{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:TMEDRAOV2AWFZYUGUNQHRJZ4TO","short_pith_number":"pith:TMEDRAOV","canonical_record":{"source":{"id":"2405.15466","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-05-24T11:40:58Z","cross_cats_sorted":[],"title_canon_sha256":"59eb70a5003484c2bb04d72a06ebb7e35950852086fc043b7c38f1974faf6a54","abstract_canon_sha256":"deb16381d298e79f675e037896d5f6912efaaa4418a548981e2fd7a50a7f16c1"},"schema_version":"1.0"},"canonical_sha256":"9b083881d5d02c5ce286a36078a73c9b86016e00e809be80cf65526fa94794bf","source":{"kind":"arxiv","id":"2405.15466","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.15466","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"arxiv_version","alias_value":"2405.15466v2","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.15466","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"pith_short_12","alias_value":"TMEDRAOV2AWF","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"pith_short_16","alias_value":"TMEDRAOV2AWFZYUG","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"pith_short_8","alias_value":"TMEDRAOV","created_at":"2026-05-21T01:05:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:TMEDRAOV2AWFZYUGUNQHRJZ4TO","target":"record","payload":{"canonical_record":{"source":{"id":"2405.15466","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-05-24T11:40:58Z","cross_cats_sorted":[],"title_canon_sha256":"59eb70a5003484c2bb04d72a06ebb7e35950852086fc043b7c38f1974faf6a54","abstract_canon_sha256":"deb16381d298e79f675e037896d5f6912efaaa4418a548981e2fd7a50a7f16c1"},"schema_version":"1.0"},"canonical_sha256":"9b083881d5d02c5ce286a36078a73c9b86016e00e809be80cf65526fa94794bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:05:02.369188Z","signature_b64":"AwU+WCDKVcYIH0K1xov1eaiaUP009r37lk4iV47pafAmzmTfwj4TdtvLqVQey7UjHwHCsXtGVlTfTZy17aYqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b083881d5d02c5ce286a36078a73c9b86016e00e809be80cf65526fa94794bf","last_reissued_at":"2026-05-21T01:05:02.368283Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:05:02.368283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.15466","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":"2026-05-21T01:05:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7vTz2+Ew1LvyoVQrF6Ujcq82aH45JSckDoDScCqp4CbawTqmxd42r5z1GeI17nh3gXaHnqZhEka+Mc6zSHFkBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:41:55.475349Z"},"content_sha256":"3548594d1017fe589c5c303428f25a5e31c1144694fcd9520906925b2d7645a5","schema_version":"1.0","event_id":"sha256:3548594d1017fe589c5c303428f25a5e31c1144694fcd9520906925b2d7645a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:TMEDRAOV2AWFZYUGUNQHRJZ4TO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Skew-group $A_{\\infty}$-categories as Fukaya categories of orbifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Claire Amiot, Pierre-Guy Plamondon","submitted_at":"2024-05-24T11:40:58Z","abstract_excerpt":"We study the partially wrapped Fukaya category of a surface with boundary with an action of a group of order two. Inspired by skew-group algebras and categories, we define the notion of a skew-group $A_\\infty$-category and let it play the role of the partially wrapped Fukaya category of an orbifold surface. We classify indecomposable objects in terms of graded curves with signs, or taggings, at orbifold points. We compute morphisms between a class of objects, and we use this to describe tilting objects and find algebras derived-equivalent to skew-gentle algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.15466","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/2405.15466/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":"2026-05-21T01:05:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wkp76Lil0/yr08G5ILKDhCZnKtc5OEp5jBoCNY2Um6EfcAquklSaEPlwaTEABmKvsG6s9+DP97+VGfloI+tIBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:41:55.476098Z"},"content_sha256":"88b4dfc76d2cb6f95e759c0d6999fd4f1d6085514ada4f95dbfe49ec29abb105","schema_version":"1.0","event_id":"sha256:88b4dfc76d2cb6f95e759c0d6999fd4f1d6085514ada4f95dbfe49ec29abb105"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TMEDRAOV2AWFZYUGUNQHRJZ4TO/bundle.json","state_url":"https://pith.science