{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:C5YOHED3LUCJIVENKDT6BJDIMK","short_pith_number":"pith:C5YOHED3","schema_version":"1.0","canonical_sha256":"1770e3907b5d0494548d50e7e0a468629e18b0b21d841e9723162e493114fda9","source":{"kind":"arxiv","id":"1712.04141","version":1},"attestation_state":"computed","paper":{"title":"Ideals in the Goldman Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Minh Nguyen","submitted_at":"2017-12-12T06:29:02Z","abstract_excerpt":"The goal of this work is to study the ideals of the Goldman Lie algebra $S$. To do so, we construct an algebra homomorphism from $S$ to a simpler algebraic structure, and focus on finding ideals of this new structure instead. The structure $S$ can be regarded as either a $\\mathbb{Q}$-module or a $\\mathbb{Q}$-module generated by free homotopy classes. For $\\mathbb{Z}$-module case, we proved that there is an infinite class of ideals of $S$ that contain a certain finite set of free homotopy classes. For $\\mathbb{Q}$-module case, we can classify all the ideals of the new structure and consequently"},"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":"1712.04141","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-12-12T06:29:02Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"ad8cdafe1616f3164ed834a4ad3b60a3ac44b5ae08a64e2d03674d90a5cf352d","abstract_canon_sha256":"9548c9317ce8195740cb1114cd368fae21dbfa1827dd59ef35e709bb9343b72f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:09.002516Z","signature_b64":"QMPlq0pPP+PHEdjgSoHP3rt6pywF9SvIP0ZgKOFHXWyZSbhD5CWLrYLm1txNxPyekci1PBEgvqJMFFvCrI39BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1770e3907b5d0494548d50e7e0a468629e18b0b21d841e9723162e493114fda9","last_reissued_at":"2026-05-18T00:28:09.001765Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:09.001765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ideals in the Goldman Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Minh Nguyen","submitted_at":"2017-12-12T06:29:02Z","abstract_excerpt":"The goal of this work is to study the ideals of the Goldman Lie algebra $S$. To do so, we construct an algebra homomorphism from $S$ to a simpler algebraic structure, and focus on finding ideals of this new structure instead. The structure $S$ can be regarded as either a $\\mathbb{Q}$-module or a $\\mathbb{Q}$-module generated by free homotopy classes. For $\\mathbb{Z}$-module case, we proved that there is an infinite class of ideals of $S$ that contain a certain finite set of free homotopy classes. For $\\mathbb{Q}$-module case, we can classify all the ideals of the new structure and consequently"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04141","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":"1712.04141","created_at":"2026-05-18T00:28:09.001917+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.04141v1","created_at":"2026-05-18T00:28:09.001917+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04141","created_at":"2026-05-18T00:28:09.001917+00:00"},{"alias_kind":"pith_short_12","alias_value":"C5YOHED3LUCJ","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"C5YOHED3LUCJIVEN","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"C5YOHED3","created_at":"2026-05-18T12:31:08.081275+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/C5YOHED3LUCJIVENKDT6BJDIMK","json":"https://pith.science/pith/C5YOHED3LUCJIVENKDT6BJDIMK.json","graph_json":"https://pith.science/api/pith-number/C5YOHED3LUCJIVENKDT6BJDIMK/graph.json","events_json":"https://pith.science/api/pith-number/C5YOHED3LUCJIVENKDT6BJDIMK/events.json","paper":"https://pith.science/paper/C5YOHED3"},"agent_actions":{"view_html":"https://pith.science/pith/C5YOHED3LUCJIVENKDT6BJDIMK","download_json":"https://pith.science/pith/C5YOHED3LUCJIVENKDT6BJDIMK.json","view_paper":"https://pith.science/paper/C5YOHED3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.04141&json=true","fetch_graph":"https://pith.science/api/pith-number/C5YOHED3LUCJIVENKDT6BJDIMK/graph.json","fetch_events":"https://pith.science/api/pith-number/C5YOHED3LUCJIVENKDT6BJDIMK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C5YOHED3LUCJIVENKDT6BJDIMK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C5YOHED3LUCJIVENKDT6BJDIMK/action/storage_attestation","attest_author":"https://pith.science/pith/C5YOHED3LUCJIVENKDT6BJDIMK/action/author_attestation","sign_citation":"https://pith.science/pith/C5YOHED3LUCJIVENKDT6BJDIMK/action/citation_signature","submit_replication":"https://pith.science/pith/C5YOHED3LUCJIVENKDT6BJDIMK/action/replication_record"}},"created_at":"2026-05-18T00:28:09.001917+00:00","updated_at":"2026-05-18T00:28:09.001917+00:00"}