (\\mathcal{E}_{\\geq 0}, \\mathcal{E}_{\\leq 0})$, we show that $\\mathcal{X} \\otimes \\mathcal{E}$ is equipped with a canonical $t$-structure whose coconnective part is given in $\\mathcal{X} \\otimes \\mathcal{E}_{\\leq 0}$. When $\\mathcal{X}$ is an $\\infty$-topos, we give a more explicit descr","authors_text":"Jean-Baptiste Teyssier, Mauro Porta, Peter J. Haine","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2025-04-10T05:55:43Z","title":"Standard $t$-structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.07473","kind":"arxiv","version":1},"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:eb676efe79e81858828a99d3cbeff2aeb695fe1007c7995deb2cbd3bb8276222","target":"record","created_at":"2026-07-05T10:47:09Z","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":"aa33141cc0a2e879afde0f708616503c7f61523e364f7bc2750de42931aae00a","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2025-04-10T05:55:43Z","title_canon_sha256":"d350a689e4243e5056cf26503ed339fc0e2d526a5bd972d24dde7b54d943f974"},"schema_version":"1.0","source":{"id":"2504.07473","kind":"arxiv","version":1}},"canonical_sha256":"b982b0249412f7f81943d4e5ac79e5dce5263f7a9c9ab27e6b4faa8cec4c13e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b982b0249412f7f81943d4e5ac79e5dce5263f7a9c9ab27e6b4faa8cec4c13e5","first_computed_at":"2026-07-05T10:47:09.603703Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:47:09.603703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hjfb/vOAVFvVJDN9fbeDWQj2xbPdDNej8Gwq3kjNkAtQg+Wl99lNQY/8yYrm9pCHrnV/S9pViqZKWqMrt+ErBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:47:09.604184Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.07473","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb676efe79e81858828a99d3cbeff2aeb695fe1007c7995deb2cbd3bb8276222","sha256:12b337074777b5ae652acfbeec88edad21dda70bd46522ba0a1e0dbd0bf14105"],"state_sha256":"dbd8a48192c3643b5f01515eb6c68242242ce8a03c2109f744013509466db1c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H3TGDxpDQaIdsdLn57UIWCbj4O2pbKzeoQhqNN8QohgGZl/Qs1CglxQsuArx9DsSw4lVMlbCl56JerJu/qQQAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T23:26:47.937359Z","bundle_sha256":"1f8929bab75c81d27539c2117a5018c80b44b39d74e2abcf461c363fe4f22942"}}