{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:MXNAFSZWZNQXGZELNIWOH67Q2A","short_pith_number":"pith:MXNAFSZW","canonical_record":{"source":{"id":"2006.08961","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-06-16T07:33:48Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"ed76733699a2552286183de3f4c7f603e7ad5346b224082de9c05c3965201aa0","abstract_canon_sha256":"f4e0c204dd70efa9195815d740a7b32089128d51e2da455579a9bcbcda19c64a"},"schema_version":"1.0"},"canonical_sha256":"65da02cb36cb6173648b6a2ce3fbf0d01d48e08d025d767daa30bb903affd120","source":{"kind":"arxiv","id":"2006.08961","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.08961","created_at":"2026-07-05T02:29:27Z"},{"alias_kind":"arxiv_version","alias_value":"2006.08961v2","created_at":"2026-07-05T02:29:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.08961","created_at":"2026-07-05T02:29:27Z"},{"alias_kind":"pith_short_12","alias_value":"MXNAFSZWZNQX","created_at":"2026-07-05T02:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"MXNAFSZWZNQXGZEL","created_at":"2026-07-05T02:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"MXNAFSZW","created_at":"2026-07-05T02:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:MXNAFSZWZNQXGZELNIWOH67Q2A","target":"record","payload":{"canonical_record":{"source":{"id":"2006.08961","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-06-16T07:33:48Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"ed76733699a2552286183de3f4c7f603e7ad5346b224082de9c05c3965201aa0","abstract_canon_sha256":"f4e0c204dd70efa9195815d740a7b32089128d51e2da455579a9bcbcda19c64a"},"schema_version":"1.0"},"canonical_sha256":"65da02cb36cb6173648b6a2ce3fbf0d01d48e08d025d767daa30bb903affd120","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:29:27.713653Z","signature_b64":"jF9oE2P6shcueWz6ekfWzdwxLHc5dVLpi5qK0h7m2edqAN47X7jWf0BzHdrFmZBFDdhUl1HABu5y/H944Hg5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65da02cb36cb6173648b6a2ce3fbf0d01d48e08d025d767daa30bb903affd120","last_reissued_at":"2026-07-05T02:29:27.713163Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:29:27.713163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.08961","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":"2026-07-05T02:29:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+OC7V7ywFHdT0TcEMHjlXUwVhE2/VNwbz85wGBQ70z4s0IgkmjSh1ipRjXD1fWldU3/j5Yzj0Ku95jdhNI2YCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T16:01:52.013368Z"},"content_sha256":"3a7b82bfbd42887d8434f4a99393d712ad0eedb92b94ea1e7b8f620e9dcb05e6","schema_version":"1.0","event_id":"sha256:3a7b82bfbd42887d8434f4a99393d712ad0eedb92b94ea1e7b8f620e9dcb05e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:MXNAFSZWZNQXGZELNIWOH67Q2A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complementary Projection Defects and Decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"hep-th","authors_text":"Daniel Roggenkamp, Fabian Klos","submitted_at":"2020-06-16T07:33:48Z","abstract_excerpt":"As put forward in [arXiv:1907.12339] topological quantum field theories can be projected using so-called projection defects. The projected theory and its correlation functions can be completely realized within the unprojected one. An interesting example is the case of topological quantum field theories associated to IR fixed points of renormalization group flows, which by this method can be realized inside the theories associated to the UV. In this note we show that projection defects in triangulated defect categories (such as defects in 2d topologically twisted N=(2,2) theories) always come w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.08961","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/2006.08961/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":"2026-07-05T02:29:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dJ2XUE4ocV3Z7+0KTAdB4VGAIQPeCgHRUqYJoRIroray1yP+DjbMx8CUPPfTVAwG9LN+yFuf7lMMJxSW1xFcBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T16:01:52.015199Z"},"content_sha256":"e52ff9fe7ddaee273f11c89a34def07d28cabec44bf5d43b481a8e07e72c4961","schema_version":"1.0","event_id":"sha256:e52ff9fe7ddaee273f11c89a34def07d28cabec44bf5d43b481a8e07e72c4961"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MXNAFSZWZNQXGZELNIWOH67Q2A/bundle.json","state_url":"https://pith.science/pith/MXNAFSZWZNQXGZELNIWOH67Q2A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MXNAFSZWZNQXGZELNIWOH67Q2A/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":"2026-08-05T16:01:52Z","links":{"resolver":"https://pith.science/pith/MXNAFSZWZNQXGZELNIWOH67Q2A","bundle":"https://pith.science/pith/MXNAFSZWZNQXGZELNIWOH67Q2A/bundle.json","state":"https://pith.science/pith/MXNAFSZWZNQXGZELNIWOH67Q2A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MXNAFSZWZNQXGZELNIWOH67Q2A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:MXNAFSZWZNQXGZELNIWOH67Q2A","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":"f4e0c204dd70efa9195815d740a7b32089128d51e2da455579a9bcbcda19c64a","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-06-16T07:33:48Z","title_canon_sha256":"ed76733699a2552286183de3f4c7f603e7ad5346b224082de9c05c3965201aa0"},"schema_version":"1.0","source":{"id":"2006.08961","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.08961","created_at":"2026-07-05T02:29:27Z"},{"alias_kind":"arxiv_version","alias_value":"2006.08961v2","created_at":"2026-07-05T02:29:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.08961","created_at":"2026-07-05T02:29:27Z"},{"alias_kind":"pith_short_12","alias_value":"MXNAFSZWZNQX","created_at":"2026-07-05T02:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"MXNAFSZWZNQXGZEL","created_at":"2026-07-05T02:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"MXNAFSZW","created_at":"2026-07-05T02:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:e52ff9fe7ddaee273f11c89a34def07d28cabec44bf5d43b481a8e07e72c4961","target":"graph","created_at":"2026-07-05T02:29:27Z","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/2006.08961/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"As put forward in [arXiv:1907.12339] topological quantum field theories can be projected using so-called projection defects. The projected theory and its correlation functions can be completely realized within the unprojected one. An interesting example is the case of topological quantum field theories associated to IR fixed points of renormalization group flows, which by this method can be realized inside the theories associated to the UV. In this note we show that projection defects in triangulated defect categories (such as defects in 2d topologically twisted N=(2,2) theories) always come w","authors_text":"Daniel Roggenkamp, Fabian Klos","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-06-16T07:33:48Z","title":"Complementary Projection Defects and Decompositions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.08961","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":"sha256:3a7b82bfbd42887d8434f4a99393d712ad0eedb92b94ea1e7b8f620e9dcb05e6","target":"record","created_at":"2026-07-05T02:29:27Z","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":"f4e0c204dd70efa9195815d740a7b32089128d51e2da455579a9bcbcda19c64a","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-06-16T07:33:48Z","title_canon_sha256":"ed76733699a2552286183de3f4c7f603e7ad5346b224082de9c05c3965201aa0"},"schema_version":"1.0","source":{"id":"2006.08961","kind":"arxiv","version":2}},"canonical_sha256":"65da02cb36cb6173648b6a2ce3fbf0d01d48e08d025d767daa30bb903affd120","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65da02cb36cb6173648b6a2ce3fbf0d01d48e08d025d767daa30bb903affd120","first_computed_at":"2026-07-05T02:29:27.713163Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:29:27.713163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jF9oE2P6shcueWz6ekfWzdwxLHc5dVLpi5qK0h7m2edqAN47X7jWf0BzHdrFmZBFDdhUl1HABu5y/H944Hg5Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T02:29:27.713653Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.08961","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a7b82bfbd42887d8434f4a99393d712ad0eedb92b94ea1e7b8f620e9dcb05e6","sha256:e52ff9fe7ddaee273f11c89a34def07d28cabec44bf5d43b481a8e07e72c4961"],"state_sha256":"47e6779f150b48965766acfede978f3d270816dfd147afccac5366a3a49a7269"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Hrtds3CibDfjDpbF96tGnKh6oD3QsFW4zJrmi41UJ9MWN66BDQZVktVqd/3BssspjRFxXLksLtthE8QEZXcBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T16:01:52.026531Z","bundle_sha256":"df53fbd7b2baae13d0c7dbd966026fd17897de950811d881ad5dab3e8abab014"}}