{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:45PWJL4XUBXTQCQNM55FV6RJWM","short_pith_number":"pith:45PWJL4X","canonical_record":{"source":{"id":"2402.10694","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-02-16T13:57:24Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"fc2fcc38abb16221bf436e08c3a83ead8d4d959c8e9c097f717da3129b2e982d","abstract_canon_sha256":"ee33da47008bd3f8f0698acb28099d3f80ef3a494882004d45dcc7a377c3ad29"},"schema_version":"1.0"},"canonical_sha256":"e75f64af97a06f380a0d677a5afa29b32dd58167261d538ebf5705176c40df3d","source":{"kind":"arxiv","id":"2402.10694","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.10694","created_at":"2026-07-05T07:48:03Z"},{"alias_kind":"arxiv_version","alias_value":"2402.10694v2","created_at":"2026-07-05T07:48:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.10694","created_at":"2026-07-05T07:48:03Z"},{"alias_kind":"pith_short_12","alias_value":"45PWJL4XUBXT","created_at":"2026-07-05T07:48:03Z"},{"alias_kind":"pith_short_16","alias_value":"45PWJL4XUBXTQCQN","created_at":"2026-07-05T07:48:03Z"},{"alias_kind":"pith_short_8","alias_value":"45PWJL4X","created_at":"2026-07-05T07:48:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:45PWJL4XUBXTQCQNM55FV6RJWM","target":"record","payload":{"canonical_record":{"source":{"id":"2402.10694","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-02-16T13:57:24Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"fc2fcc38abb16221bf436e08c3a83ead8d4d959c8e9c097f717da3129b2e982d","abstract_canon_sha256":"ee33da47008bd3f8f0698acb28099d3f80ef3a494882004d45dcc7a377c3ad29"},"schema_version":"1.0"},"canonical_sha256":"e75f64af97a06f380a0d677a5afa29b32dd58167261d538ebf5705176c40df3d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:48:03.728945Z","signature_b64":"405J/O/PRpIlvJDpioVRqd4DK2V66qQxVs9Qyd4dO8J4IuqpfvEpt+kDIrKx3fH1pjsabYWppL81RkbQzD1OCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e75f64af97a06f380a0d677a5afa29b32dd58167261d538ebf5705176c40df3d","last_reissued_at":"2026-07-05T07:48:03.728403Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:48:03.728403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.10694","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:48:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ngCAjOrUFtTKif3XzqdRaPbE04agA4XMU3sa9dHnmjBS/ZmguzmhyQfVYV0XPeDp3HckJ1+Lsf7h55Fjqd+EAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T20:14:30.814109Z"},"content_sha256":"6cdfe401f3095bfba8c568825ff8d2cbb924881f34db32922ac02589d73b7449","schema_version":"1.0","event_id":"sha256:6cdfe401f3095bfba8c568825ff8d2cbb924881f34db32922ac02589d73b7449"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:45PWJL4XUBXTQCQNM55FV6RJWM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact dg categories I : Foundations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Xiaofa Chen","submitted_at":"2024-02-16T13:57:24Z","abstract_excerpt":"We introduce the notion of exact dg category, which provides a differential graded enhancement of Nakaoka--Palu's notion of extriangulated category. We give a definition in complete analogy with Quillen's but where the category of kernel-cokernel pairs is replaced with a more sophisticated homotopy category. We introduce the notion of stable dg category, and prove that the $H^0$-category of an exact dg category $\\mathcal{A}$ is triangulated if and only if $\\mathcal{A}$ is stable. We illustrate our theory with several examples including the homotopy category of two-term complexes and Amiot's fu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.10694","kind":"arxiv","version":2},"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/2402.10694/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":"2026-07-05T07:48:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gs7iVXHdAZgxZhp02qQiMMy/w2p+lbVPfttjbN/iCVh3iTtwG3k0LSdTbQu5fgQ/hteKklhAnpOoZAD8oREABg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T20:14:30.814621Z"},"content_sha256":"ea802b7bbe50afd696f44bac89aeeaf5a6f0f763c228a36b9ea8f9a857c72c1d","schema_version":"1.0","event_id":"sha256:ea802b7bbe50afd696f44bac89aeeaf5a6f0f763c228a36b9ea8f9a857c72c1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/45PWJL4XUBXTQCQNM55FV6RJWM/bundle.json","state_url":"https://pith.science/pith/45PWJL4XUBXTQCQNM55FV6