{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:Z2W742VFXBFCTBEIW6W2SGIFD7","short_pith_number":"pith:Z2W742VF","canonical_record":{"source":{"id":"2605.22798","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-21T17:51:25Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0fa65672ca67e3c79ce2f14f96c2bc6e8115616fe58539000268c8a0086f8ccc","abstract_canon_sha256":"8b9b4b64a5f218eddc2efedfc5d4de8c936b691c481a1f673b27c053bc24eb78"},"schema_version":"1.0"},"canonical_sha256":"ceadfe6aa5b84a298488b7ada919051fc81c1d182306c59c3b653677f4b46ab5","source":{"kind":"arxiv","id":"2605.22798","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22798","created_at":"2026-05-22T02:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22798v1","created_at":"2026-05-22T02:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22798","created_at":"2026-05-22T02:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"Z2W742VFXBFC","created_at":"2026-05-22T02:04:55Z"},{"alias_kind":"pith_short_16","alias_value":"Z2W742VFXBFCTBEI","created_at":"2026-05-22T02:04:55Z"},{"alias_kind":"pith_short_8","alias_value":"Z2W742VF","created_at":"2026-05-22T02:04:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:Z2W742VFXBFCTBEIW6W2SGIFD7","target":"record","payload":{"canonical_record":{"source":{"id":"2605.22798","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-21T17:51:25Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0fa65672ca67e3c79ce2f14f96c2bc6e8115616fe58539000268c8a0086f8ccc","abstract_canon_sha256":"8b9b4b64a5f218eddc2efedfc5d4de8c936b691c481a1f673b27c053bc24eb78"},"schema_version":"1.0"},"canonical_sha256":"ceadfe6aa5b84a298488b7ada919051fc81c1d182306c59c3b653677f4b46ab5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T02:04:55.329457Z","signature_b64":"5CON+tuDiY7ZSlQsTuREJ2cMu1aAUZpu/mUB3Cbb+MupXhk0I3sgSOkPOtcPROnP99Cm87cMZcyyJrnGeV9kCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ceadfe6aa5b84a298488b7ada919051fc81c1d182306c59c3b653677f4b46ab5","last_reissued_at":"2026-05-22T02:04:55.329001Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T02:04:55.329001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.22798","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":"2026-05-22T02:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c8sZ5ypVoguJLAXR2hwHBSl4Iywy8P+mmPs3Sk9tygB+8s1Wd67WrcyEpBiw4xMgGt7E17PFFpuLNqJXPhgmBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T11:26:57.411469Z"},"content_sha256":"fc049224d4f12f17f6d248b5e422b35b59f4dea678b16870f8867d3ea7df656c","schema_version":"1.0","event_id":"sha256:fc049224d4f12f17f6d248b5e422b35b59f4dea678b16870f8867d3ea7df656c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:Z2W742VFXBFCTBEIW6W2SGIFD7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complex spinorial forms, Brinkmann four-manifolds, and self-dual bundle gerbes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Alejandro Gil-Garc\\'ia, C. S. Shahbazi","submitted_at":"2026-05-21T17:51:25Z","abstract_excerpt":"We develop the differential theory of complex spinorial forms associated with irreducible complex spinors across all dimensions and signatures. This framework enables the study of constrained parallelicity conditions for irreducible complex spinors by reformulating them as equivalent differential systems for exterior forms within a prescribed semi-algebraic body of the K\\\"ahler-Atiyah bundle. To illustrate this approach, we first apply it to the spin-c Killing spinor equation in low dimensions, refining existing results by relaxing standard assumptions of simply connectedness and completeness."