{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:2RL34MQW45GPBDBWFSRCCV6XRQ","short_pith_number":"pith:2RL34MQW","schema_version":"1.0","canonical_sha256":"d457be3216e74cf08c362ca22157d78c362ac204e3e2c15769819dc5557cae75","source":{"kind":"arxiv","id":"1101.5012","version":1},"attestation_state":"computed","paper":{"title":"Invariant theory of foliations of the projective plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Eduardo Esteves, Marina Marchisio","submitted_at":"2011-01-26T09:34:57Z","abstract_excerpt":"We study the invariant theory of singular foliations of the projective plane. Our first main result is that a foliation of degree m>1 is not stable only if it has singularities in dimension 1 or contains an isolated singular point with multiplicity at least (m^2-1)/(2m+1). Our second main result is the construction of an invariant map from the space of foliations of degree m to that of curves of degree m^2+m-2. We describe this map explicitly in case m=2."},"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":"1101.5012","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-26T09:34:57Z","cross_cats_sorted":[],"title_canon_sha256":"dad0de85d579a5da3b17de85be5fe0ac2cb9af969d6651718feacecfadc2770a","abstract_canon_sha256":"27c588c1931788d970292f8303bdc1463a71e7c587dadb47952052e1d6934aea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:47.010686Z","signature_b64":"uatqWVzAcyGrvSLNOl0Mj7ozH6GAVr8vEzxFfq//uhbw/adS4pZjMmbuSitdaq12m24HmVYikz6fyVGgA2jDCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d457be3216e74cf08c362ca22157d78c362ac204e3e2c15769819dc5557cae75","last_reissued_at":"2026-05-18T04:30:47.010040Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:47.010040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariant theory of foliations of the projective plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Eduardo Esteves, Marina Marchisio","submitted_at":"2011-01-26T09:34:57Z","abstract_excerpt":"We study the invariant theory of singular foliations of the projective plane. Our first main result is that a foliation of degree m>1 is not stable only if it has singularities in dimension 1 or contains an isolated singular point with multiplicity at least (m^2-1)/(2m+1). Our second main result is the construction of an invariant map from the space of foliations of degree m to that of curves of degree m^2+m-2. We describe this map explicitly in case m=2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5012","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":"1101.5012","created_at":"2026-05-18T04:30:47.010135+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.5012v1","created_at":"2026-05-18T04:30:47.010135+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.5012","created_at":"2026-05-18T04:30:47.010135+00:00"},{"alias_kind":"pith_short_12","alias_value":"2RL34MQW45GP","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"2RL34MQW45GPBDBW","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"2RL34MQW","created_at":"2026-05-18T12:26:18.847500+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/2RL34MQW45GPBDBWFSRCCV6XRQ","json":"https://pith.science/pith/2RL34MQW45GPBDBWFSRCCV6XRQ.json","graph_json":"https://pith.science/api/pith-number/2RL34MQW45GPBDBWFSRCCV6XRQ/graph.json","events_json":"https://pith.science/api/pith-number/2RL34MQW45GPBDBWFSRCCV6XRQ/events.json","paper":"https://pith.science/paper/2RL34MQW"},"agent_actions":{"view_html":"https://pith.science/pith/2RL34MQW45GPBDBWFSRCCV6XRQ","download_json":"https://pith.science/pith/2RL34MQW45GPBDBWFSRCCV6XRQ.json","view_paper":"https://pith.science/paper/2RL34MQW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.5012&json=true","fetch_graph":"https://pith.science/api/pith-number/2RL34MQW45GPBDBWFSRCCV6XRQ/graph.json","fetch_events":"https://pith.science/api/pith-number/2RL34MQW45GPBDBWFSRCCV6XRQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2RL34MQW45GPBDBWFSRCCV6XRQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2RL34MQW45GPBDBWFSRCCV6XRQ/action/storage_attestation","attest_author":"https://pith.science/pith/2RL34MQW45GPBDBWFSRCCV6XRQ/action/author_attestation","sign_citation":"https://pith.science/pith/2RL34MQW45GPBDBWFSRCCV6XRQ/action/citation_signature","submit_replication":"https://pith.science/pith/2RL34MQW45GPBDBWFSRCCV6XRQ/action/replication_record"}},"created_at":"2026-05-18T04:30:47.010135+00:00","updated_at":"2026-05-18T04:30:47.010135+00:00"}