{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:PN5MOKOBUGV4IL3TVNUMNBFZZH","short_pith_number":"pith:PN5MOKOB","schema_version":"1.0","canonical_sha256":"7b7ac729c1a1abc42f73ab68c684b9c9fb479dfe9c031e9baf0bc92de8463d49","source":{"kind":"arxiv","id":"1211.5458","version":1},"attestation_state":"computed","paper":{"title":"Smoothable locally Cohen--Macaulay and non Cohen--Macaulay multiple structures on curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Bangere P. Purnaprajna, Francisco Javier Gallego, Miguel Gonz\\'alez","submitted_at":"2012-11-23T10:28:48Z","abstract_excerpt":"In this article we show that a wide range of multiple structures on curves arise whenever a family of embeddings degenerates to a morphism $\\varphi$ of degree $n$. One could expect to see, when an embedding degenerates to such a morphism, the appearance of a locally Cohen-Macaulay multiple structure of certain kind (a so-called rope of multiplicity $n$). We show that this expectation is naive and that both locally Cohen-Macaulay and non Cohen-Macaulay multiple structures might occur in this situation. In seeing this we find out that many multiple structures can be smoothed. When we specialize "},"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":"1211.5458","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-23T10:28:48Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"7ca368f3359d2c0794aa74743c0f7a4325c9095df872725db524705baddbb252","abstract_canon_sha256":"29c8cd6454bfbb1b107368bd90e37caec3b606c5670676f0904725dfc08081c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:02.509601Z","signature_b64":"sDzRddEZwee3Ysmk9+gcwVBa2JmXuwOXzQ4KGQiUewtFopCaZQLOK2MQitYgyRHldF4FvHK/g+czVQowgSkVCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b7ac729c1a1abc42f73ab68c684b9c9fb479dfe9c031e9baf0bc92de8463d49","last_reissued_at":"2026-05-18T03:40:02.508850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:02.508850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Smoothable locally Cohen--Macaulay and non Cohen--Macaulay multiple structures on curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Bangere P. Purnaprajna, Francisco Javier Gallego, Miguel Gonz\\'alez","submitted_at":"2012-11-23T10:28:48Z","abstract_excerpt":"In this article we show that a wide range of multiple structures on curves arise whenever a family of embeddings degenerates to a morphism $\\varphi$ of degree $n$. One could expect to see, when an embedding degenerates to such a morphism, the appearance of a locally Cohen-Macaulay multiple structure of certain kind (a so-called rope of multiplicity $n$). We show that this expectation is naive and that both locally Cohen-Macaulay and non Cohen-Macaulay multiple structures might occur in this situation. In seeing this we find out that many multiple structures can be smoothed. When we specialize "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5458","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":"1211.5458","created_at":"2026-05-18T03:40:02.508975+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.5458v1","created_at":"2026-05-18T03:40:02.508975+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5458","created_at":"2026-05-18T03:40:02.508975+00:00"},{"alias_kind":"pith_short_12","alias_value":"PN5MOKOBUGV4","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"PN5MOKOBUGV4IL3T","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"PN5MOKOB","created_at":"2026-05-18T12:27:18.751474+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/PN5MOKOBUGV4IL3TVNUMNBFZZH","json":"https://pith.science/pith/PN5MOKOBUGV4IL3TVNUMNBFZZH.json","graph_json":"https://pith.science/api/pith-number/PN5MOKOBUGV4IL3TVNUMNBFZZH/graph.json","events_json":"https://pith.science/api/pith-number/PN5MOKOBUGV4IL3TVNUMNBFZZH/events.json","paper":"https://pith.science/paper/PN5MOKOB"},"agent_actions":{"view_html":"https://pith.science/pith/PN5MOKOBUGV4IL3TVNUMNBFZZH","download_json":"https://pith.science/pith/PN5MOKOBUGV4IL3TVNUMNBFZZH.json","view_paper":"https://pith.science/paper/PN5MOKOB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.5458&json=true","fetch_graph":"https://pith.science/api/pith-number/PN5MOKOBUGV4IL3TVNUMNBFZZH/graph.json","fetch_events":"https://pith.science/api/pith-number/PN5MOKOBUGV4IL3TVNUMNBFZZH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PN5MOKOBUGV4IL3TVNUMNBFZZH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PN5MOKOBUGV4IL3TVNUMNBFZZH/action/storage_attestation","attest_author":"https://pith.science/pith/PN5MOKOBUGV4IL3TVNUMNBFZZH/action/author_attestation","sign_citation":"https://pith.science/pith/PN5MOKOBUGV4IL3TVNUMNBFZZH/action/citation_signature","submit_replication":"https://pith.science/pith/PN5MOKOBUGV4IL3TVNUMNBFZZH/action/replication_record"}},"created_at":"2026-05-18T03:40:02.508975+00:00","updated_at":"2026-05-18T03:40:02.508975+00:00"}