{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:JT33737INBVOTSGNBWG3A74OX4","short_pith_number":"pith:JT33737I","canonical_record":{"source":{"id":"2606.30637","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-29T17:58:26Z","cross_cats_sorted":["hep-th","math-ph","math.DG","math.MP"],"title_canon_sha256":"8fa8ce8b9986a5a6006e56bb1beb3bd3c9c5957a789a12c13c791b23e17d7ecd","abstract_canon_sha256":"d5e393d42ac470fdf366836e26e6743d64eaa2fa32d78d312141081b0625b497"},"schema_version":"1.0"},"canonical_sha256":"4cf7bfefe8686ae9c8cd0d8db07f8ebf373cb84ee62ab479a90f5b3324d3978a","source":{"kind":"arxiv","id":"2606.30637","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30637","created_at":"2026-06-30T02:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30637v1","created_at":"2026-06-30T02:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30637","created_at":"2026-06-30T02:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"JT33737INBVO","created_at":"2026-06-30T02:18:23Z"},{"alias_kind":"pith_short_16","alias_value":"JT33737INBVOTSGN","created_at":"2026-06-30T02:18:23Z"},{"alias_kind":"pith_short_8","alias_value":"JT33737I","created_at":"2026-06-30T02:18:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:JT33737INBVOTSGNBWG3A74OX4","target":"record","payload":{"canonical_record":{"source":{"id":"2606.30637","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-29T17:58:26Z","cross_cats_sorted":["hep-th","math-ph","math.DG","math.MP"],"title_canon_sha256":"8fa8ce8b9986a5a6006e56bb1beb3bd3c9c5957a789a12c13c791b23e17d7ecd","abstract_canon_sha256":"d5e393d42ac470fdf366836e26e6743d64eaa2fa32d78d312141081b0625b497"},"schema_version":"1.0"},"canonical_sha256":"4cf7bfefe8686ae9c8cd0d8db07f8ebf373cb84ee62ab479a90f5b3324d3978a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:18:23.832309Z","signature_b64":"y9u7MXiRn2ccVz9zmZb5YI7H+sWkZEPJH8wN3CVsZvxmBe1ogbobBb8GuZeSX1Hh3bskkVxQarwGA6wxmk74Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cf7bfefe8686ae9c8cd0d8db07f8ebf373cb84ee62ab479a90f5b3324d3978a","last_reissued_at":"2026-06-30T02:18:23.831809Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:18:23.831809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.30637","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":"2026-06-30T02:18:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n7l8yNqiyt+b4GR+wOACfiu+1/RSejLpkQedr09KzjzJcyDjbrshP8gPJDjWD7/dQ8vMOpIAoQQNwWsauBWrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T12:35:28.050695Z"},"content_sha256":"bb4adced076b52f8c07406690b3287d4226775ea5e180b5a4008ec0fc27aa6f8","schema_version":"1.0","event_id":"sha256:bb4adced076b52f8c07406690b3287d4226775ea5e180b5a4008ec0fc27aa6f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:JT33737INBVOTSGNBWG3A74OX4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lagrangian correspondences of nonabelian Hodge type and shifted twistor structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.DG","math.MP"],"primary_cat":"math.AG","authors_text":"Jacob Kryczka, Shing-Tung Yau, Yuuji Tanaka","submitted_at":"2026-06-29T17:58:26Z","abstract_excerpt":"Classical nonabelian Hodge theory identifies Dolbeault and de Rham moduli spaces by providing a real-analytic isomorphism. In this paper, motivated by the Kapustin--Witten theory, we study this correspondence in the more general framework of perfect complexes on proper varieties, paying special attention to the surface case. We establish a Lagrangian correspondence which relates the shifted symplectic geometries by Pantev--To\\\"en--Vaqui\\'e--Vezzosi (PTVV) between the derived stacks of flat and Higgs perfect complexes.Furthermore, we investigate the existence of the derived twistor structure of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30637","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/2606.30637/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":"2026-06-30T02:18:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lctSrKFrY53/4ZfNNs/YYuoz5f3/VC+FMC5ZtcZoZ9ZY+O6Q0wroI8X+q5Ftd9hPgh87YJoDeeAv8AE+1wl/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T12:35:28.051066Z"},"content_sha256":"4a2f3ef127c70763a7841af33d930522cea49488b40b3c0a383546208d716594","schema_version":"1.0","event_id":"sha256:4a2f3ef127c70763a7841af33d930522cea49488b40b3c0a383546208d716594"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JT33737INBVOTSGNBWG3A74OX4/bundle.json","state_url":"https