{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:76D7EDQDMHTQEEJYK4ZHAXG54H","short_pith_number":"pith:76D7EDQD","canonical_record":{"source":{"id":"1712.00890","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-12-04T03:28:38Z","cross_cats_sorted":["math.AT","math.KT","math.NT"],"title_canon_sha256":"423dcb0f36f443e0158d3f4ce646d95375affa93202428a1b50d7542b19b21ee","abstract_canon_sha256":"57df5882afa90fda571311c0ad58e87714b402b355eb2a473cd01da1bb57d815"},"schema_version":"1.0"},"canonical_sha256":"ff87f20e0361e70211385732705cdde1e067fd6004090926c0f2d44a2c62ba70","source":{"kind":"arxiv","id":"1712.00890","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00890","created_at":"2026-07-04T23:59:14Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00890v2","created_at":"2026-07-04T23:59:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00890","created_at":"2026-07-04T23:59:14Z"},{"alias_kind":"pith_short_12","alias_value":"76D7EDQDMHTQ","created_at":"2026-07-04T23:59:14Z"},{"alias_kind":"pith_short_16","alias_value":"76D7EDQDMHTQEEJY","created_at":"2026-07-04T23:59:14Z"},{"alias_kind":"pith_short_8","alias_value":"76D7EDQD","created_at":"2026-07-04T23:59:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:76D7EDQDMHTQEEJYK4ZHAXG54H","target":"record","payload":{"canonical_record":{"source":{"id":"1712.00890","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-12-04T03:28:38Z","cross_cats_sorted":["math.AT","math.KT","math.NT"],"title_canon_sha256":"423dcb0f36f443e0158d3f4ce646d95375affa93202428a1b50d7542b19b21ee","abstract_canon_sha256":"57df5882afa90fda571311c0ad58e87714b402b355eb2a473cd01da1bb57d815"},"schema_version":"1.0"},"canonical_sha256":"ff87f20e0361e70211385732705cdde1e067fd6004090926c0f2d44a2c62ba70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:59:14.358647Z","signature_b64":"GvOnDfTcwq9E/FMnVth0DfBYnEt2NAq853YlcW+MXxAiYXfI3FdQ+xqx2kaHuThI+GNvGKxZEAGa2uQ+ZItpAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff87f20e0361e70211385732705cdde1e067fd6004090926c0f2d44a2c62ba70","last_reissued_at":"2026-07-04T23:59:14.358242Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:59:14.358242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.00890","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":"2026-07-04T23:59:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"09Sev8PS+Xq9PX4H1RWMRFSdpgaR1ccLiDIUvKhpeHG8rh2nS8BZNtIb6jBZfZTW6lZH04Nc/OiShB9SJMDvBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T02:37:17.723880Z"},"content_sha256":"086f30da4993fd35e4883581496f58e06c7da121eeb574b4fc5f252305c8cd06","schema_version":"1.0","event_id":"sha256:086f30da4993fd35e4883581496f58e06c7da121eeb574b4fc5f252305c8cd06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:76D7EDQDMHTQEEJYK4ZHAXG54H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear stable range for homology of congruence subgroups via FI-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT","math.NT"],"primary_cat":"math.RT","authors_text":"Liping Li, Wee Liang Gan","submitted_at":"2017-12-04T03:28:38Z","abstract_excerpt":"We answer positively a question of Church, Miller, Nagpal and Reinhold on existence of a linear bound on the presentation degree of the homology of a complex of FI-modules. This implies a linear stable range for the homology of congruence subgroups of general linear groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00890","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/1712.00890/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":"2026-07-04T23:59:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mdfhgza7C9eYCJyXLj3YlK9n34GAJP2C7XA4QfIDW1l/fkmakHqUUbNSOAXyntwlZ1tPbFy4a2AlEdFDbcg2CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T02:37:17.725101Z"},"content_sha256":"490499b9a38a35e26085d06d62b002bdeb78265ae32faa31a5c74ea90e8710f2","schema_version":"1.0","event_id":"sha256:490499b9a38a35e26085d06d62b002bdeb78265ae32faa31a5c74ea90e8710f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/76D7EDQDMHTQEEJYK4ZHAXG54H/bundle.json","state_url":"https://pith.science/pith/76