{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:QJJETIWCT43FSLF7DCDW7LVCTL","short_pith_number":"pith:QJJETIWC","schema_version":"1.0","canonical_sha256":"825249a2c29f36592cbf18876faea29af53c64846219a50bcfe6d8eff3d03a05","source":{"kind":"arxiv","id":"1612.08765","version":1},"attestation_state":"computed","paper":{"title":"Intersections of diagonal orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Omri N. Solan","submitted_at":"2016-12-27T22:28:23Z","abstract_excerpt":"Let $A\\subseteq SL_n(\\mathbb{R})$ group of diagonal matrices with positive diagonal, let ${\\rm ST}_n\\subseteq X_n:=SL_n(\\mathbb{R})/SL_n(\\mathbb{Z})$ be the set of stable lattices, and let ${\\rm WR}_n\\subseteq X_n$ be the set of well-rounded lattices. We prove that any $A$-orbit in $X_n$ intersects both ${\\rm ST}_n$ and ${\\rm WR}_n$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1612.08765","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-27T22:28:23Z","cross_cats_sorted":[],"title_canon_sha256":"e20527345675f03bfaf88042ec0367666def3e935a3fa710d887fe8efb292c4c","abstract_canon_sha256":"6a034b0ae2b0fa64ad9c41667f71dc3402214826789e84797a67e56a85059c20"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:47.211458Z","signature_b64":"6zUqxgwCP26aIh2eMwY6XN2US2VCJqGztCLuraHPRPaubUuuVcVctQQpudqfeZQAu/B31bQFxXxOcEZZiH4zDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"825249a2c29f36592cbf18876faea29af53c64846219a50bcfe6d8eff3d03a05","last_reissued_at":"2026-05-18T00:53:47.210973Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:47.210973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intersections of diagonal orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Omri N. Solan","submitted_at":"2016-12-27T22:28:23Z","abstract_excerpt":"Let $A\\subseteq SL_n(\\mathbb{R})$ group of diagonal matrices with positive diagonal, let ${\\rm ST}_n\\subseteq X_n:=SL_n(\\mathbb{R})/SL_n(\\mathbb{Z})$ be the set of stable lattices, and let ${\\rm WR}_n\\subseteq X_n$ be the set of well-rounded lattices. We prove that any $A$-orbit in $X_n$ intersects both ${\\rm ST}_n$ and ${\\rm WR}_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08765","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1612.08765","created_at":"2026-05-18T00:53:47.211062+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.08765v1","created_at":"2026-05-18T00:53:47.211062+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08765","created_at":"2026-05-18T00:53:47.211062+00:00"},{"alias_kind":"pith_short_12","alias_value":"QJJETIWCT43F","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"QJJETIWCT43FSLF7","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"QJJETIWC","created_at":"2026-05-18T12:30:39.010887+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QJJETIWCT43FSLF7DCDW7LVCTL","json":"https://pith.science/pith/QJJETIWCT43FSLF7DCDW7LVCTL.json","graph_json":"https://pith.science/api/pith-number/QJJETIWCT43FSLF7DCDW7LVCTL/graph.json","events_json":"https://pith.science/api/pith-number/QJJETIWCT43FSLF7DCDW7LVCTL/events.json","paper":"https://pith.science/paper/QJJETIWC"},"agent_actions":{"view_html":"https://pith.science/pith/QJJETIWCT43FSLF7DCDW7LVCTL","download_json":"https://pith.science/pith/QJJETIWCT43FSLF7DCDW7LVCTL.json","view_paper":"https://pith.science/paper/QJJETIWC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.08765&json=true","fetch_graph":"https://pith.science/api/pith-number/QJJETIWCT43FSLF7DCDW7LVCTL/graph.json","fetch_events":"https://pith.science/api/pith-number/QJJETIWCT43FSLF7DCDW7LVCTL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QJJETIWCT43FSLF7DCDW7LVCTL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QJJETIWCT43FSLF7DCDW7LVCTL/action/storage_attestation","attest_author":"https://pith.science/pith/QJJETIWCT43FSLF7DCDW7LVCTL/action/author_attestation","sign_citation":"https://pith.science/pith/QJJETIWCT43FSLF7DCDW7LVCTL/action/citation_signature","submit_replication":"https://pith.science/pith/QJJETIWCT43FSLF7DCDW7LVCTL/action/replication_record"}},"created_at":"2026-05-18T00:53:47.211062+00:00","updated_at":"2026-05-18T00:53:47.211062+00:00"}