{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:HUS4LEIGHSYI3HYV75B33UDWNL","short_pith_number":"pith:HUS4LEIG","schema_version":"1.0","canonical_sha256":"3d25c591063cb08d9f15ff43bdd0766adfbc7c342c86a770158c2822edd0b8b4","source":{"kind":"arxiv","id":"1607.08303","version":2},"attestation_state":"computed","paper":{"title":"The intersection of subgroups in free groups and linear programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.OC"],"primary_cat":"math.GR","authors_text":"Sergei V. Ivanov","submitted_at":"2016-07-28T03:27:56Z","abstract_excerpt":"We study the intersection of finitely generated subgroups of free groups by utilizing the method of linear programming. We prove that if $H_1$ is a finitely generated subgroup of a free group $F$, then the WN-coefficient $\\sigma(H_1)$ of $H_1$ is rational and can be computed in deterministic exponential time in the size of $H_1$. This coefficient $\\sigma(H_1)$ is the minimal nonnegative real number such that, for every finitely generated subgroup $H_2$ of $F$, it is true that $\\bar {\\rm r}(H_1, H_2) \\le \\sigma(H_1) \\bar {\\rm r}(H_1) \\bar {\\rm r}(H_2)$, where $\\bar{ {\\rm r}} (H) := \\max ( {\\rm "},"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":"1607.08303","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-07-28T03:27:56Z","cross_cats_sorted":["cs.DM","math.OC"],"title_canon_sha256":"48a782d3f375a6439d4a92651d8dcae25b993f70bb1e26bbf4adbe42cedc0e30","abstract_canon_sha256":"b2e988f92dd985820263bef630b8ca995febb45fe6553ad6a4efdc733d6cafbc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:02.944691Z","signature_b64":"5EHIAG9ig0B7iJrsrsX7P7uWxSPQH1ajF6Z9UCUOxrdmvVV/MwTpKx4reH7KvS53C94n6tsUJx4+VnXqv2ILCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d25c591063cb08d9f15ff43bdd0766adfbc7c342c86a770158c2822edd0b8b4","last_reissued_at":"2026-05-18T00:27:02.944179Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:02.944179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The intersection of subgroups in free groups and linear programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.OC"],"primary_cat":"math.GR","authors_text":"Sergei V. Ivanov","submitted_at":"2016-07-28T03:27:56Z","abstract_excerpt":"We study the intersection of finitely generated subgroups of free groups by utilizing the method of linear programming. We prove that if $H_1$ is a finitely generated subgroup of a free group $F$, then the WN-coefficient $\\sigma(H_1)$ of $H_1$ is rational and can be computed in deterministic exponential time in the size of $H_1$. This coefficient $\\sigma(H_1)$ is the minimal nonnegative real number such that, for every finitely generated subgroup $H_2$ of $F$, it is true that $\\bar {\\rm r}(H_1, H_2) \\le \\sigma(H_1) \\bar {\\rm r}(H_1) \\bar {\\rm r}(H_2)$, where $\\bar{ {\\rm r}} (H) := \\max ( {\\rm "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08303","kind":"arxiv","version":2},"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":"1607.08303","created_at":"2026-05-18T00:27:02.944258+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.08303v2","created_at":"2026-05-18T00:27:02.944258+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08303","created_at":"2026-05-18T00:27:02.944258+00:00"},{"alias_kind":"pith_short_12","alias_value":"HUS4LEIGHSYI","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"HUS4LEIGHSYI3HYV","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"HUS4LEIG","created_at":"2026-05-18T12:30:22.444734+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/HUS4LEIGHSYI3HYV75B33UDWNL","json":"https://pith.science/pith/HUS4LEIGHSYI3HYV75B33UDWNL.json","graph_json":"https://pith.science/api/pith-number/HUS4LEIGHSYI3HYV75B33UDWNL/graph.json","events_json":"https://pith.science/api/pith-number/HUS4LEIGHSYI3HYV75B33UDWNL/events.json","paper":"https://pith.science/paper/HUS4LEIG"},"agent_actions":{"view_html":"https://pith.science/pith/HUS4LEIGHSYI3HYV75B33UDWNL","download_json":"https://pith.science/pith/HUS4LEIGHSYI3HYV75B33UDWNL.json","view_paper":"https://pith.science/paper/HUS4LEIG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.08303&json=true","fetch_graph":"https://pith.science/api/pith-number/HUS4LEIGHSYI3HYV75B33UDWNL/graph.json","fetch_events":"https://pith.science/api/pith-number/HUS4LEIGHSYI3HYV75B33UDWNL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HUS4LEIGHSYI3HYV75B33UDWNL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HUS4LEIGHSYI3HYV75B33UDWNL/action/storage_attestation","attest_author":"https://pith.science/pith/HUS4LEIGHSYI3HYV75B33UDWNL/action/author_attestation","sign_citation":"https://pith.science/pith/HUS4LEIGHSYI3HYV75B33UDWNL/action/citation_signature","submit_replication":"https://pith.science/pith/HUS4LEIGHSYI3HYV75B33UDWNL/action/replication_record"}},"created_at":"2026-05-18T00:27:02.944258+00:00","updated_at":"2026-05-18T00:27:02.944258+00:00"}