{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:N4NW6E6YYXVG4TIF363WXIPR3U","short_pith_number":"pith:N4NW6E6Y","canonical_record":{"source":{"id":"2307.07259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2023-07-14T10:20:31Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"cc34b03842e9edc21e1d77ac5cc37ade89d1d3f37d78bff2b2044d6c30b8f8e9","abstract_canon_sha256":"5cc4444c6d4eb5b5de4fa1061cc1673dd7d6235acaf6c61dd62ae868f8d56450"},"schema_version":"1.0"},"canonical_sha256":"6f1b6f13d8c5ea6e4d05dfb76ba1f1dd3e1b85a4cb7e754c623a539cbd20c389","source":{"kind":"arxiv","id":"2307.07259","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.07259","created_at":"2026-07-05T06:30:53Z"},{"alias_kind":"arxiv_version","alias_value":"2307.07259v1","created_at":"2026-07-05T06:30:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.07259","created_at":"2026-07-05T06:30:53Z"},{"alias_kind":"pith_short_12","alias_value":"N4NW6E6YYXVG","created_at":"2026-07-05T06:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"N4NW6E6YYXVG4TIF","created_at":"2026-07-05T06:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"N4NW6E6Y","created_at":"2026-07-05T06:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:N4NW6E6YYXVG4TIF363WXIPR3U","target":"record","payload":{"canonical_record":{"source":{"id":"2307.07259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2023-07-14T10:20:31Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"cc34b03842e9edc21e1d77ac5cc37ade89d1d3f37d78bff2b2044d6c30b8f8e9","abstract_canon_sha256":"5cc4444c6d4eb5b5de4fa1061cc1673dd7d6235acaf6c61dd62ae868f8d56450"},"schema_version":"1.0"},"canonical_sha256":"6f1b6f13d8c5ea6e4d05dfb76ba1f1dd3e1b85a4cb7e754c623a539cbd20c389","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:30:53.410660Z","signature_b64":"BM1sejKp86bNNiV0qNCadO2vR53eVMwgDpNejuXalJbxaIMbrv3Skg5RpDg4Q+kY3fXpytyllLEJApqC20+PAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f1b6f13d8c5ea6e4d05dfb76ba1f1dd3e1b85a4cb7e754c623a539cbd20c389","last_reissued_at":"2026-07-05T06:30:53.410253Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:30:53.410253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2307.07259","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":"2026-07-05T06:30:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iieX78bYjhs/4OYLasA62ZAB9eV34ONPPIxyaVQ6hqXu6MCQAsQ32E78VGVKknAjJDLpe7i8n427vyxeqKVzAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T00:59:01.966305Z"},"content_sha256":"73e1d06297557e261be0a830acd59c4c38529220cdb41a2d36cfd2d5ff3894f2","schema_version":"1.0","event_id":"sha256:73e1d06297557e261be0a830acd59c4c38529220cdb41a2d36cfd2d5ff3894f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:N4NW6E6YYXVG4TIF363WXIPR3U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An $(\\infty,n)$-categorical straightening-unstraightening construction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Lyne Moser, Martina Rovelli, Nima Rasekh","submitted_at":"2023-07-14T10:20:31Z","abstract_excerpt":"We provide an $(\\infty,n)$-categorical version of the straightening-unstraightening construction, asserting an equivalence between the $(\\infty,n)$-category of double $(\\infty,n-1)$-right fibrations over an $(\\infty,n)$-category $\\mathcal{C}$ and that of the $(\\infty,n)$-functors from $\\mathcal{C}$ valued in $(\\infty,n-1)$-categories. We realize this in the form of a Quillen equivalence between appropriate model structures; on the one hand, a model structure for double $(\\infty,n-1)$-right fibrations over a generic precategory object $W$ in $(\\infty,n-1)$-categories and, on the other hand, a m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.07259","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.07259/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":"2026-07-05T06:30:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uQ3cTEgjb1tU0eldaX6gHbPWBiG3NBFJ7KRHNTPcMM4xJTMmq0innR8gzd/myr5RF/4gAMhA+yITgbv9DRJnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T00:59:01.966821Z"},"content_sha256":"4abf7cdfd6e2f154ca29f612bfccda5b4354e3f790a3e8a701c6d2f435a878f6","schema_version":"1.0","event_id":"sha256:4abf7cdfd6e2f154ca29f612bfccda5b4354e3f790a3e8a701c6d2f435a878f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N4NW6E6YYXVG4TIF363WXIPR3U/bundle.json","state_url":"https://pith.science