{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:JO5FTA5YIGKWQQF67LUUJXHC2K","short_pith_number":"pith:JO5FTA5Y","canonical_record":{"source":{"id":"2605.27585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-26T18:54:17Z","cross_cats_sorted":[],"title_canon_sha256":"eaff0f0be53ec8923531faef29b8e0c4035975f2f52ed26e690ad4d60728e869","abstract_canon_sha256":"f883d65619275b420616ffa2d550e88d900eb84e74ff5b7a59a9c6ec7905b5c5"},"schema_version":"1.0"},"canonical_sha256":"4bba5983b841956840befae944dce2d29aefcf4a12d8b1eea0572c31f2306862","source":{"kind":"arxiv","id":"2605.27585","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27585","created_at":"2026-05-28T01:04:16Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27585v1","created_at":"2026-05-28T01:04:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27585","created_at":"2026-05-28T01:04:16Z"},{"alias_kind":"pith_short_12","alias_value":"JO5FTA5YIGKW","created_at":"2026-05-28T01:04:16Z"},{"alias_kind":"pith_short_16","alias_value":"JO5FTA5YIGKWQQF6","created_at":"2026-05-28T01:04:16Z"},{"alias_kind":"pith_short_8","alias_value":"JO5FTA5Y","created_at":"2026-05-28T01:04:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:JO5FTA5YIGKWQQF67LUUJXHC2K","target":"record","payload":{"canonical_record":{"source":{"id":"2605.27585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-26T18:54:17Z","cross_cats_sorted":[],"title_canon_sha256":"eaff0f0be53ec8923531faef29b8e0c4035975f2f52ed26e690ad4d60728e869","abstract_canon_sha256":"f883d65619275b420616ffa2d550e88d900eb84e74ff5b7a59a9c6ec7905b5c5"},"schema_version":"1.0"},"canonical_sha256":"4bba5983b841956840befae944dce2d29aefcf4a12d8b1eea0572c31f2306862","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T01:04:16.971336Z","signature_b64":"O/nCk+ijRq8eZZu9FBHOMiMRfwOpTY8YvI1KvKRqJYFJ5GOceSbSMncomd6ZqoFRl858oukadiTitWj0x7muDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bba5983b841956840befae944dce2d29aefcf4a12d8b1eea0572c31f2306862","last_reissued_at":"2026-05-28T01:04:16.970919Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T01:04:16.970919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.27585","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":"2026-05-28T01:04:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yfY0d7GKfJzhy5kyJbeZGHeW79s+v6A9vIWWv8y68CuExenVbfppqYDzj257ouzSntH0ftKCDNba4sT0RMJtBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T04:09:59.102962Z"},"content_sha256":"b509e10f660203ea5fc6e328d19ec7fb0eeb3bd48ada85a0435bc6d06294371b","schema_version":"1.0","event_id":"sha256:b509e10f660203ea5fc6e328d19ec7fb0eeb3bd48ada85a0435bc6d06294371b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:JO5FTA5YIGKWQQF67LUUJXHC2K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The index of symmetry and homogeneous fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alberto Rodr\\'iguez-V\\'azquez, \\'Angel Cidre-D\\'iaz, Carlos E. Olmos","submitted_at":"2026-05-26T18:54:17Z","abstract_excerpt":"We develop new tools to compute the index of symmetry in the context of homogeneous fibrations. As a consequence of our results, we determine the index of symmetry of every homogeneous space diffeomorphic to a compact rank-one symmetric space, and of every homogeneous $S^1$-bundle over a compact irreducible symmetric space. Moreover, we construct irreducible homogeneous metrics whose leaves of symmetry are symmetric spaces of arbitrarily large rank."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27585","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/2605.27585/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":"2026-05-28T01:04:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ktJRt4TEMZcHltCuC1Ey+2A77Lx83J5Ss3L3VMpQpI0DUAqt6PILHZkhuC8JB2MTBUJbvJiXejY2jPPbEkp9Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T04:09:59.103832Z"},"content_sha256":"71385bd9e0b3cdcee403935cb164516e46045b0ff40393dfd8772de0897c7733","schema_version":"1.0","event_id":"sha256:71385bd9e0b3cdcee403935cb164516e46045b0ff40393dfd8772de0897c7733"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JO5FTA5YIGKWQQF67LUUJXHC2K/bundle.json","state_url":"https://