{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:GIE62VYOAUY4DDJLLG6IK7ORL3","short_pith_number":"pith:GIE62VYO","canonical_record":{"source":{"id":"0808.2799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-08-20T18:47:47Z","cross_cats_sorted":[],"title_canon_sha256":"abd8f41bf5d08c112c584be0aa0867fa3ab0493228b71d08198d67cc21a54eaa","abstract_canon_sha256":"13838866e14912edc5eb157549173b5119acd15f7e84c1f20f9e058b2cead205"},"schema_version":"1.0"},"canonical_sha256":"3209ed570e0531c18d2b59bc857dd15edeee5a101a3cdd1153db5f6f469f1705","source":{"kind":"arxiv","id":"0808.2799","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.2799","created_at":"2026-05-18T02:15:42Z"},{"alias_kind":"arxiv_version","alias_value":"0808.2799v1","created_at":"2026-05-18T02:15:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.2799","created_at":"2026-05-18T02:15:42Z"},{"alias_kind":"pith_short_12","alias_value":"GIE62VYOAUY4","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"GIE62VYOAUY4DDJL","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"GIE62VYO","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:GIE62VYOAUY4DDJLLG6IK7ORL3","target":"record","payload":{"canonical_record":{"source":{"id":"0808.2799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-08-20T18:47:47Z","cross_cats_sorted":[],"title_canon_sha256":"abd8f41bf5d08c112c584be0aa0867fa3ab0493228b71d08198d67cc21a54eaa","abstract_canon_sha256":"13838866e14912edc5eb157549173b5119acd15f7e84c1f20f9e058b2cead205"},"schema_version":"1.0"},"canonical_sha256":"3209ed570e0531c18d2b59bc857dd15edeee5a101a3cdd1153db5f6f469f1705","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:42.995818Z","signature_b64":"FIXvLAbvKfiR0Aypx2PoDJ94dGxu7LrSOOqfImZKKnYhidzKA8HzzJoCx71UJJucAwPUr65bU2lB4m8bI2puAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3209ed570e0531c18d2b59bc857dd15edeee5a101a3cdd1153db5f6f469f1705","last_reissued_at":"2026-05-18T02:15:42.995215Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:42.995215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0808.2799","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":"2026-05-18T02:15:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QPvz/krpPoXkQq3RkubQtnvEvdB6UCkYOOhyT+wpaYY63LII+0BaRYJqR2Gdk8IadjFKovz6opB2qcA/avsYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:07:06.139597Z"},"content_sha256":"a27ae516f2667602a49f2df5a946ea09ef03f245eb4a1618fecbe2d4aabb665a","schema_version":"1.0","event_id":"sha256:a27ae516f2667602a49f2df5a946ea09ef03f245eb4a1618fecbe2d4aabb665a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:GIE62VYOAUY4DDJLLG6IK7ORL3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Curvature structure of self-dual 4-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Iva Stavrov, Novica Blazic, Peter Gilkey, Stana Nikcevic","submitted_at":"2008-08-20T18:47:47Z","abstract_excerpt":"We show the existence of a modified Cliff(1,1) structure compatible with an Osserman 0-model of signature (2,2). We then apply this algebraic result to certain classes of pseudo-Riemannian manifolds of signature (2,2). We obtain a new characterization of the Weyl curvature tensor of an (anti-)self-dual manifold and we prove some new results regarding (Jordan) Osserman manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.2799","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":""},"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":"2026-05-18T02:15:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FOAgcaekb4Gg96n+rpyEZenGZIKu+wBtCMm7ifeE2s8aY3NzX8MUYsnq6nqMEK5x4n+M5TXdyTXuFuYx/o4LBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:07:06.139938Z"},"content_sha256":"b00e5b44320014ded6e157a47cac06e96acbd825e223fe7c6eb068ae6c31d855","schema_version":"1.0","event_id":"sha256:b00e5b44320014ded6e157a47cac06e96acbd825e223fe7c6eb068ae6c31d855"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GIE62VYOAUY4DDJLLG6IK7ORL3/bundle.json","state_