/pith/N4NW6E6YYXVG4TIF363WXIPR3U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N4NW6E6YYXVG4TIF363WXIPR3U/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":"2026-08-02T00:59:01Z","links":{"resolver":"https://pith.science/pith/N4NW6E6YYXVG4TIF363WXIPR3U","bundle":"https://pith.science/pith/N4NW6E6YYXVG4TIF363WXIPR3U/bundle.json","state":"https://pith.science/pith/N4NW6E6YYXVG4TIF363WXIPR3U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N4NW6E6YYXVG4TIF363WXIPR3U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:N4NW6E6YYXVG4TIF363WXIPR3U","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":"5cc4444c6d4eb5b5de4fa1061cc1673dd7d6235acaf6c61dd62ae868f8d56450","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2023-07-14T10:20:31Z","title_canon_sha256":"cc34b03842e9edc21e1d77ac5cc37ade89d1d3f37d78bff2b2044d6c30b8f8e9"},"schema_version":"1.0","source":{"id":"2307.07259","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.07259","created_at":"2026-07-05T06:30:53Z"},{"alias_kind":"arxiv_version","alias_value":"2307.07259v1","created_at":"2026-07-05T06:30:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.07259","created_at":"2026-07-05T06:30:53Z"},{"alias_kind":"pith_short_12","alias_value":"N4NW6E6YYXVG","created_at":"2026-07-05T06:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"N4NW6E6YYXVG4TIF","created_at":"2026-07-05T06:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"N4NW6E6Y","created_at":"2026-07-05T06:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:4abf7cdfd6e2f154ca29f612bfccda5b4354e3f790a3e8a701c6d2f435a878f6","target":"graph","created_at":"2026-07-05T06:30:53Z","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/2307.07259/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide an $(\\infty,n)$-categorical version of the straightening-unstraightening construction, asserting an equivalence between the $(\\infty,n)$-category of double $(\\infty,n-1)$-right fibrations over an $(\\infty,n)$-category $\\mathcal{C}$ and that of the $(\\infty,n)$-functors from $\\mathcal{C}$ valued in $(\\infty,n-1)$-categories. We realize this in the form of a Quillen equivalence between appropriate model structures; on the one hand, a model structure for double $(\\infty,n-1)$-right fibrations over a generic precategory object $W$ in $(\\infty,n-1)$-categories and, on the other hand, a m","authors_text":"Lyne Moser, Martina Rovelli, Nima Rasekh","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2023-07-14T10:20:31Z","title":"An $(\\infty,n)$-categorical straightening-unstraightening construction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.07259","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":"sha256:73e1d06297557e261be0a830acd59c4c38529220cdb41a2d36cfd2d5ff3894f2","target":"record","created_at":"2026-07-05T06:30:53Z","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":"5cc4444c6d4eb5b5de4fa1061cc1673dd7d6235acaf6c61dd62ae868f8d56450","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2023-07-14T10:20:31Z","title_canon_sha256":"cc34b03842e9edc21e1d77ac5cc37ade89d1d3f37d78bff2b2044d6c30b8f8e9"},"schema_version":"1.0","source":{"id":"2307.07259","kind":"arxiv","version":1}},"canonical_sha256":"6f1b6f13d8c5ea6e4d05dfb76ba1f1dd3e1b85a4cb7e754c623a539cbd20c389","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f1b6f13d8c5ea6e4d05dfb76ba1f1dd3e1b85a4cb7e754c623a539cbd20c389","first_computed_at":"2026-07-05T06:30:53.410253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:30:53.410253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BM1sejKp86bNNiV0qNCadO2vR53eVMwgDpNejuXalJbxaIMbrv3Skg5RpDg4Q+kY3fXpytyllLEJApqC20+PAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:30:53.410660Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.07259","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73e1d06297557e261be0a830acd59c4c38529220cdb41a2d36cfd2d5ff3894f2","sha256:4abf7cdfd6e2f154ca29f612bfccda5b4354e3f790a3e8a701c6d2f435a878f6"],"state_sha256":"7336bd33d3a8c11581cf34998b46dc3b37e1ae2c7b71d5bf55dbbbedf5e0da7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yLiaK2IEPdOiQqFWZkxfUjCf982xifnHdrJXnRxzwlHVMNsdukNrvKolQginYGPMkWoMIY/Xo9c5svgsFFHJAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-02T00:59:01.970388Z","bundle_sha256":"61648d0ab1138da9eecd9811ca97ca1c3659a3ac60b7f863667a0fcec0395701"}}