{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:I3XPHFN6WJOQRZHQM36C6X7MY5","short_pith_number":"pith:I3XPHFN6","canonical_record":{"source":{"id":"1808.00915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-08-02T17:01:21Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"d256238beedeaa92862acc05a9574705fca9874b5adf14beb37a9af838630033","abstract_canon_sha256":"cef3ba3fc8e83d5bd6d2e0af55313da310fd223d5718b9b45c3ce14309a42448"},"schema_version":"1.0"},"canonical_sha256":"46eef395beb25d08e4f066fc2f5fecc76940674ef19a2a22ed3687f2e53c82dd","source":{"kind":"arxiv","id":"1808.00915","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.00915","created_at":"2026-05-18T00:09:01Z"},{"alias_kind":"arxiv_version","alias_value":"1808.00915v1","created_at":"2026-05-18T00:09:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.00915","created_at":"2026-05-18T00:09:01Z"},{"alias_kind":"pith_short_12","alias_value":"I3XPHFN6WJOQ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"I3XPHFN6WJOQRZHQ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"I3XPHFN6","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:I3XPHFN6WJOQRZHQM36C6X7MY5","target":"record","payload":{"canonical_record":{"source":{"id":"1808.00915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-08-02T17:01:21Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"d256238beedeaa92862acc05a9574705fca9874b5adf14beb37a9af838630033","abstract_canon_sha256":"cef3ba3fc8e83d5bd6d2e0af55313da310fd223d5718b9b45c3ce14309a42448"},"schema_version":"1.0"},"canonical_sha256":"46eef395beb25d08e4f066fc2f5fecc76940674ef19a2a22ed3687f2e53c82dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:01.029835Z","signature_b64":"HGRN5AePyCDK/pYJIeATn4FikmDM3djdhm1D2B866M3eI062yD9/OROXF5XGeZwAVynewQL/aDzVszhN7a9yDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46eef395beb25d08e4f066fc2f5fecc76940674ef19a2a22ed3687f2e53c82dd","last_reissued_at":"2026-05-18T00:09:01.029381Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:01.029381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.00915","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":"2026-05-18T00:09:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uTohGmCdOZYABaheiAfNFvTx61/QLg9ro3F4t+Hv5Sp8yUZuyni1H7NUFJRr+cHE01Rri38zHBtHwg7wWMFJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:18:35.711837Z"},"content_sha256":"28335e928edd96d0e3259baf060eeb41937658c79a785061414397fd66ba32d4","schema_version":"1.0","event_id":"sha256:28335e928edd96d0e3259baf060eeb41937658c79a785061414397fd66ba32d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:I3XPHFN6WJOQRZHQM36C6X7MY5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Identity Types in Algebraic Model Structures and Cubical Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CT","authors_text":"Andrew Swan","submitted_at":"2018-08-02T17:01:21Z","abstract_excerpt":"We give a general technique for constructing a functorial choice of very good paths objects, which can be used to implement identity types in models of type theories in direct manner with little reliance on general coherence results. We give a simple proof that applies in algebraic model structures that possess a notion of structured weak equivalence, in a sense that we define here. We then give a more direct proof that applies both to the original BCH cubical set model and more recent variants. We give an explanation how this construction relates to the one used in the CCHM cubical set model "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00915","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":"2026-05-18T00:09:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gLviLessiO+YkK0qjMjSE5pDIdWu9ixpPET56FxC6xAvUXAF71uRvU34uHRjR7mmFsvgMkIvVBL+CDYsj2nJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:18:35.712185Z"},"content_sha256":"e2bf5726b28a9dc115f79d05ec75717e2d351555c67df1e75de4fe571a595aac","schema_version":"1.0","event_id":"sha256:e2bf5726b28a9dc115f79d05ec75717e2d351555c67df1e75de4fe571a595aac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I3XPHFN6WJOQRZHQM36C6X7MY5/bundle.json","state_url":"https://