pith.science/pith/JO5FTA5YIGKWQQF67LUUJXHC2K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JO5FTA5YIGKWQQF67LUUJXHC2K/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":"2026-06-10T04:09:59Z","links":{"resolver":"https://pith.science/pith/JO5FTA5YIGKWQQF67LUUJXHC2K","bundle":"https://pith.science/pith/JO5FTA5YIGKWQQF67LUUJXHC2K/bundle.json","state":"https://pith.science/pith/JO5FTA5YIGKWQQF67LUUJXHC2K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JO5FTA5YIGKWQQF67LUUJXHC2K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JO5FTA5YIGKWQQF67LUUJXHC2K","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":"f883d65619275b420616ffa2d550e88d900eb84e74ff5b7a59a9c6ec7905b5c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-26T18:54:17Z","title_canon_sha256":"eaff0f0be53ec8923531faef29b8e0c4035975f2f52ed26e690ad4d60728e869"},"schema_version":"1.0","source":{"id":"2605.27585","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27585","created_at":"2026-05-28T01:04:16Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27585v1","created_at":"2026-05-28T01:04:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27585","created_at":"2026-05-28T01:04:16Z"},{"alias_kind":"pith_short_12","alias_value":"JO5FTA5YIGKW","created_at":"2026-05-28T01:04:16Z"},{"alias_kind":"pith_short_16","alias_value":"JO5FTA5YIGKWQQF6","created_at":"2026-05-28T01:04:16Z"},{"alias_kind":"pith_short_8","alias_value":"JO5FTA5Y","created_at":"2026-05-28T01:04:16Z"}],"graph_snapshots":[{"event_id":"sha256:71385bd9e0b3cdcee403935cb164516e46045b0ff40393dfd8772de0897c7733","target":"graph","created_at":"2026-05-28T01:04:16Z","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/2605.27585/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop new tools to compute the index of symmetry in the context of homogeneous fibrations. As a consequence of our results, we determine the index of symmetry of every homogeneous space diffeomorphic to a compact rank-one symmetric space, and of every homogeneous $S^1$-bundle over a compact irreducible symmetric space. Moreover, we construct irreducible homogeneous metrics whose leaves of symmetry are symmetric spaces of arbitrarily large rank.","authors_text":"Alberto Rodr\\'iguez-V\\'azquez, \\'Angel Cidre-D\\'iaz, Carlos E. Olmos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-26T18:54:17Z","title":"The index of symmetry and homogeneous fibrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27585","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:b509e10f660203ea5fc6e328d19ec7fb0eeb3bd48ada85a0435bc6d06294371b","target":"record","created_at":"2026-05-28T01:04:16Z","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":"f883d65619275b420616ffa2d550e88d900eb84e74ff5b7a59a9c6ec7905b5c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-26T18:54:17Z","title_canon_sha256":"eaff0f0be53ec8923531faef29b8e0c4035975f2f52ed26e690ad4d60728e869"},"schema_version":"1.0","source":{"id":"2605.27585","kind":"arxiv","version":1}},"canonical_sha256":"4bba5983b841956840befae944dce2d29aefcf4a12d8b1eea0572c31f2306862","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bba5983b841956840befae944dce2d29aefcf4a12d8b1eea0572c31f2306862","first_computed_at":"2026-05-28T01:04:16.970919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T01:04:16.970919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O/nCk+ijRq8eZZu9FBHOMiMRfwOpTY8YvI1KvKRqJYFJ5GOceSbSMncomd6ZqoFRl858oukadiTitWj0x7muDQ==","signature_status":"signed_v1","signed_at":"2026-05-28T01:04:16.971336Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.27585","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b509e10f660203ea5fc6e328d19ec7fb0eeb3bd48ada85a0435bc6d06294371b","sha256:71385bd9e0b3cdcee403935cb164516e46045b0ff40393dfd8772de0897c7733"],"state_sha256":"cf36cb1f2dad378c445d336ce8c60f6597f5d8509a1e7a144ad4aa043a9001c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oFoD4FT3d4EYQTr3gilxw9QfKxIigEl3Dg+wmkNFPmau6ygGJb+Sbv/EF957JcM11njs323k8Xtkkbhg4uTjCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T04:09:59.108678Z","bundle_sha256":"814a28ad51a8c77d9cff0ed2b33a8b26895c0a63f757bba9385783dfecd82b57"}}