://pith.science/pith/JT33737INBVOTSGNBWG3A74OX4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JT33737INBVOTSGNBWG3A74OX4/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":"2026-06-30T12:35:28Z","links":{"resolver":"https://pith.science/pith/JT33737INBVOTSGNBWG3A74OX4","bundle":"https://pith.science/pith/JT33737INBVOTSGNBWG3A74OX4/bundle.json","state":"https://pith.science/pith/JT33737INBVOTSGNBWG3A74OX4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JT33737INBVOTSGNBWG3A74OX4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JT33737INBVOTSGNBWG3A74OX4","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":"d5e393d42ac470fdf366836e26e6743d64eaa2fa32d78d312141081b0625b497","cross_cats_sorted":["hep-th","math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-29T17:58:26Z","title_canon_sha256":"8fa8ce8b9986a5a6006e56bb1beb3bd3c9c5957a789a12c13c791b23e17d7ecd"},"schema_version":"1.0","source":{"id":"2606.30637","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30637","created_at":"2026-06-30T02:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30637v1","created_at":"2026-06-30T02:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30637","created_at":"2026-06-30T02:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"JT33737INBVO","created_at":"2026-06-30T02:18:23Z"},{"alias_kind":"pith_short_16","alias_value":"JT33737INBVOTSGN","created_at":"2026-06-30T02:18:23Z"},{"alias_kind":"pith_short_8","alias_value":"JT33737I","created_at":"2026-06-30T02:18:23Z"}],"graph_snapshots":[{"event_id":"sha256:4a2f3ef127c70763a7841af33d930522cea49488b40b3c0a383546208d716594","target":"graph","created_at":"2026-06-30T02:18:23Z","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/2606.30637/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Classical nonabelian Hodge theory identifies Dolbeault and de Rham moduli spaces by providing a real-analytic isomorphism. In this paper, motivated by the Kapustin--Witten theory, we study this correspondence in the more general framework of perfect complexes on proper varieties, paying special attention to the surface case. We establish a Lagrangian correspondence which relates the shifted symplectic geometries by Pantev--To\\\"en--Vaqui\\'e--Vezzosi (PTVV) between the derived stacks of flat and Higgs perfect complexes.Furthermore, we investigate the existence of the derived twistor structure of","authors_text":"Jacob Kryczka, Shing-Tung Yau, Yuuji Tanaka","cross_cats":["hep-th","math-ph","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-29T17:58:26Z","title":"Lagrangian correspondences of nonabelian Hodge type and shifted twistor structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30637","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:bb4adced076b52f8c07406690b3287d4226775ea5e180b5a4008ec0fc27aa6f8","target":"record","created_at":"2026-06-30T02:18:23Z","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":"d5e393d42ac470fdf366836e26e6743d64eaa2fa32d78d312141081b0625b497","cross_cats_sorted":["hep-th","math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-29T17:58:26Z","title_canon_sha256":"8fa8ce8b9986a5a6006e56bb1beb3bd3c9c5957a789a12c13c791b23e17d7ecd"},"schema_version":"1.0","source":{"id":"2606.30637","kind":"arxiv","version":1}},"canonical_sha256":"4cf7bfefe8686ae9c8cd0d8db07f8ebf373cb84ee62ab479a90f5b3324d3978a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4cf7bfefe8686ae9c8cd0d8db07f8ebf373cb84ee62ab479a90f5b3324d3978a","first_computed_at":"2026-06-30T02:18:23.831809Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T02:18:23.831809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y9u7MXiRn2ccVz9zmZb5YI7H+sWkZEPJH8wN3CVsZvxmBe1ogbobBb8GuZeSX1Hh3bskkVxQarwGA6wxmk74Ag==","signature_status":"signed_v1","signed_at":"2026-06-30T02:18:23.832309Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.30637","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb4adced076b52f8c07406690b3287d4226775ea5e180b5a4008ec0fc27aa6f8","sha256:4a2f3ef127c70763a7841af33d930522cea49488b40b3c0a383546208d716594"],"state_sha256":"5b39cf467fac7d12037c5adfc32060a2ec60b1589d8f21c23056028c77174023"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZI1G334+LAkPmtPHrhqDG9QvChV1L1s2GBZcZDTosJGUPWQnTY+10ZrpbmL0hggYvdVZwS0lIRPWl74UrfFwCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T12:35:28.052974Z","bundle_sha256":"b1394ce1488d1ff3606b6c00f77b20a572f5e4daf944c390a17aef10515906c6"}}