{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:MZRMUAAJ4QSTY4BVFZF2TRCN2M","short_pith_number":"pith:MZRMUAAJ","schema_version":"1.0","canonical_sha256":"6662ca0009e4253c70352e4ba9c44dd334fe0de0a68b26e7435da9ce909fa0df","source":{"kind":"arxiv","id":"1009.2644","version":1},"attestation_state":"computed","paper":{"title":"A complete locally convex space of countable dimension admitting an operator with no invariant subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Stanislav Shkarin","submitted_at":"2010-09-14T12:55:42Z","abstract_excerpt":"We construct a complete locally convex topological vector space $X$ of countable algebraic dimension and a continuous linear operator $T:X\\to X$ such that $T$ has no non-trivial closed invariant subspaces."},"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":"1009.2644","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-14T12:55:42Z","cross_cats_sorted":[],"title_canon_sha256":"2a7055626472bc529d23667b58a62223d402d74aa34fa8f21ed1ab3d683b20bb","abstract_canon_sha256":"70d80904276418fe6e09dc6e9e95cbb47d53b8702ba8eb7d2b4a4b7e1d79e6b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:56.654807Z","signature_b64":"mAjhDCw9SgysMAkn2GQpbAZduvckggqgcE9rCasCw9SLYzqyLUZQTdM4S2m96HEG+84wCBPwoRaPBjM+5xf1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6662ca0009e4253c70352e4ba9c44dd334fe0de0a68b26e7435da9ce909fa0df","last_reissued_at":"2026-05-18T04:40:56.654176Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:56.654176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A complete locally convex space of countable dimension admitting an operator with no invariant subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Stanislav Shkarin","submitted_at":"2010-09-14T12:55:42Z","abstract_excerpt":"We construct a complete locally convex topological vector space $X$ of countable algebraic dimension and a continuous linear operator $T:X\\to X$ such that $T$ has no non-trivial closed invariant subspaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2644","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":"1009.2644","created_at":"2026-05-18T04:40:56.654261+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.2644v1","created_at":"2026-05-18T04:40:56.654261+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2644","created_at":"2026-05-18T04:40:56.654261+00:00"},{"alias_kind":"pith_short_12","alias_value":"MZRMUAAJ4QST","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"MZRMUAAJ4QSTY4BV","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"MZRMUAAJ","created_at":"2026-05-18T12:26:10.704358+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/MZRMUAAJ4QSTY4BVFZF2TRCN2M","json":"https://pith.science/pith/MZRMUAAJ4QSTY4BVFZF2TRCN2M.json","graph_json":"https://pith.science/api/pith-number/MZRMUAAJ4QSTY4BVFZF2TRCN2M/graph.json","events_json":"https://pith.science/api/pith-number/MZRMUAAJ4QSTY4BVFZF2TRCN2M/events.json","paper":"https://pith.science/paper/MZRMUAAJ"},"agent_actions":{"view_html":"https://pith.science/pith/MZRMUAAJ4QSTY4BVFZF2TRCN2M","download_json":"https://pith.science/pith/MZRMUAAJ4QSTY4BVFZF2TRCN2M.json","view_paper":"https://pith.science/paper/MZRMUAAJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.2644&json=true","fetch_graph":"https://pith.science/api/pith-number/MZRMUAAJ4QSTY4BVFZF2TRCN2M/graph.json","fetch_events":"https://pith.science/api/pith-number/MZRMUAAJ4QSTY4BVFZF2TRCN2M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MZRMUAAJ4QSTY4BVFZF2TRCN2M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MZRMUAAJ4QSTY4BVFZF2TRCN2M/action/storage_attestation","attest_author":"https://pith.science/pith/MZRMUAAJ4QSTY4BVFZF2TRCN2M/action/author_attestation","sign_citation":"https://pith.science/pith/MZRMUAAJ4QSTY4BVFZF2TRCN2M/action/citation_signature","submit_replication":"https://pith.science/pith/MZRMUAAJ4QSTY4BVFZF2TRCN2M/action/replication_record"}},"created_at":"2026-05-18T04:40:56.654261+00:00","updated_at":"2026-05-18T04:40:56.654261+00:00"}