{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CEIVV6MKOMJWJWX2MM36ICWMFK","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":"b41ad4291250602b46f27dcd3186e3c75b58c88b6d8b5163a07afa148dbe8a15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-02T10:49:33Z","title_canon_sha256":"8244a3e9e5cc20591986d606ed45d2c611661bf47b4483c0979ef5b29e838a67"},"schema_version":"1.0","source":{"id":"2606.03472","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.03472","created_at":"2026-06-03T01:05:58Z"},{"alias_kind":"arxiv_version","alias_value":"2606.03472v1","created_at":"2026-06-03T01:05:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03472","created_at":"2026-06-03T01:05:58Z"},{"alias_kind":"pith_short_12","alias_value":"CEIVV6MKOMJW","created_at":"2026-06-03T01:05:58Z"},{"alias_kind":"pith_short_16","alias_value":"CEIVV6MKOMJWJWX2","created_at":"2026-06-03T01:05:58Z"},{"alias_kind":"pith_short_8","alias_value":"CEIVV6MK","created_at":"2026-06-03T01:05:58Z"}],"graph_snapshots":[{"event_id":"sha256:54688baf5eb0ff8cd199fa66ee3563d239a58037b835b4b7228d28251c487418","target":"graph","created_at":"2026-06-03T01:05:58Z","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/2606.03472/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $Q=-x_1^1-x_2^2-x_3^2+x_4^2$ be the standard signature $(1,3)$ quadratic form. To each non-degenerate rational plane $L$ in the four-dimensional quadratic space $(\\mathbb{Q}^4,Q)$ we can naturally attach a periodic geodesic on the Bianchi orbifold $\\mathrm{SL}_2(\\mathbb{Z}[i])\\backslash \\mathbb{H}^3$ which records the position of $L$ in the Grassmannian up to integer rotations. Moreover, each such plane $L$ defines a CM point and a periodic geodesic on the modular curve through restriction of $Q$ to $L$ and its orthogonal complement. Lastly, the local isomorphism between $\\mathrm{SO}_{1,3}","authors_text":"Andreas Wieser, Konstantin Andritsch, Menny Aka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-02T10:49:33Z","title":"Planes in quadratic 4-space and associated shapes of lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03472","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":"sha256:75443e2481cd421f9621294503d40d849c70886b4f01db5271b1945c08600157","target":"record","created_at":"2026-06-03T01:05:58Z","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":"b41ad4291250602b46f27dcd3186e3c75b58c88b6d8b5163a07afa148dbe8a15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-02T10:49:33Z","title_canon_sha256":"8244a3e9e5cc20591986d606ed45d2c611661bf47b4483c0979ef5b29e838a67"},"schema_version":"1.0","source":{"id":"2606.03472","kind":"arxiv","version":1}},"canonical_sha256":"11115af98a731364dafa6337e40acc2a96dfba586136f683a1470c7c3a835cb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11115af98a731364dafa6337e40acc2a96dfba586136f683a1470c7c3a835cb8","first_computed_at":"2026-06-03T01:05:58.773370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T01:05:58.773370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GfHGb9BghfCULnmUHZhSaokVZkQSo5pCzvd95LFHGtHbdtAtuolwn9vjeasBOAdPaER7pumRfSx+30FpQ1dXDg==","signature_status":"signed_v1","signed_at":"2026-06-03T01:05:58.773748Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.03472","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75443e2481cd421f9621294503d40d849c70886b4f01db5271b1945c08600157","sha256:54688baf5eb0ff8cd199fa66ee3563d239a58037b835b4b7228d28251c487418"],"state_sha256":"e4b1bd5aa88076dab2a309024bf7d07702ccb3faa6fa837ca9779b2ed17ca259"}