{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:6CWELLOEIQDEUY5P3XR5ABRKKB","short_pith_number":"pith:6CWELLOE","canonical_record":{"source":{"id":"math/0006186","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2000-06-24T20:37:18Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1fa912adafd9af8e1474930055dfc21fdcf32973adc050b71e27fa5060a79cbc","abstract_canon_sha256":"2f0eb60923338e3de5f6acb64019b2b9d5e36e0023ffe34e97e161ed742f7b3a"},"schema_version":"1.0"},"canonical_sha256":"f0ac45adc444064a63afdde3d0062a504680e2b0be8a5ce1f589c1d8810fd092","source":{"kind":"arxiv","id":"math/0006186","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0006186","created_at":"2026-07-04T14:34:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/0006186v2","created_at":"2026-07-04T14:34:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0006186","created_at":"2026-07-04T14:34:34Z"},{"alias_kind":"pith_short_12","alias_value":"6CWELLOEIQDE","created_at":"2026-07-04T14:34:34Z"},{"alias_kind":"pith_short_16","alias_value":"6CWELLOEIQDEUY5P","created_at":"2026-07-04T14:34:34Z"},{"alias_kind":"pith_short_8","alias_value":"6CWELLOE","created_at":"2026-07-04T14:34:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:6CWELLOEIQDEUY5P3XR5ABRKKB","target":"record","payload":{"canonical_record":{"source":{"id":"math/0006186","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2000-06-24T20:37:18Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1fa912adafd9af8e1474930055dfc21fdcf32973adc050b71e27fa5060a79cbc","abstract_canon_sha256":"2f0eb60923338e3de5f6acb64019b2b9d5e36e0023ffe34e97e161ed742f7b3a"},"schema_version":"1.0"},"canonical_sha256":"f0ac45adc444064a63afdde3d0062a504680e2b0be8a5ce1f589c1d8810fd092","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:34:34.825202Z","signature_b64":"d1yfJEHXojXjFc5TGycW8smzavGkmsnbqPpAmY9TLKYK8fQZt05YcXAOtCK6kGB5noBo/wHulLE+fbmaQf4LCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0ac45adc444064a63afdde3d0062a504680e2b0be8a5ce1f589c1d8810fd092","last_reissued_at":"2026-07-04T14:34:34.824792Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:34:34.824792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0006186","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":"2026-07-04T14:34:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y9mGxNkhJMCWXfGGdO8qYUS4jYtGjVG/jM2TjdoAbo1/XVVnI00LO5thzjEO3egiWa/k2HxzrOIslrEpGHB/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T16:50:45.061224Z"},"content_sha256":"b02e56cb21be07b14e81f467a1b7e8695ce606ffeeb3db4633dd491a2402d618","schema_version":"1.0","event_id":"sha256:b02e56cb21be07b14e81f467a1b7e8695ce606ffeeb3db4633dd491a2402d618"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:6CWELLOEIQDEUY5P3XR5ABRKKB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Robert L. Bryant","submitted_at":"2000-06-24T20:37:18Z","abstract_excerpt":"I use local differential geometric techniques to prove that the algebraic cycles in certain extremal homology classes in Hermitian symmetric spaces are either rigid (i.e., deformable only by ambient motions) or quasi-rigid (roughly speaking, foliated by rigid subvarieties in a nontrivial way).\n  These rigidity results have a number of applications: First, they prove that many subvarieties in Grassmannians and other Hermitian symmetric spaces cannot be smoothed (i.e., are not homologous to a smooth subvariety). Second, they provide characterizations of holomorphic bundles over compact Kahler ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0006186","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/math/0006186/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":"2026-07-04T14:34:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KdVqwql8rxH8DsongUdWm4728/RXamQVK3svLUA84ZF+jBqY44gnqoOAhuASkiYtBjqGCavfXrOeGhuzGwIeAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T16:50:45.061744Z"},"content_sha256":"323923dad7237687e6c5ca85c926bb05ec541f228272d92e144ed5c56d03d030","schema_version":"1.0","event_id":"sha256:323923dad7237687e6c5ca85c926bb05ec541f228272d92e144ed5c56d03d030"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6CWELLOEIQDEUY5P3XR5ABRKKB/bundle.json","state_url":"https://pith.science/pith/6CWELLOEIQDEUY5P3XR5ABRKKB