{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:VSVH722MSCZSNW2GCBQI76OYZE","short_pith_number":"pith:VSVH722M","canonical_record":{"source":{"id":"0710.0093","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2007-09-29T20:16:27Z","cross_cats_sorted":[],"title_canon_sha256":"494bf083172067d2fe80cdadc68ed395e0de8a73d029b6063801ebe209d87c2d","abstract_canon_sha256":"3e695ccdff562c970e98a2a459d8dff95b431a17dbef8df22c26180b24cce873"},"schema_version":"1.0"},"canonical_sha256":"acaa7feb4c90b326db4610608ff9d8c91f64e412d0f8d969fb639b60aeca1b70","source":{"kind":"arxiv","id":"0710.0093","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.0093","created_at":"2026-05-18T04:09:14Z"},{"alias_kind":"arxiv_version","alias_value":"0710.0093v2","created_at":"2026-05-18T04:09:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.0093","created_at":"2026-05-18T04:09:14Z"},{"alias_kind":"pith_short_12","alias_value":"VSVH722MSCZS","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"VSVH722MSCZSNW2G","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"VSVH722M","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:VSVH722MSCZSNW2GCBQI76OYZE","target":"record","payload":{"canonical_record":{"source":{"id":"0710.0093","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2007-09-29T20:16:27Z","cross_cats_sorted":[],"title_canon_sha256":"494bf083172067d2fe80cdadc68ed395e0de8a73d029b6063801ebe209d87c2d","abstract_canon_sha256":"3e695ccdff562c970e98a2a459d8dff95b431a17dbef8df22c26180b24cce873"},"schema_version":"1.0"},"canonical_sha256":"acaa7feb4c90b326db4610608ff9d8c91f64e412d0f8d969fb639b60aeca1b70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:14.306814Z","signature_b64":"rTVNYYx/nmNV0w0BouMnnB+0Zk8m9fM/ejpg8puc7eTz4c0Zi+MWhYz7YBKC6+Km0/mRLC80EfMJc9e8+DiwDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acaa7feb4c90b326db4610608ff9d8c91f64e412d0f8d969fb639b60aeca1b70","last_reissued_at":"2026-05-18T04:09:14.306302Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:14.306302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0710.0093","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":"2026-05-18T04:09:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IXeRW/L7WXc8R1ThCSLhxklUsTVgGRJS1Lx8S1VZXbz3ixMCvqbV67uYZy3wZsQPB3quGwDgV4Y4Ta2ungHJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:46:37.820843Z"},"content_sha256":"27eec3f3cec8571efa9bb7e873580e6db1c315b702be3ab0851f99b294745fc0","schema_version":"1.0","event_id":"sha256:27eec3f3cec8571efa9bb7e873580e6db1c315b702be3ab0851f99b294745fc0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:VSVH722MSCZSNW2GCBQI76OYZE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Dolbeault sequences in parabolic geometry","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Peter Franek","submitted_at":"2007-09-29T20:16:27Z","abstract_excerpt":"In this paper, we show the existence of a sequence of invariant differential operators on a particular homogeneous model $G/P$ of a Cartan geometry. The first operator in this sequence can be locally identified with the Dirac operator in $k$ Clifford variables, $D=(D_1,..., D_k)$, where $D_i=\\sum_j e_j\\cdot \\partial_{ij}: C^\\infty((\\R^n)^k,\\S)\\to C^\\infty((\\R^n)^k,\\S)$. We describe the structure of these sequences in case the dimension $n$ is odd. It follows from the construction that all these operators are invariant with respect to the action of the group $G$.\n  These results are obtained by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.0093","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":""},"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":"2026-05-18T04:09:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xag4jWRoWRL9BwZ6qMzrYHAduM54y8nx8My+8Jm14MxwuS+SxzCtYyWr59Fnf9DHfR6Yp3dD1BDRPwLxluyGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:46:37.821192Z"},"content_sha256":"7af9ac9b51b6994839db415bcc27071761641e014081f06a7d0c15581aa1e63e","schema_version":"1.0","event_id":"sha256:7af9ac9b51b6994839db415bcc27071761641e014081f06a7d0c15581aa1e63e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VSVH722MSCZSNW2GCBQI76OYZE/bundle.json","state_url":"https://pith.science