{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:L6AOFHUZU2EJXJZS7FF4SWL4Z4","short_pith_number":"pith:L6AOFHUZ","schema_version":"1.0","canonical_sha256":"5f80e29e99a6889ba732f94bc9597ccf13f90e59a811520f5c90871c50f32837","source":{"kind":"arxiv","id":"1512.01007","version":2},"attestation_state":"computed","paper":{"title":"Orthogonal apartments in Hilbert Grassmannians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mark Pankov","submitted_at":"2015-12-03T09:31:04Z","abstract_excerpt":"Let $H$ be an infinite-dimensional complex Hilbert space and let ${\\mathcal L}(H)$ be the logic formed by all closed subspaces of $H$. For every natural $k$ we denote by ${\\mathcal G}_{k}(H)$ the Grassmannian consisting of $k$-dimensional subspaces. An orthogonal apartment of ${\\mathcal G}_{k}(H)$ is the set consisting of all $k$-dimensional subspaces spanned by subsets of a certain orthogonal base of $H$. Orthogonal apartments can be characterized as maximal sets of mutually compatible elements of ${\\mathcal G}_{k}(H)$. We show that every bijective transformation $f$ of ${\\mathcal G}_{k}(H)$ "},"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":"1512.01007","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-03T09:31:04Z","cross_cats_sorted":[],"title_canon_sha256":"6f8747bf4c11b32a5bcc57c8ad01f902fa22de09fcc4dc0a01786ff34caa181c","abstract_canon_sha256":"d695b1370b474b2095c85e99840573a0419d017a92ccb60e7cc811178c4b1700"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:14.069885Z","signature_b64":"fXGZVUKTbJLzDn7Udk1CTxDaPVMBTzvjm5C6NvMw3ViFoknsjiUqd3bdRPUwSJ9gUTL4Z1QoLdJokrFJe61mAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f80e29e99a6889ba732f94bc9597ccf13f90e59a811520f5c90871c50f32837","last_reissued_at":"2026-05-18T01:24:14.069225Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:14.069225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orthogonal apartments in Hilbert Grassmannians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mark Pankov","submitted_at":"2015-12-03T09:31:04Z","abstract_excerpt":"Let $H$ be an infinite-dimensional complex Hilbert space and let ${\\mathcal L}(H)$ be the logic formed by all closed subspaces of $H$. For every natural $k$ we denote by ${\\mathcal G}_{k}(H)$ the Grassmannian consisting of $k$-dimensional subspaces. An orthogonal apartment of ${\\mathcal G}_{k}(H)$ is the set consisting of all $k$-dimensional subspaces spanned by subsets of a certain orthogonal base of $H$. Orthogonal apartments can be characterized as maximal sets of mutually compatible elements of ${\\mathcal G}_{k}(H)$. We show that every bijective transformation $f$ of ${\\mathcal G}_{k}(H)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01007","kind":"arxiv","version":2},"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":"1512.01007","created_at":"2026-05-18T01:24:14.069330+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.01007v2","created_at":"2026-05-18T01:24:14.069330+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01007","created_at":"2026-05-18T01:24:14.069330+00:00"},{"alias_kind":"pith_short_12","alias_value":"L6AOFHUZU2EJ","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"L6AOFHUZU2EJXJZS","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"L6AOFHUZ","created_at":"2026-05-18T12:29:29.992203+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/L6AOFHUZU2EJXJZS7FF4SWL4Z4","json":"https://pith.science/pith/L6AOFHUZU2EJXJZS7FF4SWL4Z4.json","graph_json":"https://pith.science/api/pith-number/L6AOFHUZU2EJXJZS7FF4SWL4Z4/graph.json","events_json":"https://pith.science/api/pith-number/L6AOFHUZU2EJXJZS7FF4SWL4Z4/events.json","paper":"https://pith.science/paper/L6AOFHUZ"},"agent_actions":{"view_html":"https://pith.science/pith/L6AOFHUZU2EJXJZS7FF4SWL4Z4","download_json":"https://pith.science/pith/L6AOFHUZU2EJXJZS7FF4SWL4Z4.json","view_paper":"https://pith.science/paper/L6AOFHUZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.01007&json=true","fetch_graph":"https://pith.science/api/pith-number/L6AOFHUZU2EJXJZS7FF4SWL4Z4/graph.json","fetch_events":"https://pith.science/api/pith-number/L6AOFHUZU2EJXJZS7FF4SWL4Z4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L6AOFHUZU2EJXJZS7FF4SWL4Z4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L6AOFHUZU2EJXJZS7FF4SWL4Z4/action/storage_attestation","attest_author":"https://pith.science/pith/L6AOFHUZU2EJXJZS7FF4SWL4Z4/action/author_attestation","sign_citation":"https://pith.science/pith/L6AOFHUZU2EJXJZS7FF4SWL4Z4/action/citation_signature","submit_replication":"https://pith.science/pith/L6AOFHUZU2EJXJZS7FF4SWL4Z4/action/replication_record"}},"created_at":"2026-05-18T01:24:14.069330+00:00","updated_at":"2026-05-18T01:24:14.069330+00:00"}