{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VTTBM2EIAMKMVGQJCNZUFTDION","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":"5a91bbcde4b046760ed63cbf2d4b56135c6d6d85a46b6df06674b35e959c017c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-10T23:46:24Z","title_canon_sha256":"38a31b39d7065530715e2ead9933f49bbe2f6dec0f33abfd92c4134dbdfc1348"},"schema_version":"1.0","source":{"id":"1809.03636","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.03636","created_at":"2026-05-18T00:02:24Z"},{"alias_kind":"arxiv_version","alias_value":"1809.03636v2","created_at":"2026-05-18T00:02:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03636","created_at":"2026-05-18T00:02:24Z"},{"alias_kind":"pith_short_12","alias_value":"VTTBM2EIAMKM","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VTTBM2EIAMKMVGQJ","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VTTBM2EI","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:5c3696413f9c081c138d8642a6a55f5f9d33aca16dbc7905db08ec8fb7e2476b","target":"graph","created_at":"2026-05-18T00:02:24Z","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 establish an integral-geometric formula for minimal two-spheres inside homogeneous three-spheres, and use it to provide a characterisation of each homogeneous metric on the three-dimensional real projective space as the unique metric with the largest possible two-systole among metrics with the same volume in its conformal class.","authors_text":"Lucas Ambrozio, Rafael Montezuma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-10T23:46:24Z","title":"On the two-systole of real projective spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03636","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:d39a3a362231f4470f0692ff323aadaedccc78b2aa088db8f2939b76d238c031","target":"record","created_at":"2026-05-18T00:02:24Z","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":"5a91bbcde4b046760ed63cbf2d4b56135c6d6d85a46b6df06674b35e959c017c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-10T23:46:24Z","title_canon_sha256":"38a31b39d7065530715e2ead9933f49bbe2f6dec0f33abfd92c4134dbdfc1348"},"schema_version":"1.0","source":{"id":"1809.03636","kind":"arxiv","version":2}},"canonical_sha256":"ace61668880314ca9a09137342cc687349503187557e7e92030c804640b4b3fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ace61668880314ca9a09137342cc687349503187557e7e92030c804640b4b3fa","first_computed_at":"2026-05-18T00:02:24.687931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:24.687931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1mZCcMOsSvwfdB2xR5etPjDG5EGP+G6GJVaNV7Lx2XsqsdgRt21XOQ7ZeXj7hFrvVzGMRpEqxILa8maxYBnWBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:24.688644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.03636","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d39a3a362231f4470f0692ff323aadaedccc78b2aa088db8f2939b76d238c031","sha256:5c3696413f9c081c138d8642a6a55f5f9d33aca16dbc7905db08ec8fb7e2476b"],"state_sha256":"a13de923314c35b8f39e66f4aa1bf808ce4f40a743b56927aac0f81a6ac1d08a"}