url":"https://pith.science/pith/GIE62VYOAUY4DDJLLG6IK7ORL3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GIE62VYOAUY4DDJLLG6IK7ORL3/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":"2026-06-03T19:07:06Z","links":{"resolver":"https://pith.science/pith/GIE62VYOAUY4DDJLLG6IK7ORL3","bundle":"https://pith.science/pith/GIE62VYOAUY4DDJLLG6IK7ORL3/bundle.json","state":"https://pith.science/pith/GIE62VYOAUY4DDJLLG6IK7ORL3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GIE62VYOAUY4DDJLLG6IK7ORL3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:GIE62VYOAUY4DDJLLG6IK7ORL3","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":"13838866e14912edc5eb157549173b5119acd15f7e84c1f20f9e058b2cead205","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-08-20T18:47:47Z","title_canon_sha256":"abd8f41bf5d08c112c584be0aa0867fa3ab0493228b71d08198d67cc21a54eaa"},"schema_version":"1.0","source":{"id":"0808.2799","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.2799","created_at":"2026-05-18T02:15:42Z"},{"alias_kind":"arxiv_version","alias_value":"0808.2799v1","created_at":"2026-05-18T02:15:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.2799","created_at":"2026-05-18T02:15:42Z"},{"alias_kind":"pith_short_12","alias_value":"GIE62VYOAUY4","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"GIE62VYOAUY4DDJL","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"GIE62VYO","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:b00e5b44320014ded6e157a47cac06e96acbd825e223fe7c6eb068ae6c31d855","target":"graph","created_at":"2026-05-18T02:15:42Z","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":"We show the existence of a modified Cliff(1,1) structure compatible with an Osserman 0-model of signature (2,2). We then apply this algebraic result to certain classes of pseudo-Riemannian manifolds of signature (2,2). We obtain a new characterization of the Weyl curvature tensor of an (anti-)self-dual manifold and we prove some new results regarding (Jordan) Osserman manifolds.","authors_text":"Iva Stavrov, Novica Blazic, Peter Gilkey, Stana Nikcevic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-08-20T18:47:47Z","title":"Curvature structure of self-dual 4-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.2799","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:a27ae516f2667602a49f2df5a946ea09ef03f245eb4a1618fecbe2d4aabb665a","target":"record","created_at":"2026-05-18T02:15:42Z","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":"13838866e14912edc5eb157549173b5119acd15f7e84c1f20f9e058b2cead205","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-08-20T18:47:47Z","title_canon_sha256":"abd8f41bf5d08c112c584be0aa0867fa3ab0493228b71d08198d67cc21a54eaa"},"schema_version":"1.0","source":{"id":"0808.2799","kind":"arxiv","version":1}},"canonical_sha256":"3209ed570e0531c18d2b59bc857dd15edeee5a101a3cdd1153db5f6f469f1705","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3209ed570e0531c18d2b59bc857dd15edeee5a101a3cdd1153db5f6f469f1705","first_computed_at":"2026-05-18T02:15:42.995215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:42.995215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FIXvLAbvKfiR0Aypx2PoDJ94dGxu7LrSOOqfImZKKnYhidzKA8HzzJoCx71UJJucAwPUr65bU2lB4m8bI2puAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:42.995818Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.2799","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a27ae516f2667602a49f2df5a946ea09ef03f245eb4a1618fecbe2d4aabb665a","sha256:b00e5b44320014ded6e157a47cac06e96acbd825e223fe7c6eb068ae6c31d855"],"state_sha256":"dccb4a3503c7f6f0cbb4179f4124756256550814696adf262f8f71c825e8ccb4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LsB7HLpI0nbieTLHTe1Fc/MisE6I6q7jKcFDF0rNjJMffnTUAmVzGG61xiDN0K9w+KUaBkw4mXnZ6JCNTExZAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T19:07:06.141956Z","bundle_sha256":"f9fcdc38ac3cb3f83e2502c5e1468703e9dcf87bcdffd89ed9d4be05bbc3d0ef"}}