{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:OKPEL4TUJNTQGMZDOOT2KWNAEG","short_pith_number":"pith:OKPEL4TU","canonical_record":{"source":{"id":"2407.06877","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-07-09T14:05:10Z","cross_cats_sorted":[],"title_canon_sha256":"bbb0afdd7bbdcfc1d70260ee321652d3cdd93ca1e7f2eed79e507f8cc37eb443","abstract_canon_sha256":"1a7afd1883851b7b47840fe9c92188e07daeece7cdc92586864feae8b5697601"},"schema_version":"1.0"},"canonical_sha256":"729e45f2744b6703332373a7a559a021bdd616406b9cb43c79440303c893e0a5","source":{"kind":"arxiv","id":"2407.06877","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.06877","created_at":"2026-07-05T08:42:06Z"},{"alias_kind":"arxiv_version","alias_value":"2407.06877v2","created_at":"2026-07-05T08:42:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.06877","created_at":"2026-07-05T08:42:06Z"},{"alias_kind":"pith_short_12","alias_value":"OKPEL4TUJNTQ","created_at":"2026-07-05T08:42:06Z"},{"alias_kind":"pith_short_16","alias_value":"OKPEL4TUJNTQGMZD","created_at":"2026-07-05T08:42:06Z"},{"alias_kind":"pith_short_8","alias_value":"OKPEL4TU","created_at":"2026-07-05T08:42:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:OKPEL4TUJNTQGMZDOOT2KWNAEG","target":"record","payload":{"canonical_record":{"source":{"id":"2407.06877","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-07-09T14:05:10Z","cross_cats_sorted":[],"title_canon_sha256":"bbb0afdd7bbdcfc1d70260ee321652d3cdd93ca1e7f2eed79e507f8cc37eb443","abstract_canon_sha256":"1a7afd1883851b7b47840fe9c92188e07daeece7cdc92586864feae8b5697601"},"schema_version":"1.0"},"canonical_sha256":"729e45f2744b6703332373a7a559a021bdd616406b9cb43c79440303c893e0a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:42:06.078840Z","signature_b64":"DxKJQK6OTD1PIHV6VJTdnAT3t0GPbXuHYdKi3qT0fcc+wacAKMSIZZHjbM/2jvmq2kCLeXkOmN4PE5Xth9jRAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"729e45f2744b6703332373a7a559a021bdd616406b9cb43c79440303c893e0a5","last_reissued_at":"2026-07-05T08:42:06.078355Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:42:06.078355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.06877","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":"2026-07-05T08:42:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PqFsGCVATh5ZuXlFOMJqqZ4bvOKr5+wINz8weaQgsI9DAZKKclCq84sXc/awQMM1w92TcU8xy5SGM2kYOZI5AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T11:01:47.883590Z"},"content_sha256":"2172770255b5993385b95bf502e9a6fd27b4f088cabde190def381f0a9ad2f9a","schema_version":"1.0","event_id":"sha256:2172770255b5993385b95bf502e9a6fd27b4f088cabde190def381f0a9ad2f9a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:OKPEL4TUJNTQGMZDOOT2KWNAEG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global spaces and the homotopy theory of stacks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Adrian Clough, Bastiaan Cnossen, Sil Linskens","submitted_at":"2024-07-09T14:05:10Z","abstract_excerpt":"We show that the $\\infty$-category of global spaces is equivalent to the homotopy localization of the $\\infty$-category of sheaves on the site of separated differentiable stacks, following a philosophy proposed by Gepner-Henriques. We further prove that this $\\infty$-category of sheaves is a cohesive $\\infty$-topos and that it fully faithfully contains the singular-cohesive $\\infty$-topos of Sati-Schreiber."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.06877","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.06877/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":"2026-07-05T08:42:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3m5yldHc1mh2vilv94aTnkI8Mt4dX2X+Hi0X522JaRK6Vl2WSq1AL7cewrGhIX/ph9MWzwxxSctOTNg3HQxUAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T11:01:47.884079Z"},"content_sha256":"373016ece07c7daeefd0138545eb21b8823bdefa34707d3aa9e61cf492e2faaa","schema_version":"1.0","event_id":"sha256:373016ece07c7daeefd0138545eb21b8823bdefa34707d3aa9e61cf492e2faaa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OKPEL4TUJNTQGMZDOOT2KWNAEG/bundle.json","state_url":"https://pith.