{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:DK5GVRLXACCV2IXECPROQT575F","short_pith_number":"pith:DK5GVRLX","canonical_record":{"source":{"id":"2209.06595","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2022-09-14T12:26:17Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"7ba644aa304c4c8fde2e8d0cbad52b215bdb5f76c86541c82ddff920375f39ef","abstract_canon_sha256":"c8a9675d82f297ac139a75999187eec2c3844e77c072459495f15e81aa40faee"},"schema_version":"1.0"},"canonical_sha256":"1aba6ac57700855d22e413e2e84fbfe95f7aabebea0e8b9183d75ee2b53249c1","source":{"kind":"arxiv","id":"2209.06595","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.06595","created_at":"2026-07-05T07:44:51Z"},{"alias_kind":"arxiv_version","alias_value":"2209.06595v2","created_at":"2026-07-05T07:44:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.06595","created_at":"2026-07-05T07:44:51Z"},{"alias_kind":"pith_short_12","alias_value":"DK5GVRLXACCV","created_at":"2026-07-05T07:44:51Z"},{"alias_kind":"pith_short_16","alias_value":"DK5GVRLXACCV2IXE","created_at":"2026-07-05T07:44:51Z"},{"alias_kind":"pith_short_8","alias_value":"DK5GVRLX","created_at":"2026-07-05T07:44:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:DK5GVRLXACCV2IXECPROQT575F","target":"record","payload":{"canonical_record":{"source":{"id":"2209.06595","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2022-09-14T12:26:17Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"7ba644aa304c4c8fde2e8d0cbad52b215bdb5f76c86541c82ddff920375f39ef","abstract_canon_sha256":"c8a9675d82f297ac139a75999187eec2c3844e77c072459495f15e81aa40faee"},"schema_version":"1.0"},"canonical_sha256":"1aba6ac57700855d22e413e2e84fbfe95f7aabebea0e8b9183d75ee2b53249c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:44:51.623751Z","signature_b64":"wiJDPTmhRSuruYEO5ejqsU7hjXrBlMdYYvfeX7GA5HrrGEoIRWo1GIqUtpO7KV16zqn/VwtuZOpdcMb0QtGTBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1aba6ac57700855d22e413e2e84fbfe95f7aabebea0e8b9183d75ee2b53249c1","last_reissued_at":"2026-07-05T07:44:51.623324Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:44:51.623324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.06595","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":"2026-07-05T07:44:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FXoyj7GEOfmb6yshng+wmS3mJIPBQFKsIWZ5Vou+DHF1RXg1LJ/KcNITtbKMSiXsSzTfRmJaRh5QsePqfusVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T15:19:13.104206Z"},"content_sha256":"80d182f14081c3923007ca3d1be1bb4c38d16f7487119d38fdaa9937f16e1b76","schema_version":"1.0","event_id":"sha256:80d182f14081c3923007ca3d1be1bb4c38d16f7487119d38fdaa9937f16e1b76"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:DK5GVRLXACCV2IXECPROQT575F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cluster theory of topological Fukaya categories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.RT","authors_text":"Merlin Christ","submitted_at":"2022-09-14T12:26:17Z","abstract_excerpt":"We establish a novel relation between the cluster categories associated with marked surfaces and the topological Fukaya categories of the surfaces. We consider a generalization of the triangulated cluster category of the surface by a $2$-Calabi-Yau extriangulated/exact $\\infty$-category, which arises via Amiot's construction from the relative Ginzburg algebra of the triangulated surface. This category is shown to be equivalent to the $1$-periodic version of the topological Fukaya category of the marked surface, as well as to Wu's Higgs category. We classify the cluster tilting objects in this "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.06595","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/2209.06595/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":"2026-07-05T07:44:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hj/03pzSV7G6kqvDqy1a68Ls+biHMxIYKkGH+qkOeak4fjMyrokDrHI6GB/Z89VlRZOhzI8Tl6BFVKWOyoktDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T15:19:13.104739Z"},"content_sha256":"3b516a832364998f6e4152fcd291ae2c7dd42a274a9252158895aa84db7d87b5","schema_version":"1.0","event_id":"sha256:3b516a832364998f6e4152fcd291ae2c7dd42a274a9252158895aa84db7d87b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DK5GVRLXACCV2IXECPROQT575F/bundle.json","state_url":"https://pith.science/pith/DK5GVRLXACCV2IXECPROQT575F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DK5GVRLXACCV2IXECPROQT575F/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":"2026-08-08T15:19:13Z","links":{"resolver":"https://pith.science/pith/DK5GVRLXACCV2IXECPROQT575F","bundle":"https://pith.science/pith/DK5GVRLXACCV2IXECPROQT575F/bundle.json","state":"https://pith.science/pith/DK5GVRLXACCV2IXECPROQT575F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DK5GVRLXACCV2IXECPROQT575F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:DK5GVRLXACCV2IXECPROQT575F","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":"c8a9675d82f297ac139a75999187eec2c3844e77c072459495f15e81aa40faee","cross_cats_sorted":["math.AT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2022-09-14T12:26:17Z","title_canon_sha256":"7ba644aa304c4c8fde2e8d0cbad52b215bdb5f76c86541c82ddff920375f39ef"},"schema_version":"1.0","source":{"id":"2209.06595","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.06595","created_at":"2026-07-05T07:44:51Z"},{"alias_kind":"arxiv_version","alias_value":"2209.06595v2","created_at":"2026-07-05T07:44:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.06595","created_at":"2026-07-05T07:44:51Z"},{"alias_kind":"pith_short_12","alias_value":"DK5GVRLXACCV","created_at":"2026-07-05T07:44:51Z"},{"alias_kind":"pith_short_16","alias_value":"DK5GVRLXACCV2IXE","created_at":"2026-07-05T07:44:51Z"},{"alias_kind":"pith_short_8","alias_value":"DK5GVRLX","created_at":"2026-07-05T07:44:51Z"}],"graph_snapshots":[{"event_id":"sha256:3b516a832364998f6e4152fcd291ae2c7dd42a274a9252158895aa84db7d87b5","target":"graph","created_at":"2026-07-05T07:44:51Z","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/2209.06595/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish a novel relation between the cluster categories associated with marked surfaces and the topological Fukaya categories of the surfaces. We consider a generalization of the triangulated cluster category of the surface by a $2$-Calabi-Yau extriangulated/exact $\\infty$-category, which arises via Amiot's construction from the relative Ginzburg algebra of the triangulated surface. This category is shown to be equivalent to the $1$-periodic version of the topological Fukaya category of the marked surface, as well as to Wu's Higgs category. We classify the cluster tilting objects in this ","authors_text":"Merlin Christ","cross_cats":["math.AT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2022-09-14T12:26:17Z","title":"Cluster theory of topological Fukaya categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.06595","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":"sha256:80d182f14081c3923007ca3d1be1bb4c38d16f7487119d38fdaa9937f16e1b76","target":"record","created_at":"2026-07-05T07:44:51Z","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":"c8a9675d82f297ac139a75999187eec2c3844e77c072459495f15e81aa40faee","cross_cats_sorted":["math.AT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2022-09-14T12:26:17Z","title_canon_sha256":"7ba644aa304c4c8fde2e8d0cbad52b215bdb5f76c86541c82ddff920375f39ef"},"schema_version":"1.0","source":{"id":"2209.06595","kind":"arxiv","version":2}},"canonical_sha256":"1aba6ac57700855d22e413e2e84fbfe95f7aabebea0e8b9183d75ee2b53249c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1aba6ac57700855d22e413e2e84fbfe95f7aabebea0e8b9183d75ee2b53249c1","first_computed_at":"2026-07-05T07:44:51.623324Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:44:51.623324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wiJDPTmhRSuruYEO5ejqsU7hjXrBlMdYYvfeX7GA5HrrGEoIRWo1GIqUtpO7KV16zqn/VwtuZOpdcMb0QtGTBw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:44:51.623751Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.06595","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80d182f14081c3923007ca3d1be1bb4c38d16f7487119d38fdaa9937f16e1b76","sha256:3b516a832364998f6e4152fcd291ae2c7dd42a274a9252158895aa84db7d87b5"],"state_sha256":"64d01a9825006304c3fa234f18f644df910dee48486e75106d429a0a0e2d0d2d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FZCHa5lTSIbxWxMXbNFmEulXcv3vz0kANP1r76KjnzJTrcq4+OrHFWgDGG4B8bU2BsOMFcSHL0BYhgKT/kuxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T15:19:13.108752Z","bundle_sha256":"c74fd7d59934a520e3e692579ac923bdd3d8b2521c62549014c912f57822ca67"}}