{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FX7N6WST3SEIUSXKZH7W5JT6VS","short_pith_number":"pith:FX7N6WST","canonical_record":{"source":{"id":"1810.05233","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-11T20:13:05Z","cross_cats_sorted":[],"title_canon_sha256":"0c3573de3af300ed8b32ac4382daac5fce32efa347055786d93ddf3b4843f4ad","abstract_canon_sha256":"c452719158b65f8edeee59875a309900b133f11d7e1dd2f72d3a289a2ce441c9"},"schema_version":"1.0"},"canonical_sha256":"2dfedf5a53dc888a4aeac9ff6ea67eac84623773c62c6a8c636b0906cbc05fbd","source":{"kind":"arxiv","id":"1810.05233","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.05233","created_at":"2026-05-18T00:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1810.05233v1","created_at":"2026-05-18T00:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05233","created_at":"2026-05-18T00:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"FX7N6WST3SEI","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FX7N6WST3SEIUSXK","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FX7N6WST","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FX7N6WST3SEIUSXKZH7W5JT6VS","target":"record","payload":{"canonical_record":{"source":{"id":"1810.05233","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-11T20:13:05Z","cross_cats_sorted":[],"title_canon_sha256":"0c3573de3af300ed8b32ac4382daac5fce32efa347055786d93ddf3b4843f4ad","abstract_canon_sha256":"c452719158b65f8edeee59875a309900b133f11d7e1dd2f72d3a289a2ce441c9"},"schema_version":"1.0"},"canonical_sha256":"2dfedf5a53dc888a4aeac9ff6ea67eac84623773c62c6a8c636b0906cbc05fbd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:31.284309Z","signature_b64":"F+oFfLMkxkYb3l5ubEW9HfjAspISt9osJjcRoqVgwv8k0swd2dt39n08eGYW3+StxZCrCgA/tQ9JrKEstBnpCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2dfedf5a53dc888a4aeac9ff6ea67eac84623773c62c6a8c636b0906cbc05fbd","last_reissued_at":"2026-05-18T00:03:31.283815Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:31.283815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.05233","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:03:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PRSrCK9+88jQp2ZBP+yvKenxGQzkWyHRgZp/vMTwUXTqdeD0GGnf3+W9Em44c51BN3ocUEot87i0hvpuP/FHBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:24:58.209310Z"},"content_sha256":"ee71d0302cfdf53f909aabd557e2e353e6f156e38eaa1a036381739d9728da96","schema_version":"1.0","event_id":"sha256:ee71d0302cfdf53f909aabd557e2e353e6f156e38eaa1a036381739d9728da96"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FX7N6WST3SEIUSXKZH7W5JT6VS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Notes on the Joyal model structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Danny Stevenson","submitted_at":"2018-10-11T20:13:05Z","abstract_excerpt":"We give a new construction of the Joyal model structure on the category of simplicial sets, and we provide a simple characterization of the fibrations in it. We characterize the inner anodyne maps in terms of categorical equivalences and use this characterization to establish the inner model structure on the category of simplicial sets whose set of zero-simplices is equal to a fixed set $O$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05233","kind":"arxiv","version":1},"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":"2026-05-18T00:03:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PNiBmYBmjoP9tsYNl+pdsFf5NjtzmRbyxSdBQVgc2Sc3ZaF/cmwRK8zD/CnzwLhYMM6Q0ZwJKcwh+i1QPX67Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:24:58.210038Z"},"content_sha256":"d6b2d4d57a0813074949d33a24fdc850c64e7189fd5cb35994d18779336d0a7f","schema_version":"1.0","event_id":"sha256:d6b2d4d57a0813074949d33a24fdc850c64e7189fd5cb35994d18779336d0a7f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FX7N6WST3SEIUSXKZH7W5JT6VS/bundle.json","state_url":"https://pith.science/pith/FX7N6WST3SEIUSXKZH7W5JT6VS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FX7N6WST3SEIUSXKZH7W5JT6VS/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":"2026-06-04T22:24:58Z","links":{"resolver":"https://pith.science/pith/FX7N6WST3SEIUSXKZH7W5JT6VS","bundle":"https://pith.science/pith/FX7N6WST3SEIUSXKZH7W5JT6VS/bundle.json","state":"https://pith.science/pith/FX7N6WST3SEIUSXKZH7W5JT6VS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FX7N6WST3SEIUSXKZH7W5JT6VS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FX7N6WST3SEIUSXKZH7W5JT6VS","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":"c452719158b65f8edeee59875a309900b133f11d7e1dd2f72d3a289a2ce441c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-11T20:13:05Z","title_canon_sha256":"0c3573de3af300ed8b32ac4382daac5fce32efa347055786d93ddf3b4843f4ad"},"schema_version":"1.0","source":{"id":"1810.05233","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.05233","created_at":"2026-05-18T00:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1810.05233v1","created_at":"2026-05-18T00:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05233","created_at":"2026-05-18T00:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"FX7N6WST3SEI","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FX7N6WST3SEIUSXK","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FX7N6WST","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:d6b2d4d57a0813074949d33a24fdc850c64e7189fd5cb35994d18779336d0a7f","target":"graph","created_at":"2026-05-18T00:03:31Z","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":"We give a new construction of the Joyal model structure on the category of simplicial sets, and we provide a simple characterization of the fibrations in it. We characterize the inner anodyne maps in terms of categorical equivalences and use this characterization to establish the inner model structure on the category of simplicial sets whose set of zero-simplices is equal to a fixed set $O$.","authors_text":"Danny Stevenson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-11T20:13:05Z","title":"Notes on the Joyal model structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05233","kind":"arxiv","version":1},"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:ee71d0302cfdf53f909aabd557e2e353e6f156e38eaa1a036381739d9728da96","target":"record","created_at":"2026-05-18T00:03:31Z","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":"c452719158b65f8edeee59875a309900b133f11d7e1dd2f72d3a289a2ce441c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-11T20:13:05Z","title_canon_sha256":"0c3573de3af300ed8b32ac4382daac5fce32efa347055786d93ddf3b4843f4ad"},"schema_version":"1.0","source":{"id":"1810.05233","kind":"arxiv","version":1}},"canonical_sha256":"2dfedf5a53dc888a4aeac9ff6ea67eac84623773c62c6a8c636b0906cbc05fbd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2dfedf5a53dc888a4aeac9ff6ea67eac84623773c62c6a8c636b0906cbc05fbd","first_computed_at":"2026-05-18T00:03:31.283815Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:31.283815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F+oFfLMkxkYb3l5ubEW9HfjAspISt9osJjcRoqVgwv8k0swd2dt39n08eGYW3+StxZCrCgA/tQ9JrKEstBnpCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:31.284309Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.05233","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee71d0302cfdf53f909aabd557e2e353e6f156e38eaa1a036381739d9728da96","sha256:d6b2d4d57a0813074949d33a24fdc850c64e7189fd5cb35994d18779336d0a7f"],"state_sha256":"749d8105c4f09dd1b5cf64dfca3fded2e5110ca2c75ac2b0a7da6214bc2d7521"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+7ylfr6ifwVO7nOrgSXa2dPKaQnGxmWmhTwfS+9/xO7KOeKR3zfOIRzWlkI8jTpKod7XuJwjqnhu2zE4zB4qAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:24:58.213311Z","bundle_sha256":"f70caee840baa8440fc29aa73ccb4e1d3d29c106b4820d7648dab434647a96e8"}}