{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PZ5WZ6X2SWMMHN4C6ZB3CEJKUC","short_pith_number":"pith:PZ5WZ6X2","canonical_record":{"source":{"id":"1706.02131","kind":"arxiv","version":6},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.SG","submitted_at":"2017-06-07T11:14:36Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"f9a7ad85ee05277b042b87773a244c67d2e39d404658d73f696a4cfddeb075c9","abstract_canon_sha256":"6606856d64eccf8b8b9a8d21d51a747d02a28a92172c0f00764d707a74378a3d"},"schema_version":"1.0"},"canonical_sha256":"7e7b6cfafa9598c3b782f643b1112aa08cb75a3850b4e2d59d8e9feff04354fe","source":{"kind":"arxiv","id":"1706.02131","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02131","created_at":"2026-07-05T10:55:13Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02131v6","created_at":"2026-07-05T10:55:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02131","created_at":"2026-07-05T10:55:13Z"},{"alias_kind":"pith_short_12","alias_value":"PZ5WZ6X2SWMM","created_at":"2026-07-05T10:55:13Z"},{"alias_kind":"pith_short_16","alias_value":"PZ5WZ6X2SWMMHN4C","created_at":"2026-07-05T10:55:13Z"},{"alias_kind":"pith_short_8","alias_value":"PZ5WZ6X2","created_at":"2026-07-05T10:55:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PZ5WZ6X2SWMMHN4C6ZB3CEJKUC","target":"record","payload":{"canonical_record":{"source":{"id":"1706.02131","kind":"arxiv","version":6},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.SG","submitted_at":"2017-06-07T11:14:36Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"f9a7ad85ee05277b042b87773a244c67d2e39d404658d73f696a4cfddeb075c9","abstract_canon_sha256":"6606856d64eccf8b8b9a8d21d51a747d02a28a92172c0f00764d707a74378a3d"},"schema_version":"1.0"},"canonical_sha256":"7e7b6cfafa9598c3b782f643b1112aa08cb75a3850b4e2d59d8e9feff04354fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:55:13.885397Z","signature_b64":"DjAqs5QJO2onPpYp1GWeBYL2WTBz7Dc/wFaxeWnS0pie99y7YASS0mWPwQwgexA2fIbAtkg+ooDP8lIcuVcXDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e7b6cfafa9598c3b782f643b1112aa08cb75a3850b4e2d59d8e9feff04354fe","last_reissued_at":"2026-07-05T10:55:13.884878Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:55:13.884878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.02131","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:55:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H8FU+riINcJ/PLo3yvBcix6B7QWe2i5P+rT/is7JYgRNuE1nMvLTBc9T0Ndz10v+S1P+U+JbqiL2VtKjfQQVDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T01:06:52.990854Z"},"content_sha256":"dfa98884187f0937a1f7835700f42a51da91085892a8c30e00589a7d72f3bd2d","schema_version":"1.0","event_id":"sha256:dfa98884187f0937a1f7835700f42a51da91085892a8c30e00589a7d72f3bd2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PZ5WZ6X2SWMMHN4C6ZB3CEJKUC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unobstructed Immersed Lagrangian Correspondence and Filtered $A_{\\infty}$ Functor","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Kenji Fukaya","submitted_at":"2017-06-07T11:14:36Z","abstract_excerpt":"In this paper, we 'construct' a 2-functor from the unobstructed immersed Weinstein category to the category of all filtered $A_{\\infty}$ categories. We consider arbitrary (compact) symplectic manifolds and its arbitrary (relatively spin) immersed Lagrangian submanifolds. The filtered $A_{\\infty}$ category associated to $(X,\\omega)$ is defined by using Lagrangian Floer theory in such generality, see Akaho-Joyce (2010) and Fukaya-Oh-Ohta-Ono (2009). The morphism of unobstructed immersed Weinstein category (from $(X_1,\\omega_1)$ to $(X_2,\\omega_2)$) is by definition a pair of an immersed Lagrangi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02131","kind":"arxiv","version":6},"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/1706.02131/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":"2026-07-05T10:55:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Snd/f7KWQViQNhM1vqqCXlSNq47Nd8nCkYnbadTPoGmDLla78PZD4mNbnWAU/oBylQ+5kzU0bt+1/1LcKda5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T01:06:52.991881Z"},"content_sha256":"95d61d1cef79a2340b5ccb7ee77cd3e4926218d7438c9dae8ce99ea886f4cf3a","schema_version":"1.0","event_id":"sha256:95d61d1cef79a2340b5ccb7ee77cd3e4926218d7438c9dae8ce99ea886f4cf3a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PZ5WZ6X2SWMMHN4C6ZB3CEJKUC/bundle.json","state_url":"https