{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:VR24IIOWFUFMQII36H4WTCLJQW","short_pith_number":"pith:VR24IIOW","canonical_record":{"source":{"id":"2410.21537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-10-28T21:03:52Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"65c58159c3240195e94732528ae58dd2801c8ef2ec7343eeb34209dda41c07d8","abstract_canon_sha256":"e156fc80c1e3d62d3936d29e76397e44579ae16365326a21a47d074090547158"},"schema_version":"1.0"},"canonical_sha256":"ac75c421d62d0ac8211bf1f969896985b9014ac44ed6bf62bd2837da9fd8ff54","source":{"kind":"arxiv","id":"2410.21537","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.21537","created_at":"2026-07-05T09:27:29Z"},{"alias_kind":"arxiv_version","alias_value":"2410.21537v1","created_at":"2026-07-05T09:27:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.21537","created_at":"2026-07-05T09:27:29Z"},{"alias_kind":"pith_short_12","alias_value":"VR24IIOWFUFM","created_at":"2026-07-05T09:27:29Z"},{"alias_kind":"pith_short_16","alias_value":"VR24IIOWFUFMQII3","created_at":"2026-07-05T09:27:29Z"},{"alias_kind":"pith_short_8","alias_value":"VR24IIOW","created_at":"2026-07-05T09:27:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:VR24IIOWFUFMQII36H4WTCLJQW","target":"record","payload":{"canonical_record":{"source":{"id":"2410.21537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-10-28T21:03:52Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"65c58159c3240195e94732528ae58dd2801c8ef2ec7343eeb34209dda41c07d8","abstract_canon_sha256":"e156fc80c1e3d62d3936d29e76397e44579ae16365326a21a47d074090547158"},"schema_version":"1.0"},"canonical_sha256":"ac75c421d62d0ac8211bf1f969896985b9014ac44ed6bf62bd2837da9fd8ff54","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:27:29.685567Z","signature_b64":"kTCzMF6u5F2muEK1YrCB2frPDq4/vJ7w1vTTuNyGJbcwmBDlIEk1JjckIU8siDs4PX9T+uW956NcFGfnbVPdCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac75c421d62d0ac8211bf1f969896985b9014ac44ed6bf62bd2837da9fd8ff54","last_reissued_at":"2026-07-05T09:27:29.685096Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:27:29.685096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.21537","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":"2026-07-05T09:27:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0HLCwccp3VPtNowtDLussigvoYIY0oAaUbNmTvvejaTFB/gZoF7y6qaI9AKwkLzD9APNkAyIFV3R6OkcAKc9Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T19:12:23.166532Z"},"content_sha256":"fc052adb81d2bb791b72d89c87c51e362612093c298195c62cc115fc415261bc","schema_version":"1.0","event_id":"sha256:fc052adb81d2bb791b72d89c87c51e362612093c298195c62cc115fc415261bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:VR24IIOWFUFMQII36H4WTCLJQW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dualizable presentable $\\infty$-categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"math.CT","authors_text":"Maxime Ramzi","submitted_at":"2024-10-28T21:03:52Z","abstract_excerpt":"We prove that for any presentably symmetric monoidal $\\infty$-category $\\mathcal{V}$, the $\\infty$-category $\\mathbf{Mod}_\\mathcal{V}(\\mathbf{Pr}^{\\mathrm{L}})^{\\mathrm{dbl}}$ of dualizable presentable $\\mathcal{V}$-modules and internal left adjoints between them is itself presentable.\n  Along the way, we survey formal properties of these dualizable $\\mathcal V$-modules. We pay close attention to the case of the $\\infty$-category of spectra, where we survey the foundational properties of ``compact morphisms''."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.21537","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/2410.21537/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":"2026-07-05T09:27:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"13lnIT6uGv9nTRmec5wVtZoPUDMvlWsq0lTBKpBFOBhVGV67d4BZ4RWZPyCtf8sYbWWAZyfH9FmVaHo7m3VBAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T19:12:23.167867Z"},"content_sha256":"c2b74014788099a9b7679ffd14ee2cc5619fffd47b2afbbb718b30ae9271b201","schema_version":"1.0","event_id":"sha256:c2b74014788099a9b7679ffd14ee2cc5619fffd47b2afbbb718b30ae9271b201"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VR24IIOWFUFMQII36H4WTCLJQW/bundle.json","state_url":"https