RJWM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/45PWJL4XUBXTQCQNM55FV6RJWM/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":"2026-08-11T20:14:30Z","links":{"resolver":"https://pith.science/pith/45PWJL4XUBXTQCQNM55FV6RJWM","bundle":"https://pith.science/pith/45PWJL4XUBXTQCQNM55FV6RJWM/bundle.json","state":"https://pith.science/pith/45PWJL4XUBXTQCQNM55FV6RJWM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/45PWJL4XUBXTQCQNM55FV6RJWM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:45PWJL4XUBXTQCQNM55FV6RJWM","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":"ee33da47008bd3f8f0698acb28099d3f80ef3a494882004d45dcc7a377c3ad29","cross_cats_sorted":["math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-02-16T13:57:24Z","title_canon_sha256":"fc2fcc38abb16221bf436e08c3a83ead8d4d959c8e9c097f717da3129b2e982d"},"schema_version":"1.0","source":{"id":"2402.10694","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.10694","created_at":"2026-07-05T07:48:03Z"},{"alias_kind":"arxiv_version","alias_value":"2402.10694v2","created_at":"2026-07-05T07:48:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.10694","created_at":"2026-07-05T07:48:03Z"},{"alias_kind":"pith_short_12","alias_value":"45PWJL4XUBXT","created_at":"2026-07-05T07:48:03Z"},{"alias_kind":"pith_short_16","alias_value":"45PWJL4XUBXTQCQN","created_at":"2026-07-05T07:48:03Z"},{"alias_kind":"pith_short_8","alias_value":"45PWJL4X","created_at":"2026-07-05T07:48:03Z"}],"graph_snapshots":[{"event_id":"sha256:ea802b7bbe50afd696f44bac89aeeaf5a6f0f763c228a36b9ea8f9a857c72c1d","target":"graph","created_at":"2026-07-05T07:48:03Z","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/2402.10694/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the notion of exact dg category, which provides a differential graded enhancement of Nakaoka--Palu's notion of extriangulated category. We give a definition in complete analogy with Quillen's but where the category of kernel-cokernel pairs is replaced with a more sophisticated homotopy category. We introduce the notion of stable dg category, and prove that the $H^0$-category of an exact dg category $\\mathcal{A}$ is triangulated if and only if $\\mathcal{A}$ is stable. We illustrate our theory with several examples including the homotopy category of two-term complexes and Amiot's fu","authors_text":"Xiaofa Chen","cross_cats":["math.CT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-02-16T13:57:24Z","title":"Exact dg categories I : Foundations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.10694","kind":"arxiv","version":2},"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":"sha256:6cdfe401f3095bfba8c568825ff8d2cbb924881f34db32922ac02589d73b7449","target":"record","created_at":"2026-07-05T07:48:03Z","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":"ee33da47008bd3f8f0698acb28099d3f80ef3a494882004d45dcc7a377c3ad29","cross_cats_sorted":["math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-02-16T13:57:24Z","title_canon_sha256":"fc2fcc38abb16221bf436e08c3a83ead8d4d959c8e9c097f717da3129b2e982d"},"schema_version":"1.0","source":{"id":"2402.10694","kind":"arxiv","version":2}},"canonical_sha256":"e75f64af97a06f380a0d677a5afa29b32dd58167261d538ebf5705176c40df3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e75f64af97a06f380a0d677a5afa29b32dd58167261d538ebf5705176c40df3d","first_computed_at":"2026-07-05T07:48:03.728403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:48:03.728403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"405J/O/PRpIlvJDpioVRqd4DK2V66qQxVs9Qyd4dO8J4IuqpfvEpt+kDIrKx3fH1pjsabYWppL81RkbQzD1OCA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:48:03.728945Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.10694","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cdfe401f3095bfba8c568825ff8d2cbb924881f34db32922ac02589d73b7449","sha256:ea802b7bbe50afd696f44bac89aeeaf5a6f0f763c228a36b9ea8f9a857c72c1d"],"state_sha256":"345406849348e76363f35ea190f3e61c19bc89a7127b1e3df6acb8deb22647c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nqlwHDqVJaxEQY+VYvBFnL0YjPfT5TNiybIkb3bBxKdE/kQXzjHLQ0UN0zOuc5ZsMfmaZpzrAU4jh2Uxes6aBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T20:14:30.821006Z","bundle_sha256":"40014f51938b5e6d745a7287cbd140a397f1aebb9601465e0b832e08c39e37c8"}}