{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HWVMXFDSTFYA6IJP4MQMQBOJNW","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":"55758810b7468f0349700466ba2208a8be541446111b77c67817323e0147256c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-01-13T21:33:16Z","title_canon_sha256":"ba2949bfc7ed738684af30de6973bbf06427ab37b1d5810fb5ae3fd48205015f"},"schema_version":"1.0","source":{"id":"1201.2958","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.2958","created_at":"2026-05-18T04:04:32Z"},{"alias_kind":"arxiv_version","alias_value":"1201.2958v1","created_at":"2026-05-18T04:04:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2958","created_at":"2026-05-18T04:04:32Z"},{"alias_kind":"pith_short_12","alias_value":"HWVMXFDSTFYA","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HWVMXFDSTFYA6IJP","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HWVMXFDS","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:fcae2fbe624e6b0aa13e1a8259fb75e3ff8f0d8b33c81152912d17c43b5650eb","target":"graph","created_at":"2026-05-18T04:04:32Z","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"},"paper":{"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.","authors_text":"Josh Ide, Lenny Jones","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-01-13T21:33:16Z","title":"Enumerating Invariant Subspaces of ${\\mathbb R}^n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2958","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:d18f64259cde5ca6078d2f2c30f319e757d4583f88b0a6063bf015b84166072a","target":"record","created_at":"2026-05-18T04:04:32Z","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":"55758810b7468f0349700466ba2208a8be541446111b77c67817323e0147256c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-01-13T21:33:16Z","title_canon_sha256":"ba2949bfc7ed738684af30de6973bbf06427ab37b1d5810fb5ae3fd48205015f"},"schema_version":"1.0","source":{"id":"1201.2958","kind":"arxiv","version":1}},"canonical_sha256":"3daacb947299700f212fe320c805c96db59eeb96eea8cc278b8e9b4733dbbe9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3daacb947299700f212fe320c805c96db59eeb96eea8cc278b8e9b4733dbbe9e","first_computed_at":"2026-05-18T04:04:32.673084Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:32.673084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nhLmuvdbyVZV9WM/YeofgGr1GVQ+P6B70vAhHfBfdig9GM/H5nzEeYjUWMh1mUyi9Q35BOhQuRzFjaumZm7lCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:32.673831Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.2958","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d18f64259cde5ca6078d2f2c30f319e757d4583f88b0a6063bf015b84166072a","sha256:fcae2fbe624e6b0aa13e1a8259fb75e3ff8f0d8b33c81152912d17c43b5650eb"],"state_sha256":"5ce634890c56009490fb7ea0b0848717c680c3483defc8970a3f3eab79fdcb85"}