{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:GPTUCNVZTZ3JQCWJOKLYAT6I5F","short_pith_number":"pith:GPTUCNVZ","canonical_record":{"source":{"id":"2210.08558","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2022-10-16T15:06:23Z","cross_cats_sorted":["math.CT","math.RA"],"title_canon_sha256":"e1d0d2410ea9b70905a63c43c33c52fd11e2cfb13356bd2f91f88e1f19a55299","abstract_canon_sha256":"a1b0729c2ab730b9bedb61356f741dc3d50d9043129c90a0985cc341f61eee6d"},"schema_version":"1.0"},"canonical_sha256":"33e74136b99e76980ac97297804fc8e970cdf367add9ca5193687f1edf7d488d","source":{"kind":"arxiv","id":"2210.08558","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.08558","created_at":"2026-07-05T06:35:45Z"},{"alias_kind":"arxiv_version","alias_value":"2210.08558v3","created_at":"2026-07-05T06:35:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.08558","created_at":"2026-07-05T06:35:45Z"},{"alias_kind":"pith_short_12","alias_value":"GPTUCNVZTZ3J","created_at":"2026-07-05T06:35:45Z"},{"alias_kind":"pith_short_16","alias_value":"GPTUCNVZTZ3JQCWJ","created_at":"2026-07-05T06:35:45Z"},{"alias_kind":"pith_short_8","alias_value":"GPTUCNVZ","created_at":"2026-07-05T06:35:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:GPTUCNVZTZ3JQCWJOKLYAT6I5F","target":"record","payload":{"canonical_record":{"source":{"id":"2210.08558","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2022-10-16T15:06:23Z","cross_cats_sorted":["math.CT","math.RA"],"title_canon_sha256":"e1d0d2410ea9b70905a63c43c33c52fd11e2cfb13356bd2f91f88e1f19a55299","abstract_canon_sha256":"a1b0729c2ab730b9bedb61356f741dc3d50d9043129c90a0985cc341f61eee6d"},"schema_version":"1.0"},"canonical_sha256":"33e74136b99e76980ac97297804fc8e970cdf367add9ca5193687f1edf7d488d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:35:45.949123Z","signature_b64":"hf+bBr/Ykp6WwntvQCq/77/b/gmZNRlPGzBJ2gzBvhmjy9WBpGf5HaCXs5rf4Fxuqo/213CBylDPkcRRUsyzAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33e74136b99e76980ac97297804fc8e970cdf367add9ca5193687f1edf7d488d","last_reissued_at":"2026-07-05T06:35:45.948635Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:35:45.948635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2210.08558","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":"2026-07-05T06:35:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"04tttuYavDXAk7EMkD/W40tYsXUF/Lk+G34giIShj5mCJpLpRvhpkg4UKX44t+FZOXIgFwMsFETcuUCnT6uYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T09:08:38.822644Z"},"content_sha256":"0ccea1539e7e731f5bd6840178c2f4f403480be916c7fdb7d5d090b02c2d9b2a","schema_version":"1.0","event_id":"sha256:0ccea1539e7e731f5bd6840178c2f4f403480be916c7fdb7d5d090b02c2d9b2a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:GPTUCNVZTZ3JQCWJOKLYAT6I5F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Representations over diagrams of abelian categories I: Global structure and homological objects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RA"],"primary_cat":"math.RT","authors_text":"Li Liang, Liping Li, Nina Yu, Zhenxing Di","submitted_at":"2022-10-16T15:06:23Z","abstract_excerpt":"Representations over diagrams of abelian categories unify quite a few notions appearing widely in literature such as representations of categories, presheaves of modules over categories, representations of species, etc. In this series of papers we study them systematically, characterizing special homological objects in representation category and constructing various structures (such as model structures and Wandhuasen category strcutres) on it. In the first paper we investigate the Grothendieck structure of the representation category, describe important functors and adjunction relations betwe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.08558","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/2210.08558/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":"2026-07-05T06:35:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wbWGxqLW8Olsfr1vpO6AJPKZrAlWklpHNBjaLRl5OLqU41x3tsH5f+dLRWm44leNlXaFxrIomhHZodGXyKS/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T09:08:38.823145Z"},"content_sha256":"c5b65a60b09e8f95a17b96253a8173bd053f3044d55518b13e4cd2582c07fb8c","schema_version":"1.0","event_id":"sha256:c5b65a60b09e8f95a17b96253a8173bd053f3044d55518b13e4cd2582c07fb8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GPTUCNVZTZ3JQCWJOKLYAT6I5F/bundle.json","