{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:IKREHU44NUBWXAPHHSR62YY76X","short_pith_number":"pith:IKREHU44","canonical_record":{"source":{"id":"1810.06456","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-10-15T15:20:48Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"8291e95422e916ea0883628021110d8c53f393b7f8218acc878ae6d38d16dcd8","abstract_canon_sha256":"7a6cb88583b26e89c497372def5634fab90b03723c1ae0d60eb93a144f5b2a9e"},"schema_version":"1.0"},"canonical_sha256":"42a243d39c6d036b81e73ca3ed631ff5e884d10f8ee37e90113d3e6773460c01","source":{"kind":"arxiv","id":"1810.06456","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.06456","created_at":"2026-05-17T23:51:05Z"},{"alias_kind":"arxiv_version","alias_value":"1810.06456v2","created_at":"2026-05-17T23:51:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06456","created_at":"2026-05-17T23:51:05Z"},{"alias_kind":"pith_short_12","alias_value":"IKREHU44NUBW","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IKREHU44NUBWXAPH","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IKREHU44","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:IKREHU44NUBWXAPHHSR62YY76X","target":"record","payload":{"canonical_record":{"source":{"id":"1810.06456","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-10-15T15:20:48Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"8291e95422e916ea0883628021110d8c53f393b7f8218acc878ae6d38d16dcd8","abstract_canon_sha256":"7a6cb88583b26e89c497372def5634fab90b03723c1ae0d60eb93a144f5b2a9e"},"schema_version":"1.0"},"canonical_sha256":"42a243d39c6d036b81e73ca3ed631ff5e884d10f8ee37e90113d3e6773460c01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:05.414636Z","signature_b64":"hh+kLURQZf5OsjRdaK4n8zb2a5Z/xtBDU7UpRusLXWPz/owMS6uo24nn/mhh5+YnrUSjzfATnvSeeX5ktKK2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42a243d39c6d036b81e73ca3ed631ff5e884d10f8ee37e90113d3e6773460c01","last_reissued_at":"2026-05-17T23:51:05.414096Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:05.414096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.06456","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":"2026-05-17T23:51:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PaUhAYr95D6J0Rx78apS4u1WW3klSYUf9tQ6iK7e3GkdVU5Mzv+WB3UKKr6ByP9WalrpHMg86/EAlhppm2wcAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:18:37.316274Z"},"content_sha256":"d6b486a4d33358e100db9464267c3f826b12ca07b4f0a6502578fbe5e357cfeb","schema_version":"1.0","event_id":"sha256:d6b486a4d33358e100db9464267c3f826b12ca07b4f0a6502578fbe5e357cfeb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:IKREHU44NUBWXAPHHSR62YY76X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Parthasarathy formula and a spectral triple for the quantum Lagrangian Grassmannian of rank two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.QA","authors_text":"Marco Matassa","submitted_at":"2018-10-15T15:20:48Z","abstract_excerpt":"We show that the Dolbeault--Dirac operator on the quantum Lagrangian Grassmannian of rank two, an example of a quantum irreducible flag manifold, satisfies an appropriate version of the Parthasarathy formula. We use this result to complete the proof that the candidate spectral triple for this space, as defined by Kr\\\"ahmer, is a spectral triple."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06456","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":"2026-05-17T23:51:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V2ApDdBvCjyDaM2MbavKCZwBiq2Ao1IwCZuHoWVvur0fp17FErleV/KKT4Q6rxza6Be5HUhAMPZGjRiVqLR4DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:18:37.316628Z"},"content_sha256":"a00de7a55b1acf193a6f193193bdbc163b2a1b9d08054d9c7e8d0a7b0dd0c68f","schema_version":"1.0","event_id":"sha256:a00de7a55b1acf193a6f193193bdbc163b2a1b9d08054d9c7e8d0a7b0dd0c68f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IKREHU44NUBWXAPHHSR62YY76X/bundle.json","state_url":"https