D7EDQDMHTQEEJYK4ZHAXG54H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/76D7EDQDMHTQEEJYK4ZHAXG54H/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":"2026-08-14T02:37:17Z","links":{"resolver":"https://pith.science/pith/76D7EDQDMHTQEEJYK4ZHAXG54H","bundle":"https://pith.science/pith/76D7EDQDMHTQEEJYK4ZHAXG54H/bundle.json","state":"https://pith.science/pith/76D7EDQDMHTQEEJYK4ZHAXG54H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/76D7EDQDMHTQEEJYK4ZHAXG54H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:76D7EDQDMHTQEEJYK4ZHAXG54H","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":"57df5882afa90fda571311c0ad58e87714b402b355eb2a473cd01da1bb57d815","cross_cats_sorted":["math.AT","math.KT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-12-04T03:28:38Z","title_canon_sha256":"423dcb0f36f443e0158d3f4ce646d95375affa93202428a1b50d7542b19b21ee"},"schema_version":"1.0","source":{"id":"1712.00890","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00890","created_at":"2026-07-04T23:59:14Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00890v2","created_at":"2026-07-04T23:59:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00890","created_at":"2026-07-04T23:59:14Z"},{"alias_kind":"pith_short_12","alias_value":"76D7EDQDMHTQ","created_at":"2026-07-04T23:59:14Z"},{"alias_kind":"pith_short_16","alias_value":"76D7EDQDMHTQEEJY","created_at":"2026-07-04T23:59:14Z"},{"alias_kind":"pith_short_8","alias_value":"76D7EDQD","created_at":"2026-07-04T23:59:14Z"}],"graph_snapshots":[{"event_id":"sha256:490499b9a38a35e26085d06d62b002bdeb78265ae32faa31a5c74ea90e8710f2","target":"graph","created_at":"2026-07-04T23:59:14Z","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/1712.00890/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We answer positively a question of Church, Miller, Nagpal and Reinhold on existence of a linear bound on the presentation degree of the homology of a complex of FI-modules. This implies a linear stable range for the homology of congruence subgroups of general linear groups.","authors_text":"Liping Li, Wee Liang Gan","cross_cats":["math.AT","math.KT","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-12-04T03:28:38Z","title":"Linear stable range for homology of congruence subgroups via FI-modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00890","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":"sha256:086f30da4993fd35e4883581496f58e06c7da121eeb574b4fc5f252305c8cd06","target":"record","created_at":"2026-07-04T23:59:14Z","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":"57df5882afa90fda571311c0ad58e87714b402b355eb2a473cd01da1bb57d815","cross_cats_sorted":["math.AT","math.KT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-12-04T03:28:38Z","title_canon_sha256":"423dcb0f36f443e0158d3f4ce646d95375affa93202428a1b50d7542b19b21ee"},"schema_version":"1.0","source":{"id":"1712.00890","kind":"arxiv","version":2}},"canonical_sha256":"ff87f20e0361e70211385732705cdde1e067fd6004090926c0f2d44a2c62ba70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff87f20e0361e70211385732705cdde1e067fd6004090926c0f2d44a2c62ba70","first_computed_at":"2026-07-04T23:59:14.358242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:59:14.358242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GvOnDfTcwq9E/FMnVth0DfBYnEt2NAq853YlcW+MXxAiYXfI3FdQ+xqx2kaHuThI+GNvGKxZEAGa2uQ+ZItpAw==","signature_status":"signed_v1","signed_at":"2026-07-04T23:59:14.358647Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.00890","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:086f30da4993fd35e4883581496f58e06c7da121eeb574b4fc5f252305c8cd06","sha256:490499b9a38a35e26085d06d62b002bdeb78265ae32faa31a5c74ea90e8710f2"],"state_sha256":"8e348655e72d560a5d804f722b150c3d6e1a571528a60b1c826fcb8bfd682fbb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"61T5zz+1IGvfDTHAtDqhpt1KwFGsLhVbILEtQm6wyaBlvyfEs3u9yv+0IxeDRHd/yRSaA43YDRV14RoH7regDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T02:37:17.732306Z","bundle_sha256":"4b7370297c7797624067a0d2e18b2c48fc26e8bf2eae9a1c96630bc5bc206dd5"}}