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22798","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/2605.22798/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":"2026-05-22T02:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7gMwS/7D3qbOO2HfpE+fdDauOYML+H6RZCnsvGDeh33uHmuDtfGxu5BwlLrJhR8FZqtbgZtmR4kzhHyA7jugDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T11:26:57.412275Z"},"content_sha256":"da32bf587ac2e5c84bae3cc7fa36c4b8887412b7ba1cccace363887d00176e0c","schema_version":"1.0","event_id":"sha256:da32bf587ac2e5c84bae3cc7fa36c4b8887412b7ba1cccace363887d00176e0c"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:Z2W742VFXBFCTBEIW6W2SGIFD7","target":"integrity","payload":{"note":"URL 'https://arxiv.org/abs/' returned status 404 (Not Found) at last check.","snippet":null,"arxiv_id":"2605.22798","detector":"external_links","evidence":{"url":"https://arxiv.org/abs/","final_url":"https://arxiv.org/abs/","host_kind":"arxiv","status_code":404,"status_text":"Not Found","verdict_class":"incontrovertible","checked_at_unix":1779514370.5666413},"severity":"advisory","ref_index":null,"audited_at":"2026-05-23T05:32:50.619551Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://arxiv.org/abs/","finding_type":"dead_url","evidence_hash":"7d3be67cd6ed8261a9c3f49a67b36195507afaee26161a1182ca6839810215c0","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6602,"payload_sha256":"09360079d45f5346a14ee79aec8f93fb8c7877f9a701aed63cc31c4409b32478","signature_b64":"rmmfYM/gYQgsmcGLt218LrKC/xKLfSWPPI6aJVPMRkCLpq8GoE56ghzpnzH5/569grr650X52uQIWreywEUaCg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-23T05:37:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dao/r4fkcKR2aqMOhJRRk1VjQyOqy4Szf0jG0e3eLfH1ypQ21Jk8ik5ym28aK6emwWo8Q8DUb/aEmF3osE98Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T11:26:57.414213Z"},"content_sha256":"c95a67d09ff8a437cb235ae5adb5978de18e84a5bdd1586c056b55ba01a5344a","schema_version":"1.0","event_id":"sha256:c95a67d09ff8a437cb235ae5adb5978de18e84a5bdd1586c056b55ba01a5344a"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:Z2W742VFXBFCTBEIW6W2SGIFD7","target":"integrity","payload":{"note":"URL 'https://doi' returned status transport error (transport error: [Errno -3] Temporary failure in name resolution) at last check.","snippet":null,"arxiv_id":"2605.22798","detector":"external_links","evidence":{"url":"https://doi","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -3] Temporary failure in name resolution","verdict_class":"incontrovertible","checked_at_unix":1779514370.5537426},"severity":"advisory","ref_index":null,"audited_at":"2026-05-23T05:32:50.619551Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://doi","finding_type":"dead_url","evidence_hash":"325a49d87e558c48ca6ae744f78049c33615b55ba6c08540e1ded4ab0bfcb9ab","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6601,"payload_sha256":"272227b9b26f1d59d3b9b5805a3393d9a2afe13b4072c0044dc0982c13474bb8","signature_b64":"fAeZ7nYVznYZJ3Zs8QezQdopDlf3q6cwuQeF4mWRJhE6tUpttPSqD5xJsrS81raQMJtr1MoA0BqbI45L4yWuDQ==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-23T05:37:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uxDU57Itb51YJu0JZoRFYTme5Txk2FyLc94PY7GA0mVaF56yfJzr20Xe6cPuhvZAYb0dzEwV1OgabgIYH61QBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T11:26:57.414782Z"},"content_sha256":"cc62a66760e5457d504e104f7e93d87e2894065936d8c9a2fb9b5045b43caa5e","schema_version":"1.0","event_id":"sha256:cc62a66760e5457d504e104f7e93d87e2894065936d8c9a2fb9b5045b43caa5e"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:Z2W742VFXBFCTBEIW6W2SGIFD7","target":"integrity","payload":{"note":"URL 'https://arxiv' returned status transport error (transport error: [Errno -3] Temporary failure in name resolution) at last check.","snippet":null,"arxiv_id":"2605.22798","detector":"external_links","evidence":{"url":"https://arxiv","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -3] Temporary