://pith.science/pith/IKREHU44NUBWXAPHHSR62YY76X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IKREHU44NUBWXAPHHSR62YY76X/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":"2026-06-03T21:18:37Z","links":{"resolver":"https://pith.science/pith/IKREHU44NUBWXAPHHSR62YY76X","bundle":"https://pith.science/pith/IKREHU44NUBWXAPHHSR62YY76X/bundle.json","state":"https://pith.science/pith/IKREHU44NUBWXAPHHSR62YY76X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IKREHU44NUBWXAPHHSR62YY76X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IKREHU44NUBWXAPHHSR62YY76X","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":"7a6cb88583b26e89c497372def5634fab90b03723c1ae0d60eb93a144f5b2a9e","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-10-15T15:20:48Z","title_canon_sha256":"8291e95422e916ea0883628021110d8c53f393b7f8218acc878ae6d38d16dcd8"},"schema_version":"1.0","source":{"id":"1810.06456","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.06456","created_at":"2026-05-17T23:51:05Z"},{"alias_kind":"arxiv_version","alias_value":"1810.06456v2","created_at":"2026-05-17T23:51:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06456","created_at":"2026-05-17T23:51:05Z"},{"alias_kind":"pith_short_12","alias_value":"IKREHU44NUBW","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IKREHU44NUBWXAPH","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IKREHU44","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:a00de7a55b1acf193a6f193193bdbc163b2a1b9d08054d9c7e8d0a7b0dd0c68f","target":"graph","created_at":"2026-05-17T23:51:05Z","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 that the Dolbeault--Dirac operator on the quantum Lagrangian Grassmannian of rank two, an example of a quantum irreducible flag manifold, satisfies an appropriate version of the Parthasarathy formula. We use this result to complete the proof that the candidate spectral triple for this space, as defined by Kr\\\"ahmer, is a spectral triple.","authors_text":"Marco Matassa","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-10-15T15:20:48Z","title":"The Parthasarathy formula and a spectral triple for the quantum Lagrangian Grassmannian of rank two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06456","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:d6b486a4d33358e100db9464267c3f826b12ca07b4f0a6502578fbe5e357cfeb","target":"record","created_at":"2026-05-17T23:51:05Z","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":"7a6cb88583b26e89c497372def5634fab90b03723c1ae0d60eb93a144f5b2a9e","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-10-15T15:20:48Z","title_canon_sha256":"8291e95422e916ea0883628021110d8c53f393b7f8218acc878ae6d38d16dcd8"},"schema_version":"1.0","source":{"id":"1810.06456","kind":"arxiv","version":2}},"canonical_sha256":"42a243d39c6d036b81e73ca3ed631ff5e884d10f8ee37e90113d3e6773460c01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42a243d39c6d036b81e73ca3ed631ff5e884d10f8ee37e90113d3e6773460c01","first_computed_at":"2026-05-17T23:51:05.414096Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:05.414096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hh+kLURQZf5OsjRdaK4n8zb2a5Z/xtBDU7UpRusLXWPz/owMS6uo24nn/mhh5+YnrUSjzfATnvSeeX5ktKK2Bw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:05.414636Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.06456","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6b486a4d33358e100db9464267c3f826b12ca07b4f0a6502578fbe5e357cfeb","sha256:a00de7a55b1acf193a6f193193bdbc163b2a1b9d08054d9c7e8d0a7b0dd0c68f"],"state_sha256":"97a6d2d5826d2bc7ac6abccc649ad1d95c6af5eb82d60c509278e5dacac30640"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NA/tiHHLx9dkQ2mSyctt+OxCO0KJlgiL8QsLUCMR4UycxAWBnxI9obQFvG8sxxnP2YGT2rSsfYJ3UP3hHMdOAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T21:18:37.318611Z","bundle_sha256":"66238176a0c525fda4add9d173c576663ba22da9fa2d2587c19bf22b4d4fa823"}}