{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:BR2W2AMTXW2B7WZKH47HEBTHA6","short_pith_number":"pith:BR2W2AMT","schema_version":"1.0","canonical_sha256":"0c756d0193bdb41fdb2a3f3e7206670791cdcd514ddfa1ac783575ddf4360090","source":{"kind":"arxiv","id":"1304.7561","version":1},"attestation_state":"computed","paper":{"title":"On the structure of fundamental groups of conic-line arrangements having a cycle in their graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GR"],"primary_cat":"math.GT","authors_text":"David Garber, Michael Friedman","submitted_at":"2013-04-29T04:38:27Z","abstract_excerpt":"The fundamental group of the complement of a plane curve is a very important topological invariant. In particular, it is interesting to find out whether this group is determined by the combinatorics of the curve or not, and whether it is a direct sum of free groups and a free abelian group, or it has a conjugation-free geometric presentation.\n  In this paper, we investigate the structure of this fundamental group when the graph of the conic-line arrangement is a unique cycle of length $n$ and the conic passes through all the multiple points of the cycle. We show that if n is odd, then the affi"},"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":"1304.7561","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-04-29T04:38:27Z","cross_cats_sorted":["math.AT","math.GR"],"title_canon_sha256":"9fa954f12b52caf94410433e52ab3ff42aff0f20378f8027e43235aa61ad4906","abstract_canon_sha256":"7fa1d098556b3cc0c730eac9c01f9cac52e765c9f3b6eb9d5c4601de827420b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:53.651351Z","signature_b64":"0+EETFZpDlYRdNP2jlm0z/zETJQXqRcDwEolmOPbKK9mFuIPHCMaYib88P2g1h1PTQAAGPqeRNBi8mnwmkV/Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c756d0193bdb41fdb2a3f3e7206670791cdcd514ddfa1ac783575ddf4360090","last_reissued_at":"2026-05-18T03:26:53.650847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:53.650847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the structure of fundamental groups of conic-line arrangements having a cycle in their graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GR"],"primary_cat":"math.GT","authors_text":"David Garber, Michael Friedman","submitted_at":"2013-04-29T04:38:27Z","abstract_excerpt":"The fundamental group of the complement of a plane curve is a very important topological invariant. In particular, it is interesting to find out whether this group is determined by the combinatorics of the curve or not, and whether it is a direct sum of free groups and a free abelian group, or it has a conjugation-free geometric presentation.\n  In this paper, we investigate the structure of this fundamental group when the graph of the conic-line arrangement is a unique cycle of length $n$ and the conic passes through all the multiple points of the cycle. We show that if n is odd, then the affi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7561","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":"1304.7561","created_at":"2026-05-18T03:26:53.650928+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.7561v1","created_at":"2026-05-18T03:26:53.650928+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7561","created_at":"2026-05-18T03:26:53.650928+00:00"},{"alias_kind":"pith_short_12","alias_value":"BR2W2AMTXW2B","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"BR2W2AMTXW2B7WZK","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"BR2W2AMT","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/BR2W2AMTXW2B7WZKH47HEBTHA6","json":"https://pith.science/pith/BR2W2AMTXW2B7WZKH47HEBTHA6.json","graph_json":"https://pith.science/api/pith-number/BR2W2AMTXW2B7WZKH47HEBTHA6/graph.json","events_json":"https://pith.science/api/pith-number/BR2W2AMTXW2B7WZKH47HEBTHA6/events.json","paper":"https://pith.science/paper/BR2W2AMT"},"agent_actions":{"view_html":"https://pith.science/pith/BR2W2AMTXW2B7WZKH47HEBTHA6","download_json":"https://pith.science/pith/BR2W2AMTXW2B7WZKH47HEBTHA6.json","view_paper":"https://pith.science/paper/BR2W2AMT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.7561&json=true","fetch_graph":"https://pith.science/api/pith-number/BR2W2AMTXW2B7WZKH47HEBTHA6/graph.json","fetch_events":"https://pith.science/api/pith-number/BR2W2AMTXW2B7WZKH47HEBTHA6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BR2W2AMTXW2B7WZKH47HEBTHA6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BR2W2AMTXW2B7WZKH47HEBTHA6/action/storage_attestation","attest_author":"https://pith.science/pith/BR2W2AMTXW2B7WZKH47HEBTHA6/action/author_attestation","sign_citation":"https://pith.science/pith/BR2W2AMTXW2B7WZKH47HEBTHA6/action/citation_signature","submit_replication":"https://pith.science/pith/BR2W2AMTXW2B7WZKH47HEBTHA6/action/replication_record"}},"created_at":"2026-05-18T03:26:53.650928+00:00","updated_at":"2026-05-18T03:26:53.650928+00:00"}