{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:WGHGFR2Y5NWAVK43MUEZF4XFLO","short_pith_number":"pith:WGHGFR2Y","schema_version":"1.0","canonical_sha256":"b18e62c758eb6c0aab9b650992f2e55b8563e792b02578b8fa684b9c99cca0bf","source":{"kind":"arxiv","id":"1012.4208","version":1},"attestation_state":"computed","paper":{"title":"Combinatorial Methods for Detecting Surface Subgroups in Right-Angled Artin Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Robert W. Bell","submitted_at":"2010-12-19T21:19:56Z","abstract_excerpt":"We give a short proof of the following theorem of Sang-hyun Kim: if $A(\\Gamma)$ is a right-angled Artin group with defining graph $\\Gamma$, then $A(\\Gamma)$ contains a hyperbolic surface subgroup if $\\Gamma$ contains an induced subgraph $\\bar{C}_n$ for some $n \\geq 5$, where $\\bar{C}_n$ denotes the complement graph of an $n$-cycle. Furthermore, we give a new proof of Kim's co-contraction theorem."},"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":"1012.4208","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-12-19T21:19:56Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"0e32cb600a2f9b9cc2821133bac1248981a37947f3f5cb65ee7ba7907f8bf6cc","abstract_canon_sha256":"a56bdc18a6fef17946ab469b52fb579445a197d72220d55a21414240929250f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:55.242062Z","signature_b64":"tOvH1LU33Xhnk63V/pqVFt8WP6VIBCOEJ5XEa52pLxJd5TUjQFL/Kn7TVgDWJLoDhRZijqp5p78UTDkHvFkNCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b18e62c758eb6c0aab9b650992f2e55b8563e792b02578b8fa684b9c99cca0bf","last_reissued_at":"2026-05-18T04:32:55.241408Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:55.241408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorial Methods for Detecting Surface Subgroups in Right-Angled Artin Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Robert W. Bell","submitted_at":"2010-12-19T21:19:56Z","abstract_excerpt":"We give a short proof of the following theorem of Sang-hyun Kim: if $A(\\Gamma)$ is a right-angled Artin group with defining graph $\\Gamma$, then $A(\\Gamma)$ contains a hyperbolic surface subgroup if $\\Gamma$ contains an induced subgraph $\\bar{C}_n$ for some $n \\geq 5$, where $\\bar{C}_n$ denotes the complement graph of an $n$-cycle. Furthermore, we give a new proof of Kim's co-contraction theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4208","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":"1012.4208","created_at":"2026-05-18T04:32:55.241509+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.4208v1","created_at":"2026-05-18T04:32:55.241509+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4208","created_at":"2026-05-18T04:32:55.241509+00:00"},{"alias_kind":"pith_short_12","alias_value":"WGHGFR2Y5NWA","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"WGHGFR2Y5NWAVK43","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"WGHGFR2Y","created_at":"2026-05-18T12:26:15.391820+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/WGHGFR2Y5NWAVK43MUEZF4XFLO","json":"https://pith.science/pith/WGHGFR2Y5NWAVK43MUEZF4XFLO.json","graph_json":"https://pith.science/api/pith-number/WGHGFR2Y5NWAVK43MUEZF4XFLO/graph.json","events_json":"https://pith.science/api/pith-number/WGHGFR2Y5NWAVK43MUEZF4XFLO/events.json","paper":"https://pith.science/paper/WGHGFR2Y"},"agent_actions":{"view_html":"https://pith.science/pith/WGHGFR2Y5NWAVK43MUEZF4XFLO","download_json":"https://pith.science/pith/WGHGFR2Y5NWAVK43MUEZF4XFLO.json","view_paper":"https://pith.science/paper/WGHGFR2Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.4208&json=true","fetch_graph":"https://pith.science/api/pith-number/WGHGFR2Y5NWAVK43MUEZF4XFLO/graph.json","fetch_events":"https://pith.science/api/pith-number/WGHGFR2Y5NWAVK43MUEZF4XFLO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WGHGFR2Y5NWAVK43MUEZF4XFLO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WGHGFR2Y5NWAVK43MUEZF4XFLO/action/storage_attestation","attest_author":"https://pith.science/pith/WGHGFR2Y5NWAVK43MUEZF4XFLO/action/author_attestation","sign_citation":"https://pith.science/pith/WGHGFR2Y5NWAVK43MUEZF4XFLO/action/citation_signature","submit_replication":"https://pith.science/pith/WGHGFR2Y5NWAVK43MUEZF4XFLO/action/replication_record"}},"created_at":"2026-05-18T04:32:55.241509+00:00","updated_at":"2026-05-18T04:32:55.241509+00:00"}