{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:DN5RZQPMBYRVKQG5N5HYLUVSDV","short_pith_number":"pith:DN5RZQPM","canonical_record":{"source":{"id":"1705.04180","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-11T13:43:15Z","cross_cats_sorted":[],"title_canon_sha256":"1153d4f7872084f7e0adc4e252d2af5c7a995f46c4a64636e6170d348b94d9a3","abstract_canon_sha256":"0ce9762fee906f0b85aa916da0b4698cee9294e90966dded5b0c1a1cc3df7a58"},"schema_version":"1.0"},"canonical_sha256":"1b7b1cc1ec0e235540dd6f4f85d2b21d7f58aad5082b1ee7f05a7ccc62c51b5c","source":{"kind":"arxiv","id":"1705.04180","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04180","created_at":"2026-05-18T00:43:49Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04180v3","created_at":"2026-05-18T00:43:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04180","created_at":"2026-05-18T00:43:49Z"},{"alias_kind":"pith_short_12","alias_value":"DN5RZQPMBYRV","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DN5RZQPMBYRVKQG5","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DN5RZQPM","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:DN5RZQPMBYRVKQG5N5HYLUVSDV","target":"record","payload":{"canonical_record":{"source":{"id":"1705.04180","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-11T13:43:15Z","cross_cats_sorted":[],"title_canon_sha256":"1153d4f7872084f7e0adc4e252d2af5c7a995f46c4a64636e6170d348b94d9a3","abstract_canon_sha256":"0ce9762fee906f0b85aa916da0b4698cee9294e90966dded5b0c1a1cc3df7a58"},"schema_version":"1.0"},"canonical_sha256":"1b7b1cc1ec0e235540dd6f4f85d2b21d7f58aad5082b1ee7f05a7ccc62c51b5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:49.825052Z","signature_b64":"0EeEXoCDJnucP3NKk0PBL+1ABg1OzMyyYTHRUgpuJK9kpa0i9t2gD+Ki0ZJrCYVKuh/yXAN+ohbl7cwp+biDCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b7b1cc1ec0e235540dd6f4f85d2b21d7f58aad5082b1ee7f05a7ccc62c51b5c","last_reissued_at":"2026-05-18T00:43:49.824595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:49.824595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.04180","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":"2026-05-18T00:43:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WeM1pZZAns0oYVOCLuM3P9sib0U0Fc89lLovb9vSnRJPfbpkQ7YjHZw0EQxxBtV4hU9uGb5LEhgBc0GiwLTPAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:00:36.390638Z"},"content_sha256":"1d45e62f8757d163f64d337c90a1cfc83fbe642a1409128b918ca8b8d4422288","schema_version":"1.0","event_id":"sha256:1d45e62f8757d163f64d337c90a1cfc83fbe642a1409128b918ca8b8d4422288"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:DN5RZQPMBYRVKQG5N5HYLUVSDV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Models in Rational homotopy theory and Torus Rank Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Qianwen Sun, Xiugui Liu, Yanlong Hao","submitted_at":"2017-05-11T13:43:15Z","abstract_excerpt":"In this paper, we focus on some models in rational homotopy theory, Sullivan model, Quillen model, C_\\infty model, and L_\\infty model. We give some connections between them. As an application, we prove the Torus Rank Conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04180","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":""},"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":"2026-05-18T00:43:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FTfjnZYkXfzbsXH/pBHNxjIgxuoKO+S/MKi2zP1ZNoDXTzIbBvvaxzapcLwcfr3wuEFQhFYQTusUISdMFxGZDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:00:36.391307Z"},"content_sha256":"6153fd7d06aeedf99c8780c07e9ccd5fa38d8a957c3cfa9b68b9dc70e491887d","schema_version":"1.0","event_id":"sha256:6153fd7d06aeedf99c8780c07e9ccd5fa38d8a957c3cfa9b68b9dc70e491887d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DN5RZQPMBYRVKQG5N5HYLUVSDV/bundle.json","state