{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:NBB4MXYITLKTO2UCSCEKAXGRMK","short_pith_number":"pith:NBB4MXYI","schema_version":"1.0","canonical_sha256":"6843c65f089ad5376a829088a05cd162a8602f6f22aee121935217dd928ec271","source":{"kind":"arxiv","id":"0909.2824","version":4},"attestation_state":"computed","paper":{"title":"Amenable actions of amalgamated free products of free groups over a cyclic subgroup and generic property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Soyoung Moon","submitted_at":"2009-09-15T15:24:28Z","abstract_excerpt":"We show that the class of amalgamated free products of two free groups over a cyclic subgroup admits amenable, faithful and transitive actions on infinite countable sets. This work generalizes the results on such actions for doubles of free group on 2 generators."},"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":"0909.2824","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-09-15T15:24:28Z","cross_cats_sorted":[],"title_canon_sha256":"858f91d9e7be5100fef23cc49f15e31dd769bf2f4d6251be5cf4db018b6ab873","abstract_canon_sha256":"7f2cbca4d26ecc5da1835f39b8e3c215870d917b80faf6f3721ae8f8c19abc1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:50.848440Z","signature_b64":"IvLYxVCrrV0BgWmT/py2MGj80Jnl8uPL1i1Yoyc2aZYo1+19+IrbMTdhoEdhixxnI/lMz4VELMR7UOWe4yssDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6843c65f089ad5376a829088a05cd162a8602f6f22aee121935217dd928ec271","last_reissued_at":"2026-05-18T04:38:50.847777Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:50.847777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Amenable actions of amalgamated free products of free groups over a cyclic subgroup and generic property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Soyoung Moon","submitted_at":"2009-09-15T15:24:28Z","abstract_excerpt":"We show that the class of amalgamated free products of two free groups over a cyclic subgroup admits amenable, faithful and transitive actions on infinite countable sets. This work generalizes the results on such actions for doubles of free group on 2 generators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.2824","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":""},"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":"0909.2824","created_at":"2026-05-18T04:38:50.847882+00:00"},{"alias_kind":"arxiv_version","alias_value":"0909.2824v4","created_at":"2026-05-18T04:38:50.847882+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.2824","created_at":"2026-05-18T04:38:50.847882+00:00"},{"alias_kind":"pith_short_12","alias_value":"NBB4MXYITLKT","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"NBB4MXYITLKTO2UC","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"NBB4MXYI","created_at":"2026-05-18T12:26:00.592388+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/NBB4MXYITLKTO2UCSCEKAXGRMK","json":"https://pith.science/pith/NBB4MXYITLKTO2UCSCEKAXGRMK.json","graph_json":"https://pith.science/api/pith-number/NBB4MXYITLKTO2UCSCEKAXGRMK/graph.json","events_json":"https://pith.science/api/pith-number/NBB4MXYITLKTO2UCSCEKAXGRMK/events.json","paper":"https://pith.science/paper/NBB4MXYI"},"agent_actions":{"view_html":"https://pith.science/pith/NBB4MXYITLKTO2UCSCEKAXGRMK","download_json":"https://pith.science/pith/NBB4MXYITLKTO2UCSCEKAXGRMK.json","view_paper":"https://pith.science/paper/NBB4MXYI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0909.2824&json=true","fetch_graph":"https://pith.science/api/pith-number/NBB4MXYITLKTO2UCSCEKAXGRMK/graph.json","fetch_events":"https://pith.science/api/pith-number/NBB4MXYITLKTO2UCSCEKAXGRMK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NBB4MXYITLKTO2UCSCEKAXGRMK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NBB4MXYITLKTO2UCSCEKAXGRMK/action/storage_attestation","attest_author":"https://pith.science/pith/NBB4MXYITLKTO2UCSCEKAXGRMK/action/author_attestation","sign_citation":"https://pith.science/pith/NBB4MXYITLKTO2UCSCEKAXGRMK/action/citation_signature","submit_replication":"https://pith.science/pith/NBB4MXYITLKTO2UCSCEKAXGRMK/action/replication_record"}},"created_at":"2026-05-18T04:38:50.847882+00:00","updated_at":"2026-05-18T04:38:50.847882+00:00"}