failure in name resolution","verdict_class":"incontrovertible","checked_at_unix":1779514370.5517278},"severity":"advisory","ref_index":null,"audited_at":"2026-05-23T05:32:50.619551Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://arxiv","finding_type":"dead_url","evidence_hash":"d49638b8ae63f676f84ff7fd16520f6dc3ff70cb774d807b04c38361e0793e82","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6600,"payload_sha256":"f39659b86b9a6961a3a8f24d0e959b6d829809a5ea13717688bc0bfc268b538b","signature_b64":"pmLsW0z1Fww2y4jpJZOA13NVQJZxL+5DGpdDBK2LXl83UjGY8S6+pagJn8NvhUEGamUDvxmFxBxWTZy7ZPJUCg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-23T05:37:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qeiviq0z3pXctXjryubHw7M53cs64Og0EdgDRAHrPg27cdaFjxVK824i+OU1mjn1fj56/L4R3AUALHjGoB24AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T11:26:57.415337Z"},"content_sha256":"acdf7243966b4361de5dc178e26ad0915cae29c6eca6c3bd902af130435cf4c4","schema_version":"1.0","event_id":"sha256:acdf7243966b4361de5dc178e26ad0915cae29c6eca6c3bd902af130435cf4c4"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:Z2W742VFXBFCTBEIW6W2SGIFD7","target":"integrity","payload":{"note":"URL 'https://arxiv.org/abs/' returned status 404 (Not Found) at last check.","snippet":null,"arxiv_id":"2605.22798","detector":"external_links","evidence":{"url":"https://arxiv.org/abs/","final_url":"https://arxiv.org/abs/","host_kind":"arxiv","status_code":404,"status_text":"Not Found","verdict_class":"incontrovertible","checked_at_unix":1779471164.9325964},"severity":"advisory","ref_index":null,"audited_at":"2026-05-22T17:32:44.969212Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://arxiv.org/abs/","finding_type":"dead_url","evidence_hash":"86d2d407fcfd9ce17aa7d7b950ca6c3c0cc9206155563f894c9965f1e6a43929","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6432,"payload_sha256":"bff8e6cdbac703aa952e70d54114c3831f7030c55eade867757c5ffdfc58f53b","signature_b64":"vSyYAY/0Q7qp5nqbr6o/IwVz3MIf/IuFRFDYR4oUUGBELlkKKj6QKzmN6CkdVSdH8StVwc2aAgPhvBRToEkRBg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-22T17:36:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fbzp9kd/40dqlSo8R5nLj43e7/PSVXHSB3/9MWxptluzC8JjzaO7qn/WSIFQa6AwievASu9aaQfEYUJ3z6u9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T11:26:57.415932Z"},"content_sha256":"3747fd88cdc51d866872610c46e28cc4bb95a5607c599510fc73d9baf7fa388c","schema_version":"1.0","event_id":"sha256:3747fd88cdc51d866872610c46e28cc4bb95a5607c599510fc73d9baf7fa388c"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:Z2W742VFXBFCTBEIW6W2SGIFD7","target":"integrity","payload":{"note":"URL 'https://doi' returned status transport error (transport error: [Errno -3] Temporary failure in name resolution) at last check.","snippet":null,"arxiv_id":"2605.22798","detector":"external_links","evidence":{"url":"https://doi","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -3] Temporary failure in name resolution","verdict_class":"incontrovertible","checked_at_unix":1779471164.9232564},"severity":"advisory","ref_index":null,"audited_at":"2026-05-22T17:32:44.969212Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://doi","finding_type":"dead_url","evidence_hash":"7ed201d01eb05b312fe87cc263fc9fa8f8e63207f3117d9be2ec81cd743c36d1","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6431,"payload_sha256":"29eb32e182999e197d278667d80ac707813890a8d4dba324d66be7d43bfa0abe","signature_b64":"fvSKqgmyFzeiz2IvUGEiG2XIoHnVYNcj9KKawsyXCQDRV5+CIfMqlQtK6DmxSAdR0VxgTHxgq5GX6Vq/Zs0tDg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-22T17:36:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1MKaZYWEfZQBtJijK9MvLe3khsBEo353e1HlYqh+R5Yk11EZtCuC22pI6o5NYLgwSvua0f04DrVLp09bUuG0Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T11:26:57.416531Z"},"content_sha256":"b237a4ec8140189bc57adfae27732c7e50dd70ca804908d3a1bd9ab2a31db33c","schema_version":"1.0","event_id":"sha256:b237a4ec8140189bc57adfae27732c7e50dd70ca804908d3a1bd9ab2a31db33c"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:Z2W742VFXBFCTBEIW6W2SGIFD7","target":"integrity","payload":{"note":"URL 'https://arxiv' returned status transport error (transport error: [Errno -3] Temporary failure in name resolution) at last check.","snippet":null,"arxiv_id":"2605.22798","detector":"external_links","evidence":{"url":"https://arxiv","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -3] Temporary failure in name resolution","verdict_class":"incontrovertible","checked_at_unix":1779471164.9218538},"severity":"advisory","ref_index":null,"audited_at":"2026-05-22T17:32:44.969212Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://arxiv","finding_type":"dead_url","evidence_hash":"c6c8fd63acc8d113bebff15aa4acb15380f79590bd7e9a1092d4da43452f5725","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6430,"payload_sha256":"87a00502d814e4a6766f6279e0bee91c313bc4dc5c7127054783e296063d2963","signature_b64":"Gk4B7bwHQQij9J4VoLkVMEY9Uo0z5H4MTEwF9sKn8oTSaDFlHQ6vTUULbn31x6hloKL6ZurPjVygs35J+I3LBw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-22T17:36:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mQLvpObuw4cygeIHVCz6WPs/q8k5fMcyPDb3yqXN8Gq0F4Guv9k1/tmYxeTFt1hpXU6gPig2Y27DDD+A4G+7CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T11:26:57.417099Z"},"content_sha256":"1b91026a6f0a21c2a930c66d4bf4ddd44c67df226c2022e81dea4bf60b4bca35","schema_version":"1.0","event_id":"sha256:1b91026a6f0a21c2a930c66d4bf4ddd44c67df226c2022e81dea4bf60b4bca35"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:Z2W742VFXBFCTBEIW6W2SGIFD7","target":"integrity","payload":{"note":"URL 'https://arxiv.org/abs/' returned status 404 (Not Found) at last check.","snippet":null,"arxiv_id":"2605.22798","detector":"external_links","evidence":{"url":"https://arxiv.org/abs/","final_url":"https://arxiv.org/abs/","host_kind":"arxiv","status_code":404,"status_text":"Not Found","verdict_class":"incontrovertible","checked_at_unix":1779427950.9508948},"severity":"advisory","ref_index":null,"audited_at":"2026-05-22T05:32:31.171576Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://arxiv.org/abs/","finding_type":"dead_url","evidence_hash":"b241d4d9fc3dd5a6ce3cf874ed83d375845a77df2aa5be2e2fedd1eaa6b71696","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6211,"payload_sha256":"7d197469c306d30bee4caa6478213e8351fab292a102060227ebc8295419fae0","signature_b64":"padA73OQJstMvmfptP0gUbJkN0djs+5Xw7LzTEdR9u9TuHj7V8dhWWhx46B+idQUyS35p9TAnNEK4dutsLN7AQ==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-22T05:35:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4y5K+UJjH+eyskIlOZLVqPxDQACjc8KQen/R5KHrl84BBXXLS+VqTKCrNrOZHSeIWUq/+6AaKxwxasS7OOqbDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T11:26:57.417675Z"},"content_sha256":"606903d9dd0fb4ad039e3bb2a9f6a6cdaf1845b6bec3894982906860ba914c20","schema_version":"1.0","event_id":"sha256:606903d9dd0fb4ad039e3bb2a9f6a6cdaf1845b6bec3894982906860ba914c20"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:Z2W742VFXBFCTBEIW6W2SGIFD7","target":"integrity","payload":{"note":"URL 'https://doi' returned status transport error (transport error: [Errno -3] Temporary failure in name resolution) at last check.","snippet":null,"arxiv_id":"2605.22798","detector":"external_links","evidence":{"url":"https://doi","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -3] Temporary failure in name