{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FODJFSKMJUB5OTNTEAUYEOHFIH","short_pith_number":"pith:FODJFSKM","schema_version":"1.0","canonical_sha256":"2b8692c94c4d03d74db320298238e541d485ee7deeda7b8f2debd109ef065e48","source":{"kind":"arxiv","id":"1609.09042","version":1},"attestation_state":"computed","paper":{"title":"Operations on Arc Diagrams and Degenerations for Invariant Subspaces of Linear Operators. Part II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Justyna Kosakowska, Mariusz Kaniecki, Markus Schmidmeier","submitted_at":"2016-09-28T19:06:36Z","abstract_excerpt":"For a partition $\\beta$, denote by $N_\\beta$ the nilpotent linear operator of Jordan type $\\beta$. Given partitions $\\beta$, $\\gamma$, we investigate the representation space ${}_2{\\mathbb V}_{\\gamma}^\\beta$ of all short exact sequences $$ \\mathcal E: 0\\to N_\\alpha \\to N_\\beta \\to N_\\gamma \\to 0$$ where $\\alpha$ is any partition with each part at most 2. Due to the condition on $\\alpha$, the isomorphism type of a sequence $\\mathcal E$ is given by an arc diagram $\\Delta$; denote by ${\\mathbb V}_\\Delta$ the subset of ${}_2{\\mathbb V}_{\\gamma}^\\beta$ of all sequences isomorphic to $\\mathcal E$.\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":"1609.09042","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-09-28T19:06:36Z","cross_cats_sorted":[],"title_canon_sha256":"f574716100add8e0dc7caed21fab8095ece774e65fc92c9a5008225d8092a4ee","abstract_canon_sha256":"56fb6060dfaf069f3cdca9cdc497c9611d3c6b40f5aac6d4863e497be1ca372e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:14.454177Z","signature_b64":"wA6quCjfSD+VyaYDL/RRJuuWHMYYJF0F8E+kzVr190MNMc4n6/ghvcBymJIbKOUALo5fR+PuOCpsaMf+kzVAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b8692c94c4d03d74db320298238e541d485ee7deeda7b8f2debd109ef065e48","last_reissued_at":"2026-05-17T23:42:14.453526Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:14.453526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Operations on Arc Diagrams and Degenerations for Invariant Subspaces of Linear Operators. Part II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Justyna Kosakowska, Mariusz Kaniecki, Markus Schmidmeier","submitted_at":"2016-09-28T19:06:36Z","abstract_excerpt":"For a partition $\\beta$, denote by $N_\\beta$ the nilpotent linear operator of Jordan type $\\beta$. Given partitions $\\beta$, $\\gamma$, we investigate the representation space ${}_2{\\mathbb V}_{\\gamma}^\\beta$ of all short exact sequences $$ \\mathcal E: 0\\to N_\\alpha \\to N_\\beta \\to N_\\gamma \\to 0$$ where $\\alpha$ is any partition with each part at most 2. Due to the condition on $\\alpha$, the isomorphism type of a sequence $\\mathcal E$ is given by an arc diagram $\\Delta$; denote by ${\\mathbb V}_\\Delta$ the subset of ${}_2{\\mathbb V}_{\\gamma}^\\beta$ of all sequences isomorphic to $\\mathcal E$.\n "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09042","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":"1609.09042","created_at":"2026-05-17T23:42:14.453625+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.09042v1","created_at":"2026-05-17T23:42:14.453625+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.09042","created_at":"2026-05-17T23:42:14.453625+00:00"},{"alias_kind":"pith_short_12","alias_value":"FODJFSKMJUB5","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FODJFSKMJUB5OTNT","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FODJFSKM","created_at":"2026-05-18T12:30:15.759754+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/FODJFSKMJUB5OTNTEAUYEOHFIH","json":"https://pith.science/pith/FODJFSKMJUB5OTNTEAUYEOHFIH.json","graph_json":"https://pith.science/api/pith-number/FODJFSKMJUB5OTNTEAUYEOHFIH/graph.json","events_json":"https://pith.science/api/pith-number/FODJFSKMJUB5OTNTEAUYEOHFIH/events.json","paper":"https://pith.science/paper/FODJFSKM"},"agent_actions":{"view_html":"https://pith.science/pith/FODJFSKMJUB5OTNTEAUYEOHFIH","download_json":"https://pith.science/pith/FODJFSKMJUB5OTNTEAUYEOHFIH.json","view_paper":"https://pith.science/paper/FODJFSKM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.09042&json=true","fetch_graph":"https://pith.science/api/pith-number/FODJFSKMJUB5OTNTEAUYEOHFIH/graph.json","fetch_events":"https://pith.science/api/pith-number/FODJFSKMJUB5OTNTEAUYEOHFIH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FODJFSKMJUB5OTNTEAUYEOHFIH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FODJFSKMJUB5OTNTEAUYEOHFIH/action/storage_attestation","attest_author":"https://pith.science/pith/FODJFSKMJUB5OTNTEAUYEOHFIH/action/author_attestation","sign_citation":"https://pith.science/pith/FODJFSKMJUB5OTNTEAUYEOHFIH/action/citation_signature","submit_replication":"https://pith.science/pith/FODJFSKMJUB5OTNTEAUYEOHFIH/action/replication_record"}},"created_at":"2026-05-17T23:42:14.453625+00:00","updated_at":"2026-05-17T23:42:14.453625+00:00"}