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6CWELLOEIQDEUY5P3XR5ABRKKB/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":"2026-08-12T16:50:45Z","links":{"resolver":"https://pith.science/pith/6CWELLOEIQDEUY5P3XR5ABRKKB","bundle":"https://pith.science/pith/6CWELLOEIQDEUY5P3XR5ABRKKB/bundle.json","state":"https://pith.science/pith/6CWELLOEIQDEUY5P3XR5ABRKKB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6CWELLOEIQDEUY5P3XR5ABRKKB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:6CWELLOEIQDEUY5P3XR5ABRKKB","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":"2f0eb60923338e3de5f6acb64019b2b9d5e36e0023ffe34e97e161ed742f7b3a","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.DG","submitted_at":"2000-06-24T20:37:18Z","title_canon_sha256":"1fa912adafd9af8e1474930055dfc21fdcf32973adc050b71e27fa5060a79cbc"},"schema_version":"1.0","source":{"id":"math/0006186","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0006186","created_at":"2026-07-04T14:34:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/0006186v2","created_at":"2026-07-04T14:34:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0006186","created_at":"2026-07-04T14:34:34Z"},{"alias_kind":"pith_short_12","alias_value":"6CWELLOEIQDE","created_at":"2026-07-04T14:34:34Z"},{"alias_kind":"pith_short_16","alias_value":"6CWELLOEIQDEUY5P","created_at":"2026-07-04T14:34:34Z"},{"alias_kind":"pith_short_8","alias_value":"6CWELLOE","created_at":"2026-07-04T14:34:34Z"}],"graph_snapshots":[{"event_id":"sha256:323923dad7237687e6c5ca85c926bb05ec541f228272d92e144ed5c56d03d030","target":"graph","created_at":"2026-07-04T14:34:34Z","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/math/0006186/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"I use local differential geometric techniques to prove that the algebraic cycles in certain extremal homology classes in Hermitian symmetric spaces are either rigid (i.e., deformable only by ambient motions) or quasi-rigid (roughly speaking, foliated by rigid subvarieties in a nontrivial way).\n  These rigidity results have a number of applications: First, they prove that many subvarieties in Grassmannians and other Hermitian symmetric spaces cannot be smoothed (i.e., are not homologous to a smooth subvariety). Second, they provide characterizations of holomorphic bundles over compact Kahler ma","authors_text":"Robert L. Bryant","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2000-06-24T20:37:18Z","title":"Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0006186","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:b02e56cb21be07b14e81f467a1b7e8695ce606ffeeb3db4633dd491a2402d618","target":"record","created_at":"2026-07-04T14:34:34Z","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":"2f0eb60923338e3de5f6acb64019b2b9d5e36e0023ffe34e97e161ed742f7b3a","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.DG","submitted_at":"2000-06-24T20:37:18Z","title_canon_sha256":"1fa912adafd9af8e1474930055dfc21fdcf32973adc050b71e27fa5060a79cbc"},"schema_version":"1.0","source":{"id":"math/0006186","kind":"arxiv","version":2}},"canonical_sha256":"f0ac45adc444064a63afdde3d0062a504680e2b0be8a5ce1f589c1d8810fd092","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0ac45adc444064a63afdde3d0062a504680e2b0be8a5ce1f589c1d8810fd092","first_computed_at":"2026-07-04T14:34:34.824792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:34:34.824792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d1yfJEHXojXjFc5TGycW8smzavGkmsnbqPpAmY9TLKYK8fQZt05YcXAOtCK6kGB5noBo/wHulLE+fbmaQf4LCA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:34:34.825202Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0006186","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b02e56cb21be07b14e81f467a1b7e8695ce606ffeeb3db4633dd491a2402d618","sha256:323923dad7237687e6c5ca85c926bb05ec541f228272d92e144ed5c56d03d030"],"state_sha256":"3065e6fe64d728f0e87f5925aafb5095c20710821bc9bd1d433bcf547f63e503"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YrG3Om7nrEBaBlBZbLDRu1v3MN/u0kAVhh6qyMJvAeRlJKmfZvNZBeTDppDHH9SNQs+sPYEHApPl9NP37M8jAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T16:50:45.066606Z","bundle_sha256":"e4243d0fa81374f7a6b8de532231a51e247036a31c46d6da7cfeb5d9b7b412a6"}}