/pith/TMEDRAOV2AWFZYUGUNQHRJZ4TO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TMEDRAOV2AWFZYUGUNQHRJZ4TO/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":"2026-05-25T14:41:55Z","links":{"resolver":"https://pith.science/pith/TMEDRAOV2AWFZYUGUNQHRJZ4TO","bundle":"https://pith.science/pith/TMEDRAOV2AWFZYUGUNQHRJZ4TO/bundle.json","state":"https://pith.science/pith/TMEDRAOV2AWFZYUGUNQHRJZ4TO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TMEDRAOV2AWFZYUGUNQHRJZ4TO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TMEDRAOV2AWFZYUGUNQHRJZ4TO","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":"deb16381d298e79f675e037896d5f6912efaaa4418a548981e2fd7a50a7f16c1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-05-24T11:40:58Z","title_canon_sha256":"59eb70a5003484c2bb04d72a06ebb7e35950852086fc043b7c38f1974faf6a54"},"schema_version":"1.0","source":{"id":"2405.15466","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.15466","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"arxiv_version","alias_value":"2405.15466v2","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.15466","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"pith_short_12","alias_value":"TMEDRAOV2AWF","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"pith_short_16","alias_value":"TMEDRAOV2AWFZYUG","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"pith_short_8","alias_value":"TMEDRAOV","created_at":"2026-05-21T01:05:02Z"}],"graph_snapshots":[{"event_id":"sha256:88b4dfc76d2cb6f95e759c0d6999fd4f1d6085514ada4f95dbfe49ec29abb105","target":"graph","created_at":"2026-05-21T01:05:02Z","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/2405.15466/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the partially wrapped Fukaya category of a surface with boundary with an action of a group of order two. Inspired by skew-group algebras and categories, we define the notion of a skew-group $A_\\infty$-category and let it play the role of the partially wrapped Fukaya category of an orbifold surface. We classify indecomposable objects in terms of graded curves with signs, or taggings, at orbifold points. We compute morphisms between a class of objects, and we use this to describe tilting objects and find algebras derived-equivalent to skew-gentle algebras.","authors_text":"Claire Amiot, Pierre-Guy Plamondon","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-05-24T11:40:58Z","title":"Skew-group $A_{\\infty}$-categories as Fukaya categories of orbifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.15466","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":"sha256:3548594d1017fe589c5c303428f25a5e31c1144694fcd9520906925b2d7645a5","target":"record","created_at":"2026-05-21T01:05:02Z","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":"deb16381d298e79f675e037896d5f6912efaaa4418a548981e2fd7a50a7f16c1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-05-24T11:40:58Z","title_canon_sha256":"59eb70a5003484c2bb04d72a06ebb7e35950852086fc043b7c38f1974faf6a54"},"schema_version":"1.0","source":{"id":"2405.15466","kind":"arxiv","version":2}},"canonical_sha256":"9b083881d5d02c5ce286a36078a73c9b86016e00e809be80cf65526fa94794bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b083881d5d02c5ce286a36078a73c9b86016e00e809be80cf65526fa94794bf","first_computed_at":"2026-05-21T01:05:02.368283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:05:02.368283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AwU+WCDKVcYIH0K1xov1eaiaUP009r37lk4iV47pafAmzmTfwj4TdtvLqVQey7UjHwHCsXtGVlTfTZy17aYqDA==","signature_status":"signed_v1","signed_at":"2026-05-21T01:05:02.369188Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.15466","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3548594d1017fe589c5c303428f25a5e31c1144694fcd9520906925b2d7645a5","sha256:88b4dfc76d2cb6f95e759c0d6999fd4f1d6085514ada4f95dbfe49ec29abb105"],"state_sha256":"b19be9870a398c066c57e5ee17376df8ba8c8ebc51bbc7cf17cfb15973e11bd0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wo0yVxwNMQiy0vGMYtBPv/uJvGAN9rJDcWYotGSEb7yUWEixvWyKMj/wU1MQtgC+MYiQMKvagfxVCrXdvJ4qCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T14:41:55.481266Z","bundle_sha256":"5fe33b12fd3184f9071bd9c8d4b69158ac4802736f52f47bb4fe227794b27a2d"}}