{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:WISO2OZVOMPFXH7AHZT3C7ONUB","short_pith_number":"pith:WISO2OZV","schema_version":"1.0","canonical_sha256":"b224ed3b35731e5b9fe03e67b17dcda05b1af0e4a8786db42820bedc141779d6","source":{"kind":"arxiv","id":"2607.10961","version":1},"attestation_state":"computed","paper":{"title":"Irreducible fast sets of bump homeomorphisms generate copies of Thompson's groups $F_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Gili Golan","submitted_at":"2026-07-12T23:55:48Z","abstract_excerpt":"A homeomorphism of an interval is a positive bump if its support is a single open interval on which it moves every point to the right. Choosing a fundamental domain $[m,b(m))$ for the action of a positive bump $b$ on its support splits the remainder of the support into two intervals, called the feet of $b$. A finite set of positive bumps is geometrically fast if fundamental domains can be chosen so that all the resulting feet are pairwise disjoint. The crossing graph of such a set has the bumps as its vertices, two bumps being adjacent whenever their supports overlap but are not nested, and th"},"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":"2607.10961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-07-12T23:55:48Z","cross_cats_sorted":[],"title_canon_sha256":"9d5eacd7ac5093d76e3f2697947bd969b97e1836c423199a5589fd82ce968fb2","abstract_canon_sha256":"05fb5b4972fce3cbf0f1e1b6272239ab82a3a368bf07c773bb28000b4f834573"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T01:21:49.609937Z","signature_b64":"N/wCz/CWD0tOCdps6LFjquPA0jdbM9WYrXf6OqnhmoJLOq9i/WjbrCWDtjvFu0+dGt/Ad/aTm/1rNaSuOkz/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b224ed3b35731e5b9fe03e67b17dcda05b1af0e4a8786db42820bedc141779d6","last_reissued_at":"2026-07-14T01:21:49.609135Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T01:21:49.609135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Irreducible fast sets of bump homeomorphisms generate copies of Thompson's groups $F_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Gili Golan","submitted_at":"2026-07-12T23:55:48Z","abstract_excerpt":"A homeomorphism of an interval is a positive bump if its support is a single open interval on which it moves every point to the right. Choosing a fundamental domain $[m,b(m))$ for the action of a positive bump $b$ on its support splits the remainder of the support into two intervals, called the feet of $b$. A finite set of positive bumps is geometrically fast if fundamental domains can be chosen so that all the resulting feet are pairwise disjoint. The crossing graph of such a set has the bumps as its vertices, two bumps being adjacent whenever their supports overlap but are not nested, and th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10961","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.10961/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2607.10961","created_at":"2026-07-14T01:21:49.609550+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.10961v1","created_at":"2026-07-14T01:21:49.609550+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.10961","created_at":"2026-07-14T01:21:49.609550+00:00"},{"alias_kind":"pith_short_12","alias_value":"WISO2OZVOMPF","created_at":"2026-07-14T01:21:49.609550+00:00"},{"alias_kind":"pith_short_16","alias_value":"WISO2OZVOMPFXH7A","created_at":"2026-07-14T01:21:49.609550+00:00"},{"alias_kind":"pith_short_8","alias_value":"WISO2OZV","created_at":"2026-07-14T01:21:49.609550+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/WISO2OZVOMPFXH7AHZT3C7ONUB","json":"https://pith.science/pith/WISO2OZVOMPFXH7AHZT3C7ONUB.json","graph_json":"https://pith.science/api/pith-number/WISO2OZVOMPFXH7AHZT3C7ONUB/graph.json","events_json":"https://pith.science/api/pith-number/WISO2OZVOMPFXH7AHZT3C7ONUB/events.json","paper":"https://pith.science/paper/WISO2OZV"},"agent_actions":{"view_html":"https://pith.science/pith/WISO2OZVOMPFXH7AHZT3C7ONUB","download_json":"https://pith.science/pith/WISO2OZVOMPFXH7AHZT3C7ONUB.json","view_paper":"https://pith.science/paper/WISO2OZV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.10961&json=true","fetch_graph":"https://pith.science/api/pith-number/WISO2OZVOMPFXH7AHZT3C7ONUB/graph.json","fetch_events":"https://pith.science/api/pith-number/WISO2OZVOMPFXH7AHZT3C7ONUB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WISO2OZVOMPFXH7AHZT3C7ONUB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WISO2OZVOMPFXH7AHZT3C7ONUB/action/storage_attestation","attest_author":"https://pith.science/pith/WISO2OZVOMPFXH7AHZT3C7ONUB/action/author_attestation","sign_citation":"https://pith.science/pith/WISO2OZVOMPFXH7AHZT3C7ONUB/action/citation_signature","submit_replication":"https://pith.science/pith/WISO2OZVOMPFXH7AHZT3C7ONUB/action/replication_record"}},"created_at":"2026-07-14T01:21:49.609550+00:00","updated_at":"2026-07-14T01:21:49.609550+00:00"}