://pith.science/pith/PZ5WZ6X2SWMMHN4C6ZB3CEJKUC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PZ5WZ6X2SWMMHN4C6ZB3CEJKUC/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":"2026-08-11T01:06:53Z","links":{"resolver":"https://pith.science/pith/PZ5WZ6X2SWMMHN4C6ZB3CEJKUC","bundle":"https://pith.science/pith/PZ5WZ6X2SWMMHN4C6ZB3CEJKUC/bundle.json","state":"https://pith.science/pith/PZ5WZ6X2SWMMHN4C6ZB3CEJKUC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PZ5WZ6X2SWMMHN4C6ZB3CEJKUC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PZ5WZ6X2SWMMHN4C6ZB3CEJKUC","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":"6606856d64eccf8b8b9a8d21d51a747d02a28a92172c0f00764d707a74378a3d","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.SG","submitted_at":"2017-06-07T11:14:36Z","title_canon_sha256":"f9a7ad85ee05277b042b87773a244c67d2e39d404658d73f696a4cfddeb075c9"},"schema_version":"1.0","source":{"id":"1706.02131","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02131","created_at":"2026-07-05T10:55:13Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02131v6","created_at":"2026-07-05T10:55:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02131","created_at":"2026-07-05T10:55:13Z"},{"alias_kind":"pith_short_12","alias_value":"PZ5WZ6X2SWMM","created_at":"2026-07-05T10:55:13Z"},{"alias_kind":"pith_short_16","alias_value":"PZ5WZ6X2SWMMHN4C","created_at":"2026-07-05T10:55:13Z"},{"alias_kind":"pith_short_8","alias_value":"PZ5WZ6X2","created_at":"2026-07-05T10:55:13Z"}],"graph_snapshots":[{"event_id":"sha256:95d61d1cef79a2340b5ccb7ee77cd3e4926218d7438c9dae8ce99ea886f4cf3a","target":"graph","created_at":"2026-07-05T10:55:13Z","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/1706.02131/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we 'construct' a 2-functor from the unobstructed immersed Weinstein category to the category of all filtered $A_{\\infty}$ categories. We consider arbitrary (compact) symplectic manifolds and its arbitrary (relatively spin) immersed Lagrangian submanifolds. The filtered $A_{\\infty}$ category associated to $(X,\\omega)$ is defined by using Lagrangian Floer theory in such generality, see Akaho-Joyce (2010) and Fukaya-Oh-Ohta-Ono (2009). The morphism of unobstructed immersed Weinstein category (from $(X_1,\\omega_1)$ to $(X_2,\\omega_2)$) is by definition a pair of an immersed Lagrangi","authors_text":"Kenji Fukaya","cross_cats":["math.DG"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.SG","submitted_at":"2017-06-07T11:14:36Z","title":"Unobstructed Immersed Lagrangian Correspondence and Filtered $A_{\\infty}$ Functor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02131","kind":"arxiv","version":6},"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:dfa98884187f0937a1f7835700f42a51da91085892a8c30e00589a7d72f3bd2d","target":"record","created_at":"2026-07-05T10:55:13Z","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":"6606856d64eccf8b8b9a8d21d51a747d02a28a92172c0f00764d707a74378a3d","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.SG","submitted_at":"2017-06-07T11:14:36Z","title_canon_sha256":"f9a7ad85ee05277b042b87773a244c67d2e39d404658d73f696a4cfddeb075c9"},"schema_version":"1.0","source":{"id":"1706.02131","kind":"arxiv","version":6}},"canonical_sha256":"7e7b6cfafa9598c3b782f643b1112aa08cb75a3850b4e2d59d8e9feff04354fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e7b6cfafa9598c3b782f643b1112aa08cb75a3850b4e2d59d8e9feff04354fe","first_computed_at":"2026-07-05T10:55:13.884878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:55:13.884878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DjAqs5QJO2onPpYp1GWeBYL2WTBz7Dc/wFaxeWnS0pie99y7YASS0mWPwQwgexA2fIbAtkg+ooDP8lIcuVcXDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:55:13.885397Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02131","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfa98884187f0937a1f7835700f42a51da91085892a8c30e00589a7d72f3bd2d","sha256:95d61d1cef79a2340b5ccb7ee77cd3e4926218d7438c9dae8ce99ea886f4cf3a"],"state_sha256":"974c6394363207f9635c41a7682b85c0304738c11f66890ef0ef6f47f0a9452f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d0Ws+1/0mbiFNzQ4xtYc0FwZppjxintmKS5yCS8ilwLP8QrwdjVEjN+O8fzwcwTQVwGUei/v6MQrm5ismaexAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T01:06:53.021624Z","bundle_sha256":"5a88db41da39e021d75111119c5f04a69826b7d996d4b1afa44671a87d25b645"}}