state_url":"https://pith.science/pith/GPTUCNVZTZ3JQCWJOKLYAT6I5F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GPTUCNVZTZ3JQCWJOKLYAT6I5F/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":"2026-08-21T09:08:38Z","links":{"resolver":"https://pith.science/pith/GPTUCNVZTZ3JQCWJOKLYAT6I5F","bundle":"https://pith.science/pith/GPTUCNVZTZ3JQCWJOKLYAT6I5F/bundle.json","state":"https://pith.science/pith/GPTUCNVZTZ3JQCWJOKLYAT6I5F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GPTUCNVZTZ3JQCWJOKLYAT6I5F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:GPTUCNVZTZ3JQCWJOKLYAT6I5F","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":"a1b0729c2ab730b9bedb61356f741dc3d50d9043129c90a0985cc341f61eee6d","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2022-10-16T15:06:23Z","title_canon_sha256":"e1d0d2410ea9b70905a63c43c33c52fd11e2cfb13356bd2f91f88e1f19a55299"},"schema_version":"1.0","source":{"id":"2210.08558","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.08558","created_at":"2026-07-05T06:35:45Z"},{"alias_kind":"arxiv_version","alias_value":"2210.08558v3","created_at":"2026-07-05T06:35:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.08558","created_at":"2026-07-05T06:35:45Z"},{"alias_kind":"pith_short_12","alias_value":"GPTUCNVZTZ3J","created_at":"2026-07-05T06:35:45Z"},{"alias_kind":"pith_short_16","alias_value":"GPTUCNVZTZ3JQCWJ","created_at":"2026-07-05T06:35:45Z"},{"alias_kind":"pith_short_8","alias_value":"GPTUCNVZ","created_at":"2026-07-05T06:35:45Z"}],"graph_snapshots":[{"event_id":"sha256:c5b65a60b09e8f95a17b96253a8173bd053f3044d55518b13e4cd2582c07fb8c","target":"graph","created_at":"2026-07-05T06:35:45Z","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/2210.08558/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Representations over diagrams of abelian categories unify quite a few notions appearing widely in literature such as representations of categories, presheaves of modules over categories, representations of species, etc. In this series of papers we study them systematically, characterizing special homological objects in representation category and constructing various structures (such as model structures and Wandhuasen category strcutres) on it. In the first paper we investigate the Grothendieck structure of the representation category, describe important functors and adjunction relations betwe","authors_text":"Li Liang, Liping Li, Nina Yu, Zhenxing Di","cross_cats":["math.CT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2022-10-16T15:06:23Z","title":"Representations over diagrams of abelian categories I: Global structure and homological objects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.08558","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":"sha256:0ccea1539e7e731f5bd6840178c2f4f403480be916c7fdb7d5d090b02c2d9b2a","target":"record","created_at":"2026-07-05T06:35:45Z","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":"a1b0729c2ab730b9bedb61356f741dc3d50d9043129c90a0985cc341f61eee6d","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2022-10-16T15:06:23Z","title_canon_sha256":"e1d0d2410ea9b70905a63c43c33c52fd11e2cfb13356bd2f91f88e1f19a55299"},"schema_version":"1.0","source":{"id":"2210.08558","kind":"arxiv","version":3}},"canonical_sha256":"33e74136b99e76980ac97297804fc8e970cdf367add9ca5193687f1edf7d488d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33e74136b99e76980ac97297804fc8e970cdf367add9ca5193687f1edf7d488d","first_computed_at":"2026-07-05T06:35:45.948635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:35:45.948635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hf+bBr/Ykp6WwntvQCq/77/b/gmZNRlPGzBJ2gzBvhmjy9WBpGf5HaCXs5rf4Fxuqo/213CBylDPkcRRUsyzAg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:35:45.949123Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.08558","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ccea1539e7e731f5bd6840178c2f4f403480be916c7fdb7d5d090b02c2d9b2a","sha256:c5b65a60b09e8f95a17b96253a8173bd053f3044d55518b13e4cd2582c07fb8c"],"state_sha256":"85132332a3bb2493070d662ca209509b15671e9761f4115a49dcb9c3d41f1d56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a4adh6rgqWth+pVQTjwbeKnAeIN5lPoWykq3u+bBXrHB6ZA1S6MxxJe7LcefMI8Lxt3gKzxvvm+CXfl2MlhNCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T09:08:38.844454Z","bundle_sha256":"105270f900734c46b039449c5a1c259934ee473828a44bff8c0eab129e07edaf"}}