://pith.science/pith/VR24IIOWFUFMQII36H4WTCLJQW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VR24IIOWFUFMQII36H4WTCLJQW/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":"2026-08-01T19:12:23Z","links":{"resolver":"https://pith.science/pith/VR24IIOWFUFMQII36H4WTCLJQW","bundle":"https://pith.science/pith/VR24IIOWFUFMQII36H4WTCLJQW/bundle.json","state":"https://pith.science/pith/VR24IIOWFUFMQII36H4WTCLJQW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VR24IIOWFUFMQII36H4WTCLJQW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VR24IIOWFUFMQII36H4WTCLJQW","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":"e156fc80c1e3d62d3936d29e76397e44579ae16365326a21a47d074090547158","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-10-28T21:03:52Z","title_canon_sha256":"65c58159c3240195e94732528ae58dd2801c8ef2ec7343eeb34209dda41c07d8"},"schema_version":"1.0","source":{"id":"2410.21537","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.21537","created_at":"2026-07-05T09:27:29Z"},{"alias_kind":"arxiv_version","alias_value":"2410.21537v1","created_at":"2026-07-05T09:27:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.21537","created_at":"2026-07-05T09:27:29Z"},{"alias_kind":"pith_short_12","alias_value":"VR24IIOWFUFM","created_at":"2026-07-05T09:27:29Z"},{"alias_kind":"pith_short_16","alias_value":"VR24IIOWFUFMQII3","created_at":"2026-07-05T09:27:29Z"},{"alias_kind":"pith_short_8","alias_value":"VR24IIOW","created_at":"2026-07-05T09:27:29Z"}],"graph_snapshots":[{"event_id":"sha256:c2b74014788099a9b7679ffd14ee2cc5619fffd47b2afbbb718b30ae9271b201","target":"graph","created_at":"2026-07-05T09:27:29Z","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/2410.21537/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that for any presentably symmetric monoidal $\\infty$-category $\\mathcal{V}$, the $\\infty$-category $\\mathbf{Mod}_\\mathcal{V}(\\mathbf{Pr}^{\\mathrm{L}})^{\\mathrm{dbl}}$ of dualizable presentable $\\mathcal{V}$-modules and internal left adjoints between them is itself presentable.\n  Along the way, we survey formal properties of these dualizable $\\mathcal V$-modules. We pay close attention to the case of the $\\infty$-category of spectra, where we survey the foundational properties of ``compact morphisms''.","authors_text":"Maxime Ramzi","cross_cats":["math.AT","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-10-28T21:03:52Z","title":"Dualizable presentable $\\infty$-categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.21537","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:fc052adb81d2bb791b72d89c87c51e362612093c298195c62cc115fc415261bc","target":"record","created_at":"2026-07-05T09:27:29Z","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":"e156fc80c1e3d62d3936d29e76397e44579ae16365326a21a47d074090547158","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-10-28T21:03:52Z","title_canon_sha256":"65c58159c3240195e94732528ae58dd2801c8ef2ec7343eeb34209dda41c07d8"},"schema_version":"1.0","source":{"id":"2410.21537","kind":"arxiv","version":1}},"canonical_sha256":"ac75c421d62d0ac8211bf1f969896985b9014ac44ed6bf62bd2837da9fd8ff54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac75c421d62d0ac8211bf1f969896985b9014ac44ed6bf62bd2837da9fd8ff54","first_computed_at":"2026-07-05T09:27:29.685096Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:27:29.685096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kTCzMF6u5F2muEK1YrCB2frPDq4/vJ7w1vTTuNyGJbcwmBDlIEk1JjckIU8siDs4PX9T+uW956NcFGfnbVPdCg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:27:29.685567Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.21537","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc052adb81d2bb791b72d89c87c51e362612093c298195c62cc115fc415261bc","sha256:c2b74014788099a9b7679ffd14ee2cc5619fffd47b2afbbb718b30ae9271b201"],"state_sha256":"df645f3b7ec10f85dbe6367a1e9b7f5a29cabc32e564809b7ba3268d279b5be6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3EUHmJnZvCg1oBMwo8d4GOxqXgzFmdz/0/zrnnvOYhTxsv6ZAKTHCTODe6VoIxNa7rvbwYWxQv7etam4JNRZBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-01T19:12:23.174029Z","bundle_sha256":"3c6f2afe1147f18fd6d7e39a64fe1aa711af9183bf12c1d807b573ed0deb688c"}}