{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:CKCVOW4JR3UVPAPQFB5LUJJFDI","short_pith_number":"pith:CKCVOW4J","schema_version":"1.0","canonical_sha256":"1285575b898ee95781f0287aba25251a003864c45ac4dbccbbba0937e0e96ca4","source":{"kind":"arxiv","id":"1307.4837","version":1},"attestation_state":"computed","paper":{"title":"On the fundamental groups of non-generic $\\mathbb{R}$-join-type curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christophe Eyral, Mutsuo Oka","submitted_at":"2013-07-18T06:11:48Z","abstract_excerpt":"An \\emph{$\\mathbb{R}$-join-type curve} is a curve in $\\mathbb{C}^2$ defined by an equation of the form \\begin{equation*} a\\cdot\\prod_{j=1}^\\ell (y-\\beta_j)^{\\nu_j} = b\\cdot\\prod_{i=1}^m (x-\\alpha_i)^{\\lambda_i}, \\end{equation*} where the coefficients $a$, $b$, $\\alpha_i$ and $\\beta_j$ are \\emph{real} numbers. For generic values of $a$ and $b$, the singular locus of the curve consists of the points $(\\alpha_i,\\beta_j)$ with $\\lambda_i,\\nu_j\\geq 2$ (so-called \\emph{inner} singularities). In the non-generic case, the inner singularities are not the only ones: the curve may also have \\emph{`outer'"},"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":"1307.4837","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-18T06:11:48Z","cross_cats_sorted":[],"title_canon_sha256":"0cfc2c9b18274479d55bd4a67714b7ba948affa5113727148437f5cd28056599","abstract_canon_sha256":"996495bb2ddfa7fb65b45128e85b83e0b884d2ec96cdd97081dfb0e33191a6d2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:07.454999Z","signature_b64":"bhTbYwLc2fceyfAa8tsa0qNrla2bZrHuU+rfB4YbW/nej1ijC7uQJwjQBYzspOgZzzIgJSCvUn4hpWGVcC0yCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1285575b898ee95781f0287aba25251a003864c45ac4dbccbbba0937e0e96ca4","last_reissued_at":"2026-05-18T03:18:07.454088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:07.454088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the fundamental groups of non-generic $\\mathbb{R}$-join-type curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christophe Eyral, Mutsuo Oka","submitted_at":"2013-07-18T06:11:48Z","abstract_excerpt":"An \\emph{$\\mathbb{R}$-join-type curve} is a curve in $\\mathbb{C}^2$ defined by an equation of the form \\begin{equation*} a\\cdot\\prod_{j=1}^\\ell (y-\\beta_j)^{\\nu_j} = b\\cdot\\prod_{i=1}^m (x-\\alpha_i)^{\\lambda_i}, \\end{equation*} where the coefficients $a$, $b$, $\\alpha_i$ and $\\beta_j$ are \\emph{real} numbers. For generic values of $a$ and $b$, the singular locus of the curve consists of the points $(\\alpha_i,\\beta_j)$ with $\\lambda_i,\\nu_j\\geq 2$ (so-called \\emph{inner} singularities). In the non-generic case, the inner singularities are not the only ones: the curve may also have \\emph{`outer'"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4837","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":"1307.4837","created_at":"2026-05-18T03:18:07.454255+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.4837v1","created_at":"2026-05-18T03:18:07.454255+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4837","created_at":"2026-05-18T03:18:07.454255+00:00"},{"alias_kind":"pith_short_12","alias_value":"CKCVOW4JR3UV","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"CKCVOW4JR3UVPAPQ","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"CKCVOW4J","created_at":"2026-05-18T12:27:40.988391+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/CKCVOW4JR3UVPAPQFB5LUJJFDI","json":"https://pith.science/pith/CKCVOW4JR3UVPAPQFB5LUJJFDI.json","graph_json":"https://pith.science/api/pith-number/CKCVOW4JR3UVPAPQFB5LUJJFDI/graph.json","events_json":"https://pith.science/api/pith-number/CKCVOW4JR3UVPAPQFB5LUJJFDI/events.json","paper":"https://pith.science/paper/CKCVOW4J"},"agent_actions":{"view_html":"https://pith.science/pith/CKCVOW4JR3UVPAPQFB5LUJJFDI","download_json":"https://pith.science/pith/CKCVOW4JR3UVPAPQFB5LUJJFDI.json","view_paper":"https://pith.science/paper/CKCVOW4J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.4837&json=true","fetch_graph":"https://pith.science/api/pith-number/CKCVOW4JR3UVPAPQFB5LUJJFDI/graph.json","fetch_events":"https://pith.science/api/pith-number/CKCVOW4JR3UVPAPQFB5LUJJFDI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CKCVOW4JR3UVPAPQFB5LUJJFDI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CKCVOW4JR3UVPAPQFB5LUJJFDI/action/storage_attestation","attest_author":"https://pith.science/pith/CKCVOW4JR3UVPAPQFB5LUJJFDI/action/author_attestation","sign_citation":"https://pith.science/pith/CKCVOW4JR3UVPAPQFB5LUJJFDI/action/citation_signature","submit_replication":"https://pith.science/pith/CKCVOW4JR3UVPAPQFB5LUJJFDI/action/replication_record"}},"created_at":"2026-05-18T03:18:07.454255+00:00","updated_at":"2026-05-18T03:18:07.454255+00:00"}