resolution","verdict_class":"incontrovertible","checked_at_unix":1779427950.8732278},"severity":"advisory","ref_index":null,"audited_at":"2026-05-22T05:32:31.171576Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://doi","finding_type":"dead_url","evidence_hash":"11119a28e67abed85688672c17b7d56b8b5ee242406ae55ec416c2d6f1369064","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6210,"payload_sha256":"3225cfa5e0122aa03001f3469845c0da5bed50e16e173ac8c55840e482814aff","signature_b64":"cq0JHpLE6pcYUHwIyhnU54IoyK19ZZNt7I6Nqczrf2z/kvKQuvvVdu2P7MQsx0lZmIUoC8Ad4Qhh4qE3EX4nDw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-22T05:35:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8dhE1CmJP3YgN1LuozPv3ZCHShkkluCR0EttWVSDmHDNcte4KLvaccC+MElWiZUPIQ/4D72ObcnDedPwGvzOBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T11:26:57.418230Z"},"content_sha256":"d4120760032577f2c3109e4f025036eed8498a957dc21110f278a9b8b9f2398b","schema_version":"1.0","event_id":"sha256:d4120760032577f2c3109e4f025036eed8498a957dc21110f278a9b8b9f2398b"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:Z2W742VFXBFCTBEIW6W2SGIFD7","target":"integrity","payload":{"note":"URL 'https://arxiv' returned status transport error (transport error: [Errno -3] Temporary failure in name resolution) at last check.","snippet":null,"arxiv_id":"2605.22798","detector":"external_links","evidence":{"url":"https://arxiv","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -3] Temporary failure in name resolution","verdict_class":"incontrovertible","checked_at_unix":1779427950.8710644},"severity":"advisory","ref_index":null,"audited_at":"2026-05-22T05:32:31.171576Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://arxiv","finding_type":"dead_url","evidence_hash":"c92f7d292acaafcfc84dcced7eb09bfb23c4c88916a94bc3b512602573393136","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6209,"payload_sha256":"da0dee081521d48a08058b3bc33431843743b64ccc523885cf31bcc240bb91c1","signature_b64":"JaED7iNs911wamnLApcocZj1bLie/6eaA/TchxIII7z/gKziuXf5R3JuUYvqv9hbLSAus6TI2xYYaSIggaFABw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-22T05:35:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o1xJashpr2iAA+PtooqDCBStLA9fcga/e3/8GWtrvqPcAHTBIB9O9lvWYQMhSVyK+cNsVrl5Zq6KVHiA1KfaCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T11:26:57.418829Z"},"content_sha256":"1c846bc5ca8742ae06ea5d9776a968f309b4c78f6d03590cba8ca02b00feee9a","schema_version":"1.0","event_id":"sha256:1c846bc5ca8742ae06ea5d9776a968f309b4c78f6d03590cba8ca02b00feee9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z2W742VFXBFCTBEIW6W2SGIFD7/bundle.json","state_url":"https://pith.science/pith/Z2W742VFXBFCTBEIW6W2SGIFD7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z2W742VFXBFCTBEIW6W2SGIFD7/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":"2026-05-23T11:26:57Z","links":{"resolver":"https://pith.science/pith/Z2W742VFXBFCTBEIW6W2SGIFD7","bundle":"https://pith.science/pith/Z2W742VFXBFCTBEIW6W2SGIFD7/bundle.json","state":"https://pith.science/pith/Z2W742VFXBFCTBEIW6W2SGIFD7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z2W742VFXBFCTBEIW6W2SGIFD7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:Z2W742VFXBFCTBEIW6W2SGIFD7","merge_version":"pith-open-graph-merge-v1","event_count":11,"valid_event_count":11,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8b9b4b64a5f218eddc2efedfc5d4de8c936b691c481a1f673b27c053bc24eb78","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-21T17:51:25Z","title_canon_sha256":"0fa65672ca67e3c79ce2f14f96c2bc6e8115616fe58539000268c8a0086f8ccc"},"schema_version":"1.0","source":{"id":"2605.22798","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22798","created_at":"2026-05-22T02:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22798v1","created_at":"2026-05-22T02:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22798","created_at":"2026-05-22T02:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"Z2W742VFXBFC","created_at":"2026-05-22T02:04:55Z"},{"alias_kind":"pith_short_16","alias_value":"Z2W742VFXBFCTBEI","created_at":"2026-05-22T02:04:55Z"},{"alias_kind":"pith_short_8","alias_value":"Z2W742VF","created_at":"2026-05-22T02:04:55Z"}],"graph_snapshots":[{"event_id":"sha256:da32bf587ac2e5c84bae3cc7fa36c4b8887412b7ba1cccace363887d00176e0c","target":"graph","created_at":"2026-05-22T02:04:55Z","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/2605.22798/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop the differential theory of complex spinorial forms associated with irreducible complex spinors across all dimensions and signatures. This framework enables the study of constrained parallelicity conditions for irreducible complex spinors by reformulating them as equivalent differential systems for exterior forms within a prescribed semi-algebraic body of the K\\\"ahler-Atiyah bundle. To illustrate this approach, we first apply it to the spin-c Killing spinor equation in low dimensions, refining existing results by relaxing standard assumptions of simply connectedness and completeness.","authors_text":"Alejandro Gil-Garc\\'ia, C. S. Shahbazi","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-21T17:51:25Z","title":"Complex spinorial forms, Brinkmann four-manifolds, and self-dual bundle gerbes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22798","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:fc049224d4f12f17f6d248b5e422b35b59f4dea678b16870f8867d3ea7df656c","target":"record","created_at":"2026-05-22T02:04:55Z","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":"8b9b4b64a5f218eddc2efedfc5d4de8c936b691c481a1f673b27c053bc24eb78","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-21T17:51:25Z","title_canon_sha256":"0fa65672ca67e3c79ce2f14f96c2bc6e8115616fe58539000268c8a0086f8ccc"},"schema_version":"1.0","source":{"id":"2605.22798","kind":"arxiv","version":1}},"canonical_sha256":"ceadfe6aa5b84a298488b7ada919051fc81c1d182306c59c3b653677f4b46ab5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ceadfe6aa5b84a298488b7ada919051fc81c1d182306c59c3b653677f4b46ab5","first_computed_at":"2026-05-22T02:04:55.329001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T02:04:55.329001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5CON+tuDiY7ZSlQsTuREJ2cMu1aAUZpu/mUB3Cbb+MupXhk0I3sgSOkPOtcPROnP99Cm87cMZcyyJrnGeV9kCg==","signature_status":"signed_v1","signed_at":"2026-05-22T02:04:55.329457Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.22798","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:1b91026a6f0a21c2a930c66d4bf4ddd44c67df226c2022e81dea4bf60b4bca35","sha256:1c846bc5ca8742ae06ea5d9776a968f309b4c78f6d03590cba8ca02b00feee9a","sha256:3747fd88cdc51d866872610c46e28cc4bb95a5607c599510fc73d9baf7fa388c","sha256:606903d9dd0fb4ad039e3bb2a9f6a6cdaf1845b6bec3894982906860ba914c20","sha256:acdf7243966b4361de5dc178e26ad0915cae29c6eca6c3bd902af130435cf4c4","sha256:b237a4ec8140189bc57adfae27732c7e50dd70ca804908d3a1bd9ab2a31db33c","sha256:c95a67d09ff8a437cb235ae5adb5978de18e84a5bdd1586c056b55ba01a5344a","sha256:cc62a66760e5457d504e104f7e93d87e2894065936d8c9a2fb9b5045b43caa5e","sha256:d4120760032577f2c3109e4f025036eed8498a957dc21110f278a9b8b9f2398b"]}],"invalid_events":[],"applied_event_ids":["sha256:fc049224d4f12f17f6d248b5e422b35b59f4dea678b16870f8867d3ea7df656c","sha256:da32bf587ac2e5c84bae3cc7fa36c4b8887412b7ba1cccace363887d00176e0c"],"state_sha256":"0dbb2c1c8c96e57075cdb56572a2238140d527fcc876757375addf2744f5c232"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pMNYO//2tSaX0PA9k0dO+sZVMOgok0PyWFxBHTQBWo5w5Dkl/bAtTu3AsCtKLRsrbIwnk1vrCAEOc3S230YLDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T11:26:57.426161Z","bundle_sha256":"076c8131d30c9419ed7315bc947ae9459a3bb1d614c65e5075416864238bed60"}}