_url":"https://pith.science/pith/DN5RZQPMBYRVKQG5N5HYLUVSDV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DN5RZQPMBYRVKQG5N5HYLUVSDV/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":"2026-06-07T06:00:36Z","links":{"resolver":"https://pith.science/pith/DN5RZQPMBYRVKQG5N5HYLUVSDV","bundle":"https://pith.science/pith/DN5RZQPMBYRVKQG5N5HYLUVSDV/bundle.json","state":"https://pith.science/pith/DN5RZQPMBYRVKQG5N5HYLUVSDV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DN5RZQPMBYRVKQG5N5HYLUVSDV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DN5RZQPMBYRVKQG5N5HYLUVSDV","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":"0ce9762fee906f0b85aa916da0b4698cee9294e90966dded5b0c1a1cc3df7a58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-11T13:43:15Z","title_canon_sha256":"1153d4f7872084f7e0adc4e252d2af5c7a995f46c4a64636e6170d348b94d9a3"},"schema_version":"1.0","source":{"id":"1705.04180","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04180","created_at":"2026-05-18T00:43:49Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04180v3","created_at":"2026-05-18T00:43:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04180","created_at":"2026-05-18T00:43:49Z"},{"alias_kind":"pith_short_12","alias_value":"DN5RZQPMBYRV","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DN5RZQPMBYRVKQG5","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DN5RZQPM","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:6153fd7d06aeedf99c8780c07e9ccd5fa38d8a957c3cfa9b68b9dc70e491887d","target":"graph","created_at":"2026-05-18T00:43:49Z","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":"In this paper, we focus on some models in rational homotopy theory, Sullivan model, Quillen model, C_\\infty model, and L_\\infty model. We give some connections between them. As an application, we prove the Torus Rank Conjecture.","authors_text":"Qianwen Sun, Xiugui Liu, Yanlong Hao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-11T13:43:15Z","title":"Models in Rational homotopy theory and Torus Rank Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04180","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":"sha256:1d45e62f8757d163f64d337c90a1cfc83fbe642a1409128b918ca8b8d4422288","target":"record","created_at":"2026-05-18T00:43:49Z","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":"0ce9762fee906f0b85aa916da0b4698cee9294e90966dded5b0c1a1cc3df7a58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-11T13:43:15Z","title_canon_sha256":"1153d4f7872084f7e0adc4e252d2af5c7a995f46c4a64636e6170d348b94d9a3"},"schema_version":"1.0","source":{"id":"1705.04180","kind":"arxiv","version":3}},"canonical_sha256":"1b7b1cc1ec0e235540dd6f4f85d2b21d7f58aad5082b1ee7f05a7ccc62c51b5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b7b1cc1ec0e235540dd6f4f85d2b21d7f58aad5082b1ee7f05a7ccc62c51b5c","first_computed_at":"2026-05-18T00:43:49.824595Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:49.824595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0EeEXoCDJnucP3NKk0PBL+1ABg1OzMyyYTHRUgpuJK9kpa0i9t2gD+Ki0ZJrCYVKuh/yXAN+ohbl7cwp+biDCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:49.825052Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.04180","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d45e62f8757d163f64d337c90a1cfc83fbe642a1409128b918ca8b8d4422288","sha256:6153fd7d06aeedf99c8780c07e9ccd5fa38d8a957c3cfa9b68b9dc70e491887d"],"state_sha256":"4aa4e7df221feb1c01e6fa3c840f7765c6c3645cb6507302f85ce847f849d1ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1aIA9XqIceulUH1DUIPI3h+FmW7IMAjq0snC/VRw/Twszd+mteQXDAtPefqNmGUk3ATGhQdJXaU6FhOQCX2+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:00:36.395567Z","bundle_sha256":"dc8afb7635b34a3bbfd4760e09a8876de45da6347b2447ab457f2131b63b0de3"}}