/pith/VSVH722MSCZSNW2GCBQI76OYZE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VSVH722MSCZSNW2GCBQI76OYZE/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":"2026-06-21T14:46:37Z","links":{"resolver":"https://pith.science/pith/VSVH722MSCZSNW2GCBQI76OYZE","bundle":"https://pith.science/pith/VSVH722MSCZSNW2GCBQI76OYZE/bundle.json","state":"https://pith.science/pith/VSVH722MSCZSNW2GCBQI76OYZE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VSVH722MSCZSNW2GCBQI76OYZE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:VSVH722MSCZSNW2GCBQI76OYZE","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":"3e695ccdff562c970e98a2a459d8dff95b431a17dbef8df22c26180b24cce873","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2007-09-29T20:16:27Z","title_canon_sha256":"494bf083172067d2fe80cdadc68ed395e0de8a73d029b6063801ebe209d87c2d"},"schema_version":"1.0","source":{"id":"0710.0093","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.0093","created_at":"2026-05-18T04:09:14Z"},{"alias_kind":"arxiv_version","alias_value":"0710.0093v2","created_at":"2026-05-18T04:09:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.0093","created_at":"2026-05-18T04:09:14Z"},{"alias_kind":"pith_short_12","alias_value":"VSVH722MSCZS","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"VSVH722MSCZSNW2G","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"VSVH722M","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:7af9ac9b51b6994839db415bcc27071761641e014081f06a7d0c15581aa1e63e","target":"graph","created_at":"2026-05-18T04:09:14Z","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"},"paper":{"abstract_excerpt":"In this paper, we show the existence of a sequence of invariant differential operators on a particular homogeneous model $G/P$ of a Cartan geometry. The first operator in this sequence can be locally identified with the Dirac operator in $k$ Clifford variables, $D=(D_1,..., D_k)$, where $D_i=\\sum_j e_j\\cdot \\partial_{ij}: C^\\infty((\\R^n)^k,\\S)\\to C^\\infty((\\R^n)^k,\\S)$. We describe the structure of these sequences in case the dimension $n$ is odd. It follows from the construction that all these operators are invariant with respect to the action of the group $G$.\n  These results are obtained by","authors_text":"Peter Franek","cross_cats":[],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2007-09-29T20:16:27Z","title":"Generalized Dolbeault sequences in parabolic geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.0093","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":"sha256:27eec3f3cec8571efa9bb7e873580e6db1c315b702be3ab0851f99b294745fc0","target":"record","created_at":"2026-05-18T04:09:14Z","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":"3e695ccdff562c970e98a2a459d8dff95b431a17dbef8df22c26180b24cce873","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2007-09-29T20:16:27Z","title_canon_sha256":"494bf083172067d2fe80cdadc68ed395e0de8a73d029b6063801ebe209d87c2d"},"schema_version":"1.0","source":{"id":"0710.0093","kind":"arxiv","version":2}},"canonical_sha256":"acaa7feb4c90b326db4610608ff9d8c91f64e412d0f8d969fb639b60aeca1b70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acaa7feb4c90b326db4610608ff9d8c91f64e412d0f8d969fb639b60aeca1b70","first_computed_at":"2026-05-18T04:09:14.306302Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:14.306302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rTVNYYx/nmNV0w0BouMnnB+0Zk8m9fM/ejpg8puc7eTz4c0Zi+MWhYz7YBKC6+Km0/mRLC80EfMJc9e8+DiwDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:14.306814Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.0093","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27eec3f3cec8571efa9bb7e873580e6db1c315b702be3ab0851f99b294745fc0","sha256:7af9ac9b51b6994839db415bcc27071761641e014081f06a7d0c15581aa1e63e"],"state_sha256":"3ec3c46f111868ef952ae93a6ec67887075e434fabf3dd0d2f45d258167e62fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2DxCceK7WjbqWgnhngLZ4wlIdLIJp+O2oh4gterIFZN4JgMRY8uPJhoD9yIGhgU4SiniQ/Ac5zrOMpAqcIFMCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T14:46:37.823046Z","bundle_sha256":"f31caba5f7c4164289c3dc01bbc2f6b87c2402d1c37191b3a57f5d97c2edb313"}}