{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:5SCHCN7Z46RU2PZKQFPJARKK5A","short_pith_number":"pith:5SCHCN7Z","schema_version":"1.0","canonical_sha256":"ec847137f9e7a34d3f2a815e90454ae837542fb94df3ee3e39a4b86e9322f249","source":{"kind":"arxiv","id":"1106.6343","version":1},"attestation_state":"computed","paper":{"title":"The space of nodal curves of type p,q with given Weierstra\\ss semigroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"(2) Fakult\\\"at f\\\"ur Mathematik, Ernst Kunz (2), Georg-Simon-Ohm-Hochschule N\\\"urnberg, Germany, Germany), Helmut Knebl (1), Rolf Waldi (2) ((1) Fakult\\\"at Informatik, Universit\\\"at Regensburg","submitted_at":"2011-06-30T19:09:07Z","abstract_excerpt":"We continue the investigation of curves of type p,q started in [KKW]. We study the space of such curves and the space of nodal curves with prescribed Weierstra\\ss semigroup. A necessary and sufficient criterion for a numerical semigroup to be a Weierstra\\ss semigroup is given. We find a class of Weierstra\\ss semigroups which apparently has not yet been described in the literature."},"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":"1106.6343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-30T19:09:07Z","cross_cats_sorted":[],"title_canon_sha256":"9ee3bb44d28ea309eeebdbf6b507cfda6a33f354fd5c565266029bff5feea8f8","abstract_canon_sha256":"1aa0e1d6f2d58dca70e011b5317b2fb4d5147677b47c369fce85e62364cb1227"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:03.471427Z","signature_b64":"KvJmEF9v4lIudgNWFT69YULAOQrqa/4PThO3MuI/B6R+zhVoQrK+ygDzMNOF482YvUZqaAj/Ce0VHH8pU5WbCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec847137f9e7a34d3f2a815e90454ae837542fb94df3ee3e39a4b86e9322f249","last_reissued_at":"2026-05-18T04:19:03.470741Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:03.470741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The space of nodal curves of type p,q with given Weierstra\\ss semigroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"(2) Fakult\\\"at f\\\"ur Mathematik, Ernst Kunz (2), Georg-Simon-Ohm-Hochschule N\\\"urnberg, Germany, Germany), Helmut Knebl (1), Rolf Waldi (2) ((1) Fakult\\\"at Informatik, Universit\\\"at Regensburg","submitted_at":"2011-06-30T19:09:07Z","abstract_excerpt":"We continue the investigation of curves of type p,q started in [KKW]. We study the space of such curves and the space of nodal curves with prescribed Weierstra\\ss semigroup. A necessary and sufficient criterion for a numerical semigroup to be a Weierstra\\ss semigroup is given. We find a class of Weierstra\\ss semigroups which apparently has not yet been described in the literature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.6343","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":"1106.6343","created_at":"2026-05-18T04:19:03.470831+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.6343v1","created_at":"2026-05-18T04:19:03.470831+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.6343","created_at":"2026-05-18T04:19:03.470831+00:00"},{"alias_kind":"pith_short_12","alias_value":"5SCHCN7Z46RU","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"5SCHCN7Z46RU2PZK","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"5SCHCN7Z","created_at":"2026-05-18T12:26:20.644004+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/5SCHCN7Z46RU2PZKQFPJARKK5A","json":"https://pith.science/pith/5SCHCN7Z46RU2PZKQFPJARKK5A.json","graph_json":"https://pith.science/api/pith-number/5SCHCN7Z46RU2PZKQFPJARKK5A/graph.json","events_json":"https://pith.science/api/pith-number/5SCHCN7Z46RU2PZKQFPJARKK5A/events.json","paper":"https://pith.science/paper/5SCHCN7Z"},"agent_actions":{"view_html":"https://pith.science/pith/5SCHCN7Z46RU2PZKQFPJARKK5A","download_json":"https://pith.science/pith/5SCHCN7Z46RU2PZKQFPJARKK5A.json","view_paper":"https://pith.science/paper/5SCHCN7Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.6343&json=true","fetch_graph":"https://pith.science/api/pith-number/5SCHCN7Z46RU2PZKQFPJARKK5A/graph.json","fetch_events":"https://pith.science/api/pith-number/5SCHCN7Z46RU2PZKQFPJARKK5A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5SCHCN7Z46RU2PZKQFPJARKK5A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5SCHCN7Z46RU2PZKQFPJARKK5A/action/storage_attestation","attest_author":"https://pith.science/pith/5SCHCN7Z46RU2PZKQFPJARKK5A/action/author_attestation","sign_citation":"https://pith.science/pith/5SCHCN7Z46RU2PZKQFPJARKK5A/action/citation_signature","submit_replication":"https://pith.science/pith/5SCHCN7Z46RU2PZKQFPJARKK5A/action/replication_record"}},"created_at":"2026-05-18T04:19:03.470831+00:00","updated_at":"2026-05-18T04:19:03.470831+00:00"}