{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:HWVMXFDSTFYA6IJP4MQMQBOJNW","short_pith_number":"pith:HWVMXFDS","schema_version":"1.0","canonical_sha256":"3daacb947299700f212fe320c805c96db59eeb96eea8cc278b8e9b4733dbbe9e","source":{"kind":"arxiv","id":"1201.2958","version":1},"attestation_state":"computed","paper":{"title":"Enumerating Invariant Subspaces of ${\\mathbb R}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Josh Ide, Lenny Jones","submitted_at":"2012-01-13T21:33:16Z","abstract_excerpt":"In this article, we develop an algorithm to calculate the set of all integers $m$ for which there exists a linear operator $T$ on ${\\mathbb R}^n$ such that ${\\mathbb R}^n$ has exactly $m$ $T$-invariant subspaces. A brief discussion is included as how these methods might be extended to vector spaces over arbitrary fields."},"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":"1201.2958","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-01-13T21:33:16Z","cross_cats_sorted":[],"title_canon_sha256":"ba2949bfc7ed738684af30de6973bbf06427ab37b1d5810fb5ae3fd48205015f","abstract_canon_sha256":"55758810b7468f0349700466ba2208a8be541446111b77c67817323e0147256c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:32.673831Z","signature_b64":"nhLmuvdbyVZV9WM/YeofgGr1GVQ+P6B70vAhHfBfdig9GM/H5nzEeYjUWMh1mUyi9Q35BOhQuRzFjaumZm7lCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3daacb947299700f212fe320c805c96db59eeb96eea8cc278b8e9b4733dbbe9e","last_reissued_at":"2026-05-18T04:04:32.673084Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:32.673084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Enumerating Invariant Subspaces of ${\\mathbb R}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Josh Ide, Lenny Jones","submitted_at":"2012-01-13T21:33:16Z","abstract_excerpt":"In this article, we develop an algorithm to calculate the set of all integers $m$ for which there exists a linear operator $T$ on ${\\mathbb R}^n$ such that ${\\mathbb R}^n$ has exactly $m$ $T$-invariant subspaces. A brief discussion is included as how these methods might be extended to vector spaces over arbitrary fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2958","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":"1201.2958","created_at":"2026-05-18T04:04:32.673205+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.2958v1","created_at":"2026-05-18T04:04:32.673205+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2958","created_at":"2026-05-18T04:04:32.673205+00:00"},{"alias_kind":"pith_short_12","alias_value":"HWVMXFDSTFYA","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"HWVMXFDSTFYA6IJP","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"HWVMXFDS","created_at":"2026-05-18T12:27:09.501522+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/HWVMXFDSTFYA6IJP4MQMQBOJNW","json":"https://pith.science/pith/HWVMXFDSTFYA6IJP4MQMQBOJNW.json","graph_json":"https://pith.science/api/pith-number/HWVMXFDSTFYA6IJP4MQMQBOJNW/graph.json","events_json":"https://pith.science/api/pith-number/HWVMXFDSTFYA6IJP4MQMQBOJNW/events.json","paper":"https://pith.science/paper/HWVMXFDS"},"agent_actions":{"view_html":"https://pith.science/pith/HWVMXFDSTFYA6IJP4MQMQBOJNW","download_json":"https://pith.science/pith/HWVMXFDSTFYA6IJP4MQMQBOJNW.json","view_paper":"https://pith.science/paper/HWVMXFDS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.2958&json=true","fetch_graph":"https://pith.science/api/pith-number/HWVMXFDSTFYA6IJP4MQMQBOJNW/graph.json","fetch_events":"https://pith.science/api/pith-number/HWVMXFDSTFYA6IJP4MQMQBOJNW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HWVMXFDSTFYA6IJP4MQMQBOJNW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HWVMXFDSTFYA6IJP4MQMQBOJNW/action/storage_attestation","attest_author":"https://pith.science/pith/HWVMXFDSTFYA6IJP4MQMQBOJNW/action/author_attestation","sign_citation":"https://pith.science/pith/HWVMXFDSTFYA6IJP4MQMQBOJNW/action/citation_signature","submit_replication":"https://pith.science/pith/HWVMXFDSTFYA6IJP4MQMQBOJNW/action/replication_record"}},"created_at":"2026-05-18T04:04:32.673205+00:00","updated_at":"2026-05-18T04:04:32.673205+00:00"}