science/pith/OKPEL4TUJNTQGMZDOOT2KWNAEG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OKPEL4TUJNTQGMZDOOT2KWNAEG/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":"2026-08-12T11:01:47Z","links":{"resolver":"https://pith.science/pith/OKPEL4TUJNTQGMZDOOT2KWNAEG","bundle":"https://pith.science/pith/OKPEL4TUJNTQGMZDOOT2KWNAEG/bundle.json","state":"https://pith.science/pith/OKPEL4TUJNTQGMZDOOT2KWNAEG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OKPEL4TUJNTQGMZDOOT2KWNAEG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OKPEL4TUJNTQGMZDOOT2KWNAEG","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":"1a7afd1883851b7b47840fe9c92188e07daeece7cdc92586864feae8b5697601","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-07-09T14:05:10Z","title_canon_sha256":"bbb0afdd7bbdcfc1d70260ee321652d3cdd93ca1e7f2eed79e507f8cc37eb443"},"schema_version":"1.0","source":{"id":"2407.06877","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.06877","created_at":"2026-07-05T08:42:06Z"},{"alias_kind":"arxiv_version","alias_value":"2407.06877v2","created_at":"2026-07-05T08:42:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.06877","created_at":"2026-07-05T08:42:06Z"},{"alias_kind":"pith_short_12","alias_value":"OKPEL4TUJNTQ","created_at":"2026-07-05T08:42:06Z"},{"alias_kind":"pith_short_16","alias_value":"OKPEL4TUJNTQGMZD","created_at":"2026-07-05T08:42:06Z"},{"alias_kind":"pith_short_8","alias_value":"OKPEL4TU","created_at":"2026-07-05T08:42:06Z"}],"graph_snapshots":[{"event_id":"sha256:373016ece07c7daeefd0138545eb21b8823bdefa34707d3aa9e61cf492e2faaa","target":"graph","created_at":"2026-07-05T08:42:06Z","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/2407.06877/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the $\\infty$-category of global spaces is equivalent to the homotopy localization of the $\\infty$-category of sheaves on the site of separated differentiable stacks, following a philosophy proposed by Gepner-Henriques. We further prove that this $\\infty$-category of sheaves is a cohesive $\\infty$-topos and that it fully faithfully contains the singular-cohesive $\\infty$-topos of Sati-Schreiber.","authors_text":"Adrian Clough, Bastiaan Cnossen, Sil Linskens","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-07-09T14:05:10Z","title":"Global spaces and the homotopy theory of stacks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.06877","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":"sha256:2172770255b5993385b95bf502e9a6fd27b4f088cabde190def381f0a9ad2f9a","target":"record","created_at":"2026-07-05T08:42:06Z","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":"1a7afd1883851b7b47840fe9c92188e07daeece7cdc92586864feae8b5697601","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-07-09T14:05:10Z","title_canon_sha256":"bbb0afdd7bbdcfc1d70260ee321652d3cdd93ca1e7f2eed79e507f8cc37eb443"},"schema_version":"1.0","source":{"id":"2407.06877","kind":"arxiv","version":2}},"canonical_sha256":"729e45f2744b6703332373a7a559a021bdd616406b9cb43c79440303c893e0a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"729e45f2744b6703332373a7a559a021bdd616406b9cb43c79440303c893e0a5","first_computed_at":"2026-07-05T08:42:06.078355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:42:06.078355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DxKJQK6OTD1PIHV6VJTdnAT3t0GPbXuHYdKi3qT0fcc+wacAKMSIZZHjbM/2jvmq2kCLeXkOmN4PE5Xth9jRAw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:42:06.078840Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.06877","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2172770255b5993385b95bf502e9a6fd27b4f088cabde190def381f0a9ad2f9a","sha256:373016ece07c7daeefd0138545eb21b8823bdefa34707d3aa9e61cf492e2faaa"],"state_sha256":"a79888cb401c7d6559ea10888fb62504d4d9a1e2400bc400bdce6650077d8ce8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tE0h3KzHVU2WrgnfjmCpfPLAbP3C8I2YLSDJStBg7WbrFpWBOx8CHclrDJ6R9EjTn51Pzbar85NqnzUJcFAfAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T11:01:47.896743Z","bundle_sha256":"59c5da68aa4a5dd7f9cd7cf937043dcfac80d77180985610e73862d0c22edce6"}}