{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:M236KB2UGWOVBE4OKFYV7BILWV","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":"5bc88ce7e117616e1f5cb58e5eacd69d191b6cd381021e99120a4c5a58c98edb","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-05-27T19:07:33Z","title_canon_sha256":"d085fdabb519ce57fbfff5a0c93582cbb2eec5b783c447e159425fe3b46f1cfe"},"schema_version":"1.0","source":{"id":"1905.11454","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.11454","created_at":"2026-05-17T23:44:53Z"},{"alias_kind":"arxiv_version","alias_value":"1905.11454v1","created_at":"2026-05-17T23:44:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.11454","created_at":"2026-05-17T23:44:53Z"},{"alias_kind":"pith_short_12","alias_value":"M236KB2UGWOV","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"M236KB2UGWOVBE4O","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"M236KB2U","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:87370140f62ab01affb2f6d3d4aae00b9dc062e283d3cac2f2b2452eb870664f","target":"graph","created_at":"2026-05-17T23:44:53Z","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":"Inspired by the role geometric structures play in our understanding of surfaces and three-manifolds, and Berger's observation that a surface of constant sectional curvature is determined up to local isometry by its Laplace spectrum, we explore the extent to which compact locally homogeneous three-manifolds are characterized up to local isometry by their spectra. We observe that there are eight `metrically maximal' three-dimensional geometries on which all compact locally homogeneous three-manifolds are modeled and we demonstrate that for five of these geometries the associated compact locally ","authors_text":"Benjamin Schmidt, Craig Sutton, Samuel Lin","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-05-27T19:07:33Z","title":"Geometric structures and the Laplace spectrum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.11454","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:ffb28eebec7cba9f17710acecd36bd45586cb626d58ea95029a646274502aaf3","target":"record","created_at":"2026-05-17T23:44:53Z","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":"5bc88ce7e117616e1f5cb58e5eacd69d191b6cd381021e99120a4c5a58c98edb","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-05-27T19:07:33Z","title_canon_sha256":"d085fdabb519ce57fbfff5a0c93582cbb2eec5b783c447e159425fe3b46f1cfe"},"schema_version":"1.0","source":{"id":"1905.11454","kind":"arxiv","version":1}},"canonical_sha256":"66b7e50754359d50938e51715f850bb54b24cf055962a7dea9b18643117afca7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66b7e50754359d50938e51715f850bb54b24cf055962a7dea9b18643117afca7","first_computed_at":"2026-05-17T23:44:53.354105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:53.354105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W0ZuI0TrZhzu45GI0/KVjru29Una/HTmE4PM2wmyB9+VI7RC23cqF/hz0gpQqrRZSnfbJ77dkL5ltBnWSJI1Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:53.354643Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.11454","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffb28eebec7cba9f17710acecd36bd45586cb626d58ea95029a646274502aaf3","sha256:87370140f62ab01affb2f6d3d4aae00b9dc062e283d3cac2f2b2452eb870664f"],"state_sha256":"cb79ed757f8db2b8c819687285596d4a4c9e0009cac41a95441b30888f532d2f"}