{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:OK6IGPM6DWFRSE77MNS2ZE6PVO","short_pith_number":"pith:OK6IGPM6","schema_version":"1.0","canonical_sha256":"72bc833d9e1d8b1913ff6365ac93cfabac10a922aec9f6ee071e37ed2d73d551","source":{"kind":"arxiv","id":"2511.18545","version":4},"attestation_state":"computed","paper":{"title":"On finiteness properties of separating semigroup of real curve","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Matthew Magin","submitted_at":"2025-11-23T17:25:25Z","abstract_excerpt":"A real morphism $f$ from a real algebraic curve $X$ to $\\mathbb{P}^1$ is called separating if $f^{-1}(\\mathbb{R} \\mathbb{P}^1) = \\mathbb{R} X$. A separating morphism defines a covering $\\mathbb{R} X \\to \\mathbb{R} \\mathbb{P}^1$. Let $X_1, \\ldots, X_r$ denote the components of $\\mathbb{R} X$. M. Kummer and K. Shaw defined the separating semigroup of a curve $X$ as the set of all vectors $d(f) = (d_1(f), \\ldots, d_r(f)) \\in \\mathbb{N}^{r}$ where $f$ is a separating morphism $X \\to \\mathbb{P}^1$ and $d_i(f)$ is the degree of the restriction of $f$ to $X_i$.\n  In the present paper we prove that fo"},"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":"2511.18545","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-11-23T17:25:25Z","cross_cats_sorted":[],"title_canon_sha256":"f7fd2a8a14c3b4a0f21a49567ecb049b0bc34305e7d1eed70e06e22232983a6c","abstract_canon_sha256":"e19079127188ef9fcd9255e12628d92cea4f6608030b8c2e68f81494f038bd61"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:07:13.729977Z","signature_b64":"3DQeeng2A4cXJzK/d7mW4+Wb/jCNIsdxpBYJd/YYD2/3fdSrF9rk1RKBu1GPXgzbThBi/k+NAa5wrSDSqPCYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72bc833d9e1d8b1913ff6365ac93cfabac10a922aec9f6ee071e37ed2d73d551","last_reissued_at":"2026-06-09T02:07:13.728826Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:07:13.728826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On finiteness properties of separating semigroup of real curve","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Matthew Magin","submitted_at":"2025-11-23T17:25:25Z","abstract_excerpt":"A real morphism $f$ from a real algebraic curve $X$ to $\\mathbb{P}^1$ is called separating if $f^{-1}(\\mathbb{R} \\mathbb{P}^1) = \\mathbb{R} X$. A separating morphism defines a covering $\\mathbb{R} X \\to \\mathbb{R} \\mathbb{P}^1$. Let $X_1, \\ldots, X_r$ denote the components of $\\mathbb{R} X$. M. Kummer and K. Shaw defined the separating semigroup of a curve $X$ as the set of all vectors $d(f) = (d_1(f), \\ldots, d_r(f)) \\in \\mathbb{N}^{r}$ where $f$ is a separating morphism $X \\to \\mathbb{P}^1$ and $d_i(f)$ is the degree of the restriction of $f$ to $X_i$.\n  In the present paper we prove that fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.18545","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.18545/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2511.18545","created_at":"2026-06-09T02:07:13.728957+00:00"},{"alias_kind":"arxiv_version","alias_value":"2511.18545v4","created_at":"2026-06-09T02:07:13.728957+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.18545","created_at":"2026-06-09T02:07:13.728957+00:00"},{"alias_kind":"pith_short_12","alias_value":"OK6IGPM6DWFR","created_at":"2026-06-09T02:07:13.728957+00:00"},{"alias_kind":"pith_short_16","alias_value":"OK6IGPM6DWFRSE77","created_at":"2026-06-09T02:07:13.728957+00:00"},{"alias_kind":"pith_short_8","alias_value":"OK6IGPM6","created_at":"2026-06-09T02:07:13.728957+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.15970","citing_title":"Copositive Matrices with Ordered Off-Diagonal Entries","ref_index":39,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OK6IGPM6DWFRSE77MNS2ZE6PVO","json":"https://pith.science/pith/OK6IGPM6DWFRSE77MNS2ZE6PVO.json","graph_json":"https://pith.science/api/pith-number/OK6IGPM6DWFRSE77MNS2ZE6PVO/graph.json","events_json":"https://pith.science/api/pith-number/OK6IGPM6DWFRSE77MNS2ZE6PVO/events.json","paper":"https://pith.science/paper/OK6IGPM6"},"agent_actions":{"view_html":"https://pith.science/pith/OK6IGPM6DWFRSE77MNS2ZE6PVO","download_json":"https://pith.science/pith/OK6IGPM6DWFRSE77MNS2ZE6PVO.json","view_paper":"https://pith.science/paper/OK6IGPM6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2511.18545&json=true","fetch_graph":"https://pith.science/api/pith-number/OK6IGPM6DWFRSE77MNS2ZE6PVO/graph.json","fetch_events":"https://pith.science/api/pith-number/OK6IGPM6DWFRSE77MNS2ZE6PVO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OK6IGPM6DWFRSE77MNS2ZE6PVO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OK6IGPM6DWFRSE77MNS2ZE6PVO/action/storage_attestation","attest_author":"https://pith.science/pith/OK6IGPM6DWFRSE77MNS2ZE6PVO/action/author_attestation","sign_citation":"https://pith.science/pith/OK6IGPM6DWFRSE77MNS2ZE6PVO/action/citation_signature","submit_replication":"https://pith.science/pith/OK6IGPM6DWFRSE77MNS2ZE6PVO/action/replication_record"}},"created_at":"2026-06-09T02:07:13.728957+00:00","updated_at":"2026-06-09T02:07:13.728957+00:00"}