pith.science/pith/I3XPHFN6WJOQRZHQM36C6X7MY5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I3XPHFN6WJOQRZHQM36C6X7MY5/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":"2026-05-28T12:18:35Z","links":{"resolver":"https://pith.science/pith/I3XPHFN6WJOQRZHQM36C6X7MY5","bundle":"https://pith.science/pith/I3XPHFN6WJOQRZHQM36C6X7MY5/bundle.json","state":"https://pith.science/pith/I3XPHFN6WJOQRZHQM36C6X7MY5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I3XPHFN6WJOQRZHQM36C6X7MY5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:I3XPHFN6WJOQRZHQM36C6X7MY5","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":"cef3ba3fc8e83d5bd6d2e0af55313da310fd223d5718b9b45c3ce14309a42448","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-08-02T17:01:21Z","title_canon_sha256":"d256238beedeaa92862acc05a9574705fca9874b5adf14beb37a9af838630033"},"schema_version":"1.0","source":{"id":"1808.00915","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.00915","created_at":"2026-05-18T00:09:01Z"},{"alias_kind":"arxiv_version","alias_value":"1808.00915v1","created_at":"2026-05-18T00:09:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.00915","created_at":"2026-05-18T00:09:01Z"},{"alias_kind":"pith_short_12","alias_value":"I3XPHFN6WJOQ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"I3XPHFN6WJOQRZHQ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"I3XPHFN6","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:e2bf5726b28a9dc115f79d05ec75717e2d351555c67df1e75de4fe571a595aac","target":"graph","created_at":"2026-05-18T00:09:01Z","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 general technique for constructing a functorial choice of very good paths objects, which can be used to implement identity types in models of type theories in direct manner with little reliance on general coherence results. We give a simple proof that applies in algebraic model structures that possess a notion of structured weak equivalence, in a sense that we define here. We then give a more direct proof that applies both to the original BCH cubical set model and more recent variants. We give an explanation how this construction relates to the one used in the CCHM cubical set model ","authors_text":"Andrew Swan","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-08-02T17:01:21Z","title":"Identity Types in Algebraic Model Structures and Cubical Sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00915","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":"sha256:28335e928edd96d0e3259baf060eeb41937658c79a785061414397fd66ba32d4","target":"record","created_at":"2026-05-18T00:09:01Z","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":"cef3ba3fc8e83d5bd6d2e0af55313da310fd223d5718b9b45c3ce14309a42448","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-08-02T17:01:21Z","title_canon_sha256":"d256238beedeaa92862acc05a9574705fca9874b5adf14beb37a9af838630033"},"schema_version":"1.0","source":{"id":"1808.00915","kind":"arxiv","version":1}},"canonical_sha256":"46eef395beb25d08e4f066fc2f5fecc76940674ef19a2a22ed3687f2e53c82dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46eef395beb25d08e4f066fc2f5fecc76940674ef19a2a22ed3687f2e53c82dd","first_computed_at":"2026-05-18T00:09:01.029381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:01.029381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HGRN5AePyCDK/pYJIeATn4FikmDM3djdhm1D2B866M3eI062yD9/OROXF5XGeZwAVynewQL/aDzVszhN7a9yDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:01.029835Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.00915","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28335e928edd96d0e3259baf060eeb41937658c79a785061414397fd66ba32d4","sha256:e2bf5726b28a9dc115f79d05ec75717e2d351555c67df1e75de4fe571a595aac"],"state_sha256":"d61efd8c56e3383478d2681e584c546d230ce8ffe39d0c96cc6af7326196a4b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VtXyxCRCrCmW53g+CJpDRAOsnFvpr7MlY2053eoeED1tJzLoGl3yZtDsrhHHmuhs39UUNSfQYcC7n9rLfY1xDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:18:35.714137Z","bundle_sha256":"b8fd43b0b6df2392eeeaf34e62c7d28fbc50af6969a387447a7a25ebc0d8cdce"}}