{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ECJZCUOXVDWWJ3KDVZTL65SWM5","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":"7803a0405159d076486a02014f07189d4f551f98beaf42d9bcb0da9c48a79c0c","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-07-08T20:02:02Z","title_canon_sha256":"50d2aab2afd2209c8396d2e56bf4b4573b5104f7b7a719d61cb04898ee91e9c1"},"schema_version":"1.0","source":{"id":"1907.03837","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.03837","created_at":"2026-05-17T23:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"1907.03837v1","created_at":"2026-05-17T23:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.03837","created_at":"2026-05-17T23:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"ECJZCUOXVDWW","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"ECJZCUOXVDWWJ3KD","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"ECJZCUOX","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:3c46a27e8b38860e87b3cd3ca5782b2840591769a54512205fd0fa4909cd3a31","target":"graph","created_at":"2026-05-17T23:41:06Z","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"},"paper":{"abstract_excerpt":"We prove that, given any reflective subfibration $L_\\bullet$ on an $\\infty$-topos $\\mathcal{E}$, there exists a reflective subfibration $L'_\\bullet$ on $\\mathcal{E}$ whose local maps are the $L$-separated maps, that is, the maps whose diagonals are $L$-local. This is the companion paper to \"Localization theory in an $\\infty$-topos\".","authors_text":"Marco Vergura","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-07-08T20:02:02Z","title":"$L'$-localization in an $\\infty$-topos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03837","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":"sha256:2b52e7b32a560d486b67329c4e7768eebf4270867e54848269b8ceeb787c7632","target":"record","created_at":"2026-05-17T23:41:06Z","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":"7803a0405159d076486a02014f07189d4f551f98beaf42d9bcb0da9c48a79c0c","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-07-08T20:02:02Z","title_canon_sha256":"50d2aab2afd2209c8396d2e56bf4b4573b5104f7b7a719d61cb04898ee91e9c1"},"schema_version":"1.0","source":{"id":"1907.03837","kind":"arxiv","version":1}},"canonical_sha256":"20939151d7a8ed64ed43ae66bf765667453692c60b667f3c8895cd50d742ae6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20939151d7a8ed64ed43ae66bf765667453692c60b667f3c8895cd50d742ae6f","first_computed_at":"2026-05-17T23:41:06.663807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:06.663807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D5TpYZwvKYJXURSYIJejx99fav97tpV3eqKbZkjbytXV6B9VLVoGhCUXWhI31P0X/+nqqpA+0Z14yQagJOzhCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:06.664565Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.03837","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b52e7b32a560d486b67329c4e7768eebf4270867e54848269b8ceeb787c7632","sha256:3c46a27e8b38860e87b3cd3ca5782b2840591769a54512205fd0fa4909cd3a31"],"state_sha256":"969ccf20f0b70af78924404af7216851bb374defbfaf5de6e3182a06939e82fa"}