{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WFAH3R7O6FMPZPA633HI2QQRJE","short_pith_number":"pith:WFAH3R7O","canonical_record":{"source":{"id":"1803.00681","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2018-03-02T01:48:06Z","cross_cats_sorted":["math.AG","math.AT"],"title_canon_sha256":"f1a13eaadf357b62bc037eb5ad9e7e0615921a4b5da53efcffb7729efd2d458b","abstract_canon_sha256":"cbc69ee871380a6f9694fca5d07b309346f7a33c725bddc597d8d7d2aa00aef1"},"schema_version":"1.0"},"canonical_sha256":"b1407dc7eef158fcbc1edece8d4211491e65f26e0ea159d57be9600ecc0e96b6","source":{"kind":"arxiv","id":"1803.00681","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00681","created_at":"2026-05-17T23:54:31Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00681v2","created_at":"2026-05-17T23:54:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00681","created_at":"2026-05-17T23:54:31Z"},{"alias_kind":"pith_short_12","alias_value":"WFAH3R7O6FMP","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WFAH3R7O6FMPZPA6","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WFAH3R7O","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WFAH3R7O6FMPZPA633HI2QQRJE","target":"record","payload":{"canonical_record":{"source":{"id":"1803.00681","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2018-03-02T01:48:06Z","cross_cats_sorted":["math.AG","math.AT"],"title_canon_sha256":"f1a13eaadf357b62bc037eb5ad9e7e0615921a4b5da53efcffb7729efd2d458b","abstract_canon_sha256":"cbc69ee871380a6f9694fca5d07b309346f7a33c725bddc597d8d7d2aa00aef1"},"schema_version":"1.0"},"canonical_sha256":"b1407dc7eef158fcbc1edece8d4211491e65f26e0ea159d57be9600ecc0e96b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:31.897359Z","signature_b64":"ywF0CCYnesi2pV5wef24bm98n5UmGAASbV1fTbjXt0aOrJqxd8aHawdRtJol9C1+T3eAOgHvEEVroMhnQB81AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1407dc7eef158fcbc1edece8d4211491e65f26e0ea159d57be9600ecc0e96b6","last_reissued_at":"2026-05-17T23:54:31.896697Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:31.896697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.00681","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":"2026-05-17T23:54:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fClACwtI2PAVr+mO35VX1d/p0o9bdKyCJ6XtTjeTlsd6TMFK2BVUPy3eDmneWiIrdgorWnIJiXZqyT6fWiiaBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:06:36.231559Z"},"content_sha256":"2028813b69f14468f4fc984a60020e771a72f55bcccf54c8a820a1330d5d696a","schema_version":"1.0","event_id":"sha256:2028813b69f14468f4fc984a60020e771a72f55bcccf54c8a820a1330d5d696a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WFAH3R7O6FMPZPA633HI2QQRJE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reedy Model Structures in Families","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.AT"],"primary_cat":"math.CT","authors_text":"Edouard Balzin","submitted_at":"2018-03-02T01:48:06Z","abstract_excerpt":"Given a family of model categories $\\cal E \\to \\cal R$ over a Reedy category, we outline a set of conditions which lead to the existence of a Reedy model structure on the category of sections ${\\sf Sect}(\\cal R, \\cal E)$. We prove that for a wide class of examples, this model structure serves as a strictification of the $(\\infty,1)$-category of sections of the higher-categorical family associated to $\\cal E \\to \\cal R$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00681","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":""},"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":"2026-05-17T23:54:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lg2ANxF/ZDXhMDYae/cNuRP0myPvZDoZniF3sRGXcu1LNgiwV1Xo8LXB+J8E0FIaNo4ztSHS6wiWFyw27v/cAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:06:36.231906Z"},"content_sha256":"0fa70d0f01514267aa7cd4559e98210cf64895c56301da1dd4d52d2831e80723","schema_version":"1.0","event_id":"sha256:0fa70d0f01514267aa7cd4559e98210cf64895c56301da1dd4d52d2831e80723"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WFAH3R7O6FMPZPA633HI2QQRJE/bundle.json","state_url":"https://pith.science/pith/WFAH3R7O6FMPZPA633HI2QQRJE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WFAH3R7O6FMPZPA633HI2QQRJE/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":"2026-06-02T10:06:36Z","links":{"resolver":"https://pith.science/pith/WFAH3R7O6FMPZPA633HI2QQRJE","bundle":"https://pith.science/pith/WFAH3R7O6FMPZPA633HI2QQRJE/bundle.json","state":"https://pith.science/pith/WFAH3R7O6FMPZPA633HI2QQRJE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WFAH3R7O6FMPZPA633HI2QQRJE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WFAH3R7O6FMPZPA633HI2QQRJE","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":"cbc69ee871380a6f9694fca5d07b309346f7a33c725bddc597d8d7d2aa00aef1","cross_cats_sorted":["math.AG","math.AT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2018-03-02T01:48:06Z","title_canon_sha256":"f1a13eaadf357b62bc037eb5ad9e7e0615921a4b5da53efcffb7729efd2d458b"},"schema_version":"1.0","source":{"id":"1803.00681","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00681","created_at":"2026-05-17T23:54:31Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00681v2","created_at":"2026-05-17T23:54:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00681","created_at":"2026-05-17T23:54:31Z"},{"alias_kind":"pith_short_12","alias_value":"WFAH3R7O6FMP","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WFAH3R7O6FMPZPA6","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WFAH3R7O","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:0fa70d0f01514267aa7cd4559e98210cf64895c56301da1dd4d52d2831e80723","target":"graph","created_at":"2026-05-17T23:54:31Z","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":"Given a family of model categories $\\cal E \\to \\cal R$ over a Reedy category, we outline a set of conditions which lead to the existence of a Reedy model structure on the category of sections ${\\sf Sect}(\\cal R, \\cal E)$. We prove that for a wide class of examples, this model structure serves as a strictification of the $(\\infty,1)$-category of sections of the higher-categorical family associated to $\\cal E \\to \\cal R$.","authors_text":"Edouard Balzin","cross_cats":["math.AG","math.AT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2018-03-02T01:48:06Z","title":"Reedy Model Structures in Families"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00681","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":"sha256:2028813b69f14468f4fc984a60020e771a72f55bcccf54c8a820a1330d5d696a","target":"record","created_at":"2026-05-17T23:54:31Z","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":"cbc69ee871380a6f9694fca5d07b309346f7a33c725bddc597d8d7d2aa00aef1","cross_cats_sorted":["math.AG","math.AT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2018-03-02T01:48:06Z","title_canon_sha256":"f1a13eaadf357b62bc037eb5ad9e7e0615921a4b5da53efcffb7729efd2d458b"},"schema_version":"1.0","source":{"id":"1803.00681","kind":"arxiv","version":2}},"canonical_sha256":"b1407dc7eef158fcbc1edece8d4211491e65f26e0ea159d57be9600ecc0e96b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1407dc7eef158fcbc1edece8d4211491e65f26e0ea159d57be9600ecc0e96b6","first_computed_at":"2026-05-17T23:54:31.896697Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:31.896697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ywF0CCYnesi2pV5wef24bm98n5UmGAASbV1fTbjXt0aOrJqxd8aHawdRtJol9C1+T3eAOgHvEEVroMhnQB81AA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:31.897359Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.00681","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2028813b69f14468f4fc984a60020e771a72f55bcccf54c8a820a1330d5d696a","sha256:0fa70d0f01514267aa7cd4559e98210cf64895c56301da1dd4d52d2831e80723"],"state_sha256":"5118ccda7bf91f6c9f981ce7c2c1a8a9b64c636f9dd9e96f40461c45d60378fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CXgbKFr9eRYXmK6mIV9rL7aPaUjyatVQVKdMFtJH3y+cdseEqUl4whR5+PbzTk3ZhOfCfvJv2qJCCYvHEbcABw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T10:06:36.233880Z","bundle_sha256":"198f4b09397fe08c37a2ece2b95edf3f2b0b382d5a1